1.
Scuola Normale Superiore di Pisa
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The Scuola Normale Superiore di Pisa is a public higher learning institution in Pisa, Italy. The Scuola Normale, together with the University of Pisa and SantAnna School of Advanced Studies, is a part of the Pisa University System. It is one of the three officially sanctioned special-statute public universities in Italy, being part of the process of Superior Graduate School in Italy, or Scuola Superiore Universitaria. According to the World University Ranking 2016 made by the Times, Normale is considered to be the best university in Italy and one among the best 50 in Europe. The Scuola Normale Superiore was founded in 1810 by Napoleonic decree, as twin institution of the École Normale Supérieure in Paris, ces écoles doivent être en effet le type et la règle de toutes les autres. Napoleon I rethought the project of an école normale in 1808, by establishing a hall of residence in Paris to house young students, when, in 1814, Ferdinand III, Grand Duke of Tuscany returned to Tuscany, the project of a Scuola Normale in Pisa ceased. Only at the beginning of the 1840s, in connection with the university reform of 1839-1841, was the project resumed. The question was combined with the proposals of resumption of the activities of the ancient Order of Saint Stephen. There was to be a division into two Faculties, of Arts and Sciences. In 1863, was appointed a new Director of the Scuola Normale, the new regulations, issued by Minister Michele Coppino in 1877, reviewed and simplified the internal study regulations and equalized, from an organizational point of view. The philosopher Giovanni Gentile was placed at the head of the Scuola Normale as commissioner in 1928, the new colleges were later merged in the Collegio Medico-Giuridico, which continued to operate under the jurisdiction of the Scuola Normale Superiore di Pisa. During the post-war period, there were practical difficulties, however. The new institution, while committed to the model established by the Scuola Normale Superiore di Pisa, was administered by the University of Pisa. Over time, the Scuola Normale has increasingly opened up to society, the educational programs at the Scuola Normale are divided into two levels, Undergraduate and Doctoral. The undergraduate program corresponds to the 1st-cycle and 2nd-cycle programs provided by Italian universities, the Scuola Normale is located in its original historical building, called Palazzo della Carovana, in Piazza dei Cavalieri, in the medieval centre of Pisa. The Scuola Normale offers classes in humanities and sciences. There are only sixty candidates admitted out of nearly 1000 applicants on average every year, the exam comprises questions covering the entire chosen field of study. The normalisti receive free housing, free lunches and dinners, students live in halls of residence, Collegio Domenico Timpano, Collegio Alessandro dAncona, Collegio Enrico Fermi, Collegio Giosue Carducci and Collegio Alessandro Faedo
Scuola Normale Superiore di Pisa
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A detail of the main building, Palazzo della Carovana
Scuola Normale Superiore di Pisa
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Scuola Normale of Pisa
Scuola Normale Superiore di Pisa
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The first statute of the Scuola Normale Superiore
Scuola Normale Superiore di Pisa
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Palazzo della Carovana, Scuola Normale's main building
2.
Alma mater
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Alma mater is an allegorical Latin phrase for a university or college. In modern usage, it is a school or university which an individual has attended, the phrase is variously translated as nourishing mother, nursing mother, or fostering mother, suggesting that a school provides intellectual nourishment to its students. Before its modern usage, Alma mater was a title in Latin for various mother goddesses, especially Ceres or Cybele. The source of its current use is the motto, Alma Mater Studiorum, of the oldest university in continuous operation in the Western world and it is related to the term alumnus, denoting a university graduate, which literally means a nursling or one who is nourished. The phrase can also denote a song or hymn associated with a school, although alma was a common epithet for Ceres, Cybele, Venus, and other mother goddesses, it was not frequently used in conjunction with mater in classical Latin. Alma Redemptoris Mater is a well-known 11th century antiphon devoted to Mary, the earliest documented English use of the term to refer to a university is in 1600, when University of Cambridge printer John Legate began using an emblem for the universitys press. In English etymological reference works, the first university-related usage is often cited in 1710, many historic European universities have adopted Alma Mater as part of the Latin translation of their official name. The University of Bologna Latin name, Alma Mater Studiorum, refers to its status as the oldest continuously operating university in the world. At least one, the Alma Mater Europaea in Salzburg, Austria, the College of William & Mary in Williamsburg, Virginia, has been called the Alma Mater of the Nation because of its ties to the founding of the United States. At Queens University in Kingston, Ontario, and the University of British Columbia in Vancouver, British Columbia, the ancient Roman world had many statues of the Alma Mater, some still extant. Modern sculptures are found in prominent locations on several American university campuses, outside the United States, there is an Alma Mater sculpture on the steps of the monumental entrance to the Universidad de La Habana, in Havana, Cuba. Media related to Alma mater at Wikimedia Commons The dictionary definition of alma mater at Wiktionary Alma Mater Europaea website
Alma mater
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The Alma Mater statue by Mario Korbel, at the entrance of the University of Havana in Cuba.
Alma mater
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John Legate's Alma Mater for Cambridge in 1600
Alma mater
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Alma Mater (1929, Lorado Taft), University of Illinois at Urbana–Champaign
3.
Sapienza University of Rome
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The Sapienza University of Rome, also called simply Sapienza or the University of Rome, is a collegiate research university located in Rome, Italy. Formally known as Università degli Studi di Roma La Sapienza, it is the largest European university by enrollments and one of the oldest in history, the University is also the most prestigious Italian university and also the best ranked in Southern Europe. The biggest part of the Italian ruling class studied at this University and he introduced a new tax on wine in order to raise funds for the university, the money was used to buy a palace which later housed the SantIvo alla Sapienza church. However, the Universitys days of splendour came to an end during the sack of Rome in 1527, when the studium was closed and the professors dispersed, Pope Paul III restored the university shortly after his ascension to the pontificate in 1534. In the 1650s the university known as Sapienza, meaning wisdom. University students were newly animated during the 19th-century Italian revival, in 1870, La Sapienza stopped being the papal university and became the university of the capital of Italy. In 1935 the new university campus, planned by Marcello Piacentini, was completed, Sapienza University has many campuses in Rome but its main campus is the Città Universitaria, which covers 439,000 m2 near the Roma Tiburtina Station. The university has satellite campuses outside Rome, the main of which is in Latina. In 2011 a project was launched to build a campus residence halls near Pietralata station. The Department of Philosophy is located in this building, since the 2011 reform, Sapienza University of Rome has eleven faculties and 65 departments. Today Sapienza, with 140,000 students and 8,000 among academic and technical, the university has significant research programmes in the fields of engineering, natural sciences, biomedical sciences and humanities. It offers 10 Masters Programmes taught entirely in English, as of the 2016 Academic Ranking of World Universities, Sapienza is positioned within the 151-200 group of universities and among the top 3% of universities in the world. In 2015, the Center for World University Rankings ranked the Sapienza University of Rome as the 112th in the world, in order to cope with the large demand for admission to the university courses, some faculties hold a series of entrance examinations. The entrance test often decides which candidates will have access to the undergraduate course, for some faculties, the entrance test is only a means through which the administration acknowledges the students level of preparation. Students that do not pass the test can still enroll in their chosen degree courses but have to pass an additional exam during their first year, the title of the speech would have been The Truth Makes Us Good and Goodness is Truth. Some students and professors protested in reaction to a 1990 speech that Pope Benedict XVI gave in which he, in their opinion, endorsed the actions of the church against Galileo in 1633
Sapienza University of Rome
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Palazzo della Sapienza, former home of the University until 1935.
Sapienza University of Rome
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Sapienza University of Rome
Sapienza University of Rome
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Church of Sant'Ivo alla Sapienza, originally the chapel and seat of the university library (until 1935).
Sapienza University of Rome
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The new campus of Rome University, built in 1935 by Marcello Piacentini, in a 1938 picture.
4.
Luigi Ambrosio
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Luigi Ambrosio is a professor at Scuola Normale Superiore in Pisa, Italy. His main fields of research are the calculus of variations and geometric measure theory, Ambrosio entered the Scuola Normale Superiore di Pisa in 1981. He obtained his degree under the guidance of Ennio de Giorgi in 1985 at University of Pisa, and he obtained his PhD in 1988. He is currently professor at the Scuola Normale, having taught previously at the University of Rome Tor Vergata, the University of Pisa, and the University of Pavia. Ambrosio also taught and conducted research at the Massachusetts Institute of Technology, the ETH in Zurich, and he is the Managing Editor of the scientific journal Calculus of Variations and Partial Differential Equations, and member of the editorial boards of scientific journals. In 1998 Ambrosio won the Caccioppoli Prize of the Italian Mathematical Union, in 2002 he was plenary speaker at the International Congress of Mathematicians in Beijing and in 2003 he has been awarded with the Fermat Prize. From 2005 he is a member of Accademia Nazionale dei Lincei. Ambrosio is listed as an ISI highly cited researcher, a compactness theorem for a new class of functions of bounded variation. New functionals in the calculus of variations, existence theory for a new class of variational problems. Ambrosio, Luigi, Fusco, Nicola, Pallara, Diego, functions of bounded variation and free discontinuity problems. The Clarendon Press, Oxford University Press, New York, currents in metric spaces, Acta Math. Ambrosio, Luigi, Gigli, Nicola, Savaré, Giuseppe, gradient flows in metric spaces and in the space of probability measures. Luigi Ambrosio, Edward Norman Dancer, Giuseppe Buttazzo, A. Marino, M. K. Venkatesha Murthy, Calculus of variations and partial differential equations. CS1 maint, Uses editors parameter Site of Caccioppoli Prize Luigi Ambrosio at the Mathematics Genealogy Project
Luigi Ambrosio
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Luigi Ambrosio
5.
Annali di Matematica Pura ed Applicata
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The Annali di Matematica Pura ed Applicata is a bimonthly peer-reviewed scientific journal covering all aspects of pure and applied mathematics. The founding editors-in-chief were Barnaba Tortolini and Francesco Brioschi and it is currently published by Springer Science+Business Media and the editor-in-chief is Graziano Gentili. The journal is abstracted and indexed in, According to the Journal Citation Reports, bacciotti, Andrea, Periodici di matematica italiani, passato e futuro, Bollettino dellUnione Matematica Italiana. La Matematica nella Società e nella Cultura, Serie VII, 1–A, 307–315, MR1719425
Annali di Matematica Pura ed Applicata
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Annali di Matematica Pura ed Applicata
6.
Bounded variation
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Functions of bounded variation are precisely those with respect to which one may find Riemann–Stieltjes integrals of all continuous functions. Another characterization states that the functions of bounded variation on an interval are exactly those f which can be written as a difference g − h. In the case of several variables, a function f defined on an open subset Ω of ℝn is said to have bounded variation if its derivative is a vector-valued finite Radon measure. After him, several authors applied BV functions to study Fourier series in several variables, geometric measure theory, calculus of variations, renato Caccioppoli and Ennio de Giorgi used them to define measure of nonsmooth boundaries of sets. His chain rule formula was extended by Luigi Ambrosio and Gianni Dal Maso in the paper. The total variation of a function f, defined on an interval ⊂ℝ is the quantity V a b = sup P ∈ P ∑ i =0 n P −1 | f − f |. Where the supremum is taken over the set P = of all partitions of the interval considered. If f is differentiable and its derivative is Riemann-integrable, its variation is the vertical component of the arc-length of its graph. A real-valued function f on the line is said to be of bounded variation on a chosen interval ⊂ℝ if its total variation is finite. Through the Stieltjes integral, any function of bounded variation on a closed interval defines a linear functional on C. In this special case, the Riesz representation theorem states that every bounded linear functional arises uniquely in this way, the normalised positive functionals or probability measures correspond to positive non-decreasing lower semicontinuous functions. This point of view has been important in theory, in particular in its application to ordinary differential equations. Functions of bounded variation, BV functions, are functions whose derivative is a finite Radon measure. Let Ω be a subset of ℝn. An equivalent definition is the following, given a function u belonging to L1, the total variation of u in Ω is defined as V, = sup where ∥ ∥ L ∞ is the essential supremum norm. Sometimes, especially in the theory of Caccioppoli sets, the notation is used ∫ Ω | D u | = V in order to emphasize that V is the total variation of the distributional / weak gradient of u. This notation reminds also that if u is of class C1 then its variation is exactly the integral of the value of its gradient. Since C c 1 ⊂ C0 as a linear subspace, hence the continuous linear functional defines a Radon measure by the Riesz-Markov Theorem
Bounded variation
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The function f (x)=sin(1/ x) is not of bounded variation on the interval.
7.
Gaetano Fichera
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Gaetano Fichera was an Italian mathematician, working in mathematical analysis, linear elasticity, partial differential equations and several complex variables. He was born in Acireale, and died in Rome and he was born in Acireale, a town near Catania in Sicily, the elder of the four sons of Giuseppe Fichera and Marianna Abate. His father Giuseppe was a professor of mathematics and influenced the young Gaetano starting his lifelong passion, in his young years he was a talented football player. After the war he was first in Rome and then in Trieste, where he met Matelda Colautti, which become his wife in 1952. After graduating from the liceo classico in only two years, he entered the University of Catania at the age of 16, being there from 1937 to 1939 and studying under Pia Nalli. Then he went to the university of Rome, where in 1941 he earned his laurea with magna cum laude under the direction of Mauro Picone, when he was only 19. He was immediately appointed by Picone as an assistant professor to his chair and as a researcher at the Istituto Nazionale per le Applicazioni del Calcolo, becoming his pupil. After the war he went back to Rome working with Mauro Picone, in 1948 he became Libero Docente of mathematical analysis, as he remembers in, in both cases one of the members of the judging commission was Renato Caccioppoli, which become a close friend of him. He was member of several academies, notably of the Accademia Nazionale dei Lincei and his lifelong friendship with his teacher Mauro Picone is remembered by him in several occasions. The young, in effect child, Gaetano, was kept by Picone in his arms, from 1939 to 1941 the young Fichera developed his research directly under the supervision of Picone, as he remembers, it was a time of intense work. e. The theory of functions of several complex variables. The close friendship between Angelo Pescarini and Fichera has not his roots in their interests, it is another war story. –. Gaetano quickly answered, – Non solo ti darò la condizione sufficiente, one of his best friends and appreciated scientific collaborator was Olga Arsenievna Oleinik, she cured the redaction of his last posthumous paper, as Colautti Fichera recalls. He is the author of more than 250 papers and 18 books, his work concerns mainly the fields of pure and his work in elasticity theory includes the paper, where Fichera proves the Ficheras maximum principle, his work on variational inequalities. At last, it is worth to mention that Clifford Truesdell invited him to write the contributions and he studied deeply the mixed boundary value problem i. e. He contributed also to the eigenvalue problem for symmetric operators. One of the most famous examples of this kind of theorem is Mergelyans theorem, the paper surveys the contribution to the solution of this and related problems by Sergey Mergelyan, Lennart Carleson, Gábor Szegő as well as others, including his own. His contributions to potential theory are very important, the results of his paper occupy paragraph 24 of chapter II of the textbook, as remarked by in Oleinik
Gaetano Fichera
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Gaetano Fichera in 1976 (photo by Konrad Jacobs)
8.
Enzo Martinelli
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He was born in Pescia on 11 November 1911, where his father was the Director of the local agricultural school. His family later went to Rome, where his father ended his career as the Director-general of the Italian Ministry of Public Education. Enzo Martilnelli lived in Rome almost all of his life, the exception was a period of nearly eight years, from 1947 to 1954. They had a son, Roberto, and a daughter, Maria Renata, from 1934 to 1946 he worked as an assistant professor first to the chair of mathematical analysis held by Francesco Severi and then to the chair of geometry held by Enrico Bompiani. In 1939 he became Libero Docente of Mathematical analysis, he taught courses on analytic geometry, algebraic geometry. Martinelli held that chair from 1946 to 1954, teaching also mathematical analysis, function theory, differential geometry, in the years 1968–1969, during a very difficult period for the Sapienza University of Rome, he served the university as the director of the Guido Castelnuovo Institute of Mathematics. He attended to various conferences and meetings, in 1943 and in 1946 he was invited in Zurich by Rudolf Fueter, in order to present his researches, later and during all his career he lectured in almost all Italian and foreign universities. He was also a member of the UMI Scientific Commission, of the boards of the Rendiconti di Matematica e delle sue Applicazioni. According to Rizza, Enzos talent for mathematics was already evident when he was only a lyceum student, finally, in 1980 he was elected Corresponding Member of the Accademia delle Scienze di Torino and then, in 1994, Full Member. Also, in 1986, the Sapienza University of Rome, to which Enzo Martinelli was particularly tied for all his life, another episode illustrating this aspect of Martinellis personality is recalled by Gaetano Fichera. Martinelli, very tactfully, told him that the idea was already developed by Élie Cartan. His doctoral advisor was Francesco Severi, other great Italian mathematicians where among his teachers, concerned by the growing interference of bureaucracy in university education, already in the 1950s he was heard by Rizza complaining that, In Italia mancano le menti semplificatrici. Fin troppo meticoloso, scriveva più volte ogni suo lavoro, curandone fin nei minimi particolari sostanza e forma, È difficile trovare nei suoi scritti un concetto che possa essere espresso in modo migliore. Martinelli, Enzo, Alcuni teoremi integrali per le funzioni analitiche di più variabili complesse, memorie della Classe di Scienze Fisiche, Matematiche e Naturali,9, 269–283, JFM64.0322.04, Zbl 0022.24002. The first paper where the now called Bochner-Martinelli formula is introduced and proved, memorie della Classe di Scienze Fisiche, Matematiche e Naturali,12, 143–167, JFM67.0299.01, MR0017810, Zbl 0025.40503. In this paper, Martinelli proves a result of Luigi Amoroso on the boundary values of pluriharmonic function by using tensor calculus. Martinelli, Enzo, Sopra una dimostrazione di R. Fueter per un teorema di Hartogs, Commentarii Mathematici Helvetici,15, 340–349, doi,10. 5169/seals-14896, MR0010729, in this paper Martinelli gives a proof of Hartogs extension theorem by using the Bochner-Martinelli formula. The concluding work of Martinelli on the theory of representations of holomorphic functions of n complex variables. 1007/BF02412084, MR0170032
Enzo Martinelli
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Enzo Martinelli around 1960
9.
International Standard Serial Number
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An International Standard Serial Number is an eight-digit serial number used to uniquely identify a serial publication. The ISSN is especially helpful in distinguishing between serials with the same title, ISSN are used in ordering, cataloging, interlibrary loans, and other practices in connection with serial literature. The ISSN system was first drafted as an International Organization for Standardization international standard in 1971, ISO subcommittee TC 46/SC9 is responsible for maintaining the standard. When a serial with the content is published in more than one media type. For example, many serials are published both in print and electronic media, the ISSN system refers to these types as print ISSN and electronic ISSN, respectively. The format of the ISSN is an eight digit code, divided by a hyphen into two four-digit numbers, as an integer number, it can be represented by the first seven digits. The last code digit, which may be 0-9 or an X, is a check digit. Formally, the form of the ISSN code can be expressed as follows, NNNN-NNNC where N is in the set, a digit character. The ISSN of the journal Hearing Research, for example, is 0378-5955, where the final 5 is the check digit, for calculations, an upper case X in the check digit position indicates a check digit of 10. To confirm the check digit, calculate the sum of all eight digits of the ISSN multiplied by its position in the number, the modulus 11 of the sum must be 0. There is an online ISSN checker that can validate an ISSN, ISSN codes are assigned by a network of ISSN National Centres, usually located at national libraries and coordinated by the ISSN International Centre based in Paris. The International Centre is an organization created in 1974 through an agreement between UNESCO and the French government. The International Centre maintains a database of all ISSNs assigned worldwide, at the end of 2016, the ISSN Register contained records for 1,943,572 items. ISSN and ISBN codes are similar in concept, where ISBNs are assigned to individual books, an ISBN might be assigned for particular issues of a serial, in addition to the ISSN code for the serial as a whole. An ISSN, unlike the ISBN code, is an identifier associated with a serial title. For this reason a new ISSN is assigned to a serial each time it undergoes a major title change, separate ISSNs are needed for serials in different media. Thus, the print and electronic versions of a serial need separate ISSNs. Also, a CD-ROM version and a web version of a serial require different ISSNs since two different media are involved, however, the same ISSN can be used for different file formats of the same online serial
International Standard Serial Number
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ISSN encoded in an EAN-13 barcode with sequence variant 0 and issue number 5
10.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
International Standard Book Number
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A 13-digit ISBN, 978-3-16-148410-0, as represented by an EAN-13 bar code
11.
Adobe Systems
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Adobe Systems Incorporated /əˈdoʊbiː/ is an American multinational computer software company. The company is headquartered in San Jose, California, United States, Adobe has historically focused upon the creation of multimedia and creativity software products, with a more recent foray towards rich Internet application software development. It is best known for Photoshop, an image editing software, Acrobat Reader, Adobe was founded in February 1982 by John Warnock and Charles Geschke, who established the company after leaving Xerox PARC in order to develop and sell the PostScript page description language. In 1985, Apple Computer licensed PostScript for use in its LaserWriter printers, as of 2015, Adobe Systems has about 13,500 employees, about 40% of whom work in San Jose. The name of the company, Adobe, comes from Adobe Creek in Los Altos, California, Adobes corporate logo features a stylized A and was designed by the wife of John Warnock, Marva Warnock, who is a graphic designer. Adobes first products after PostScript were digital fonts, which released in a proprietary format called Type 1. Apple subsequently developed a standard, TrueType, which provided full scalability and precise control of the pixel pattern created by the fonts outlines. In the mid-1980s, Adobe entered the software market with Illustrator. Illustrator, which grew from the firms in-house font-development software, helped popularize PostScript-enabled laser printers, Adobe Systems entered NASDAQ in 1986. Its revenue has grown from roughly $1 billion in 1999 to roughly $4 billion in 2012, Adobes fiscal years run from December to November. For example, the 2007 fiscal year ended on November 30,2007, in 1989, Adobe introduced what was to become its flagship product, a graphics editing program for the Macintosh called Photoshop. Stable and full-featured, Photoshop 1.0 was ably marketed by Adobe, in 1993, Adobe introduced PDF, the Portable Document Format, and its Adobe Acrobat and Reader software. PDF is now an International Standard, ISO 32000-1,2008, in December 1991, Adobe released Adobe Premiere, which Adobe rebranded as Adobe Premiere Pro in 2003. In 1992, Adobe acquired OCR Systems, Inc, in 1994, Adobe acquired Aldus and added PageMaker and After Effects to its product line later in the year, it also controls the TIFF file format. In 1995, Adobe added FrameMaker, the long-document DTP application, in 1996, Adobe Systems Inc added Ares Software Corp. In 2002, Adobe acquired Canadian company Accelio, on December 12,2005, Adobe acquired its main rival, Macromedia, in a stock swap valued at about $3. Adobe released Adobe Media Player in April 2008, on April 27, Adobe discontinued development and sales of its older HTML/web development software, GoLive in favor of Dreamweaver. Adobe offered a discount on Dreamweaver for GoLive users and supports those who still use GoLive with online tutorials, on June 1, Adobe launched Acrobat. com, a series of web applications geared for collaborative work
Adobe Systems
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Adobe Systems headquarters in San Jose, California
Adobe Systems
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Adobe Systems Incorporated
Adobe Systems
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Adobe Systems Canada in Ottawa, Ontario (not far from archrival Corel).
12.
Scuola Normale Superiore
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The Scuola Normale Superiore di Pisa is a public higher learning institution in Pisa, Italy. The Scuola Normale, together with the University of Pisa and SantAnna School of Advanced Studies, is a part of the Pisa University System. It is one of the three officially sanctioned special-statute public universities in Italy, being part of the process of Superior Graduate School in Italy, or Scuola Superiore Universitaria. According to the World University Ranking 2016 made by the Times, Normale is considered to be the best university in Italy and one among the best 50 in Europe. The Scuola Normale Superiore was founded in 1810 by Napoleonic decree, as twin institution of the École Normale Supérieure in Paris, ces écoles doivent être en effet le type et la règle de toutes les autres. Napoleon I rethought the project of an école normale in 1808, by establishing a hall of residence in Paris to house young students, when, in 1814, Ferdinand III, Grand Duke of Tuscany returned to Tuscany, the project of a Scuola Normale in Pisa ceased. Only at the beginning of the 1840s, in connection with the university reform of 1839-1841, was the project resumed. The question was combined with the proposals of resumption of the activities of the ancient Order of Saint Stephen. There was to be a division into two Faculties, of Arts and Sciences. In 1863, was appointed a new Director of the Scuola Normale, the new regulations, issued by Minister Michele Coppino in 1877, reviewed and simplified the internal study regulations and equalized, from an organizational point of view. The philosopher Giovanni Gentile was placed at the head of the Scuola Normale as commissioner in 1928, the new colleges were later merged in the Collegio Medico-Giuridico, which continued to operate under the jurisdiction of the Scuola Normale Superiore di Pisa. During the post-war period, there were practical difficulties, however. The new institution, while committed to the model established by the Scuola Normale Superiore di Pisa, was administered by the University of Pisa. Over time, the Scuola Normale has increasingly opened up to society, the educational programs at the Scuola Normale are divided into two levels, Undergraduate and Doctoral. The undergraduate program corresponds to the 1st-cycle and 2nd-cycle programs provided by Italian universities, the Scuola Normale is located in its original historical building, called Palazzo della Carovana, in Piazza dei Cavalieri, in the medieval centre of Pisa. The Scuola Normale offers classes in humanities and sciences. There are only sixty candidates admitted out of nearly 1000 applicants on average every year, the exam comprises questions covering the entire chosen field of study. The normalisti receive free housing, free lunches and dinners, students live in halls of residence, Collegio Domenico Timpano, Collegio Alessandro dAncona, Collegio Enrico Fermi, Collegio Giosue Carducci and Collegio Alessandro Faedo
Scuola Normale Superiore
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A detail of the main building, Palazzo della Carovana
Scuola Normale Superiore
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Scuola Normale of Pisa
Scuola Normale Superiore
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The first statute of the Scuola Normale Superiore
Scuola Normale Superiore
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Palazzo della Carovana, Scuola Normale's main building
13.
Notices of the AMS
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Notices of the American Mathematical Society is the membership journal of the American Mathematical Society, published monthly except for the combined June/July issue. The first volume appeared in 1953, each issue of the magazine since January 1995 is available in its entirety on the journal web site. Articles are peer-reviewed by a board of mathematical experts. Since 2016, the editor-in-chief is Frank Morgan, the cover regularly features mathematical visualizations. The Notices is the worlds most widely read mathematical journal, as the membership journal of the American Mathematical Society, the Notices is sent to the approximately 30,000 AMS members worldwide, one-third of whom reside outside the United States. By publishing high-level exposition, the Notices provides opportunities for mathematicians to find out what is going on in the field, each issue contains one or two such expository articles that describe current developments in mathematical research, written by professional mathematicians. The Notices also carries articles on the history of mathematics, mathematics education, American Mathematical Monthly, another most widely read mathematics journal in the world Official website
Notices of the AMS
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March 2005 issue
14.
Heidelberg
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Heidelberg is a college town situated on the river Neckar in south-west Germany. At the 2015 census, its population was 156,257, located about 78 km south of Frankfurt, Heidelberg is the fifth-largest city in the German state of Baden-Württemberg. Heidelberg is part of the densely populated Rhine-Neckar Metropolitan Region, founded in 1386, Heidelberg University is Germanys oldest and one of Europes most reputable universities. A scientific hub in Germany, the city of Heidelberg is home to internationally renowned research facilities adjacent to its university. Heidelberg is in the Rhine Rift Valley, on the bank of the lower part of the Neckar in a steep valley in the Odenwald. It is bordered by the Königsstuhl and the Gaisberg mountains, the Neckar here flows in an east-west direction. On the right bank of the river, the Heiligenberg mountain rises to a height of 445 meters, the Neckar flows into the Rhine approximately 22 kilometres north-west in Mannheim. Villages incorporated during the 20th century stretch from the Neckar Valley along the Bergstraße, Heidelberg is on European walking route E1. Alongside the Philosophenweg on the side of the Old Town. There is a population of African rose-ringed parakeets, and a wild population of Siberian swan geese. Heidelberg is an authority within the Regierungsbezirk Karlsruhe. The Rhein-Neckar-Kreis rural district surrounds it and has its seat in the town, Heidelberg is a part of the Rhine-Neckar Metropolitan Region, often referred to as the Rhein-Neckar Triangle. The Rhein-Neckar Triangle became a European metropolitan area in 2005, Heidelberg consists of 15 districts distributed in six sectors of the town. The new district will have approximately 5, 000–6,000 residents, Heidelberg has an oceanic climate, defined by the protected valley between the Pfälzerwald and the Odenwald. Year-round, the temperatures are determined by maritime air masses coming from the west. In contrast to the nearby Upper Rhine Plain, Heidelbergs position in the leads to more frequent easterly winds than average. The hillsides of the Odenwald favour clouding and precipitation, the warmest month is July, the coldest is January. Temperatures often rise beyond 30 °C in midsummer, according to the German Meteorological Service, Heidelberg was the warmest place in Germany in 2009
Heidelberg
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Heidelberg, with Heidelberg Castle on the hill and the Old Bridge over river Neckar
Heidelberg
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Heidelberg with suburbs
Heidelberg
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The Altstadt from the Castle
Heidelberg
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The River Neckar at night
15.
Jacques-Louis Lions
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Jacques-Louis Lions was a French mathematician who made contributions to the theory of partial differential equations and to stochastic control, among other areas. He received the SIAMs John von Neumann prize in 1986 and numerous other distinctions, Lions is listed as an ISI highly cited researcher. After being part of the French Résistance in 1943 and 1944, Lions entered the École Normale Supérieure in 1947. He was a professor of mathematics at the Université of Nancy, the Faculty of Sciences of Paris, and he joined the prestigious Collège de France as well as the French Academy of Sciences in 1973. Throughout his career, Lions insisted on the use of mathematics in industry, with an involvement in the French space program, as well as in domains such as energy. This eventually led him to be appointed director of the Centre National dEtudes Spatiales from 1984 to 1992, Lions was elected President of the International Mathematical Union in 1991 and also received the Japan Prize and the Harvey Prize that same year. In 1992, the University of Houston awarded him a doctoral degree. He was elected president of the French Academy of Sciences in 1996 and was also a Foreign Member of the Royal Society and his son Pierre-Louis Lions is also a well-known mathematician who was awarded a Fields Medal in 1994. In fact both Father and Son have also received recognition in the form of Honorary Doctorates from Heriot-Watt University in 1986 and 1995 respectively. With Enrico Magenes, Problèmes aux limites non homogènes et applications,1968,1970 Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles. 1968 with L. Cesari, Quelques méthodes de résolution des problèmes aux limites non linéaires,1969 with Roger Dautray, Mathematical analysis and numerical methods for science and technology. 1984/5 with Philippe Ciarlet, Handbook of numerical analysis,7 vols. with Alain Bensoussan, Papanicolaou, Asymptotic analysis of periodic structures. Jacques-Louis Lions at the Mathematics Genealogy Project
Jacques-Louis Lions
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Jacques-Louis Lions
16.
Basel
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Basel is a city in northwestern Switzerland on the river Rhine. Basel is Switzerlands third-most-populous city with about 175,000 inhabitants, located where the Swiss, French and German borders meet, Basel also has suburbs in France and Germany. In 2014, the Basel agglomeration was the third largest in Switzerland with a population of 537,100 in 74 municipalities in Switzerland, the official language of Basel is German, but the main spoken language is the local variant of the Alemannic Swiss German dialect. Basel has been the seat of a Prince-Bishopric since the 11th century, the city has been a commercial hub and important cultural centre since the Renaissance, and has emerged as a centre for the chemical and pharmaceutical industry in the 20th century. It hosts the oldest university of the Swiss Confederation, There are settlement traces on the Rhine knee from the early La Tène period. The unfortified settlement was abandoned in the 1st century BC in favour of an Oppidum on the site of Basel Minster, probably in reaction to the Roman invasion of Gaul. In Roman Gaul, Augusta Raurica was established some 20 km from Basel as the administrative centre. The city of Basel eventually grew around the castle, the name of Basel is derived from the Roman-era toponym Basilia, first recorded in the 3rd century. It is presumably derived from the personal name Basilius, the Old French form Basle was adopted into English, and developed into the modern French Bâle. The Icelandic name Buslaraborg goes back to the 12th century Leiðarvísir og borgarskipan, Basel was incorporated into Germania Superior in AD83. Roman control over the area deteriorated in 3rd century, and Basel became an outpost of the Provincia Maxima Sequanorum formed by Diocletian, the Alamanni attempted to cross the Rhine several times in the 4th century, but were repelled. In a great invasion of AD406, the Alemanni appear to have crossed the Rhine river a final time, conquering and then settling what is today Alsace, from this time, Basel has been an Alemannic settlement. The Duchy of Alemannia fell under Frankish rule in the 6th century, and by the 7th century, based on the evidence of a third solidus with the inscription Basilia fit, Basel seems to have minted its own coins in the 7th century. Under bishop Haito, the first cathedral was built on the site of the Roman castle, at the partition of the Carolingian Empire, Basel was first given to West Francia, but passed to East Francia with the treaty of Meerssen of 870. The city was plundered and destroyed by a Magyar invasion of 917, the rebuilt city became part of Upper Burgundy, and as such was incorporated into the Holy Roman Empire in 1032. Since the donation by Rudolph III of Burgundy of the Moutier-Grandval Abbey and all its possessions to Bishop Adalbero II in 999 till the Reformation, in 1019, the construction of the cathedral of Basel began under German Emperor Heinrich II. In 1225–1226, the Bridge over the Rhine was constructed by Bishop Heinrich von Thun, the bridge was largely funded by Basels Jewish community which had settled there a century earlier. For many centuries to come Basel possessed the only permanent bridge over the river between Lake Constance and the sea, the Bishop also allowed the furriers to found a guild in 1226
Basel
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Basel, as seen from the Elisabethenkirche
Basel
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Map of Basel in 1642, engraved by Matthäus Merian, oriented with SW at the top and NE at the bottom.
Basel
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A panoramic view of Basel, looking North from the Münster tower over Kleinbasel (Small Basel). The blue tower in the centre, the Messeturm, was Switzerland's tallest building 2003-10; the bridge on the extreme right is the Wettsteinbrücke, Basel's second oldest bridge, but recently replaced by a new structure. The first bridge on the left is the Mittlere Brücke (Middle or Central Bridge), the oldest bridge in Basel.
Basel
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The synagogue of Basel
17.
Stuttgart
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Stuttgart is the capital and largest city of the German state of Baden-Württemberg. It is located on the Neckar river in a fertile valley known as the Stuttgart Cauldron an hour from the Swabian Jura. Stuttgarts urban area has a population of 623,738, making it the sixth largest city in Germany. 2.7 million people live in the administrative region and another 5.3 million people in its metropolitan area. Since the 6th millennium BC, the Stuttgart area has been an important agricultural area and has been host to a number of cultures seeking to utilize the rich soil of the Neckar valley. The Roman Empire conquered the area in 83 AD and built a massive Castrum near Bad Cannstatt, Stuttgarts roots were truly laid in the 10th century with its founding by Liudolf, Duke of Swabia as a stud farm for his warhorses. Overshadowed by nearby Cannstatt, the town grew steadily and was granted a charter in 1320, the fortunes of Stuttgart turned with those of the House of Württemberg, and they made it the capital of their County, Duchy, and Kingdom from the 15th Century to 1918. Stuttgart prospered despite setbacks in the forms of the Thirty Years War and devastating air raids by the Allies on the city, however, by 1952, the city had bounced back and became the major economic, industrial, tourism and publishing center it is today. Stuttgart is also an important transport junction, and possesses the sixth largest airport in Germany. Such companies as Porsche, Mercedes-Benz, Daimler AG, Dinkelacker, Stuttgart is unusual in the scheme of German cities. It is spread across a variety of hills, valleys and parks and this is often a source of surprise to visitors who associate the city with its reputation as the Cradle of the Automobile. The citys tourism slogan is Stuttgart offers more, under current plans to improve transport links to the international infrastructure, the city unveiled a new logo and slogan in March 2008 describing itself as Das neue Herz Europas. For business, it describes itself as Where business meets the future, in July 2010, Stuttgart unveiled a new city logo, designed to entice more business people to stay in the city and enjoy breaks in the area. Stuttgart is a city of mostly immigrants, according to Dorling Kindersley Publishings Eyewitness Travel Guide to Germany, In the city of Stuttgart, every third inhabitant is a foreigner. 40% of Stuttgarts residents, and 64% of the population below the age of five are of immigrant background, the reason for this being that the city was founded in 950 AD by Duke Liudolf of Swabia to breed warhorses. Originally, the most important location in the Neckar river valley as the rim of the Stuttgart basin at what is today Bad Cannstatt. As with many military installations, a settlement sprang up nearby, when they did, the town was left in the capable hands of a local brickworks that produced sophisticated architectural ceramics and pottery. When the Romans were driven back past the Rhine and Danube rivers in the 3rd Century by the Alamanni, in 700, Duke Gotfrid mentions a Chan Stada in a document regarding property
Stuttgart
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Clockwise from top left: Staatstheater, Cannstatter Volksfest in Bad Cannstatt, fountain at Schlossplatz, Fruchtkasten façade and the statue of Friedrich Schiller at Schillerplatz, New Palace, and Old Castle at Schillerplatz.
Stuttgart
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Panorama of Stuttgart looking southeast. From the Neckar valley on the left the city rises to the city center, backdropped by high woods to the south (television tower). Stuttgart South and Stuttgart West are to the right.
Stuttgart
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Stuttgart at night, looking northwest
Stuttgart
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Schlossplatz
18.
Israel Gelfand
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Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gelfand, or Izrail M. Gelfand was a prominent Soviet mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and his legacy continues through his students, who include Endre Szemerédi, Alexandre Kirillov, Edward Frenkel, Joseph Bernstein, as well as his own son, Sergei Gelfand. A native of Kherson Governorate of the Russian Empire, Gelfand was born into a Jewish family in the small southern Ukrainian town of Okny, according to his own account, Gelfand was expelled from high school because his father had been a mill owner. Bypassing both high school and college, he proceeded to study at Moscow State University, where his advisor was the preeminent mathematician Andrei Kolmogorov. He nevertheless managed to attend lectures at the University and began study at the age of 19. The Gelfand–Tsetlin basis is a widely used tool in theoretical physics, Gelfand also published works on biology and medicine. For a long time he took an interest in cell biology and he worked extensively in mathematics education, particularly with correspondence education. In 1994, he was awarded a MacArthur Fellowship for this work, Gelfand was married to Zorya Shapiro, and their two sons, Sergei and Vladimir both live in the United States. A third son, Aleksandr, died of leukemia, following the divorce from his first wife, Gelfand married his second wife, Tatiana, together they had a daughter, Tatiana. The family also includes four grandchildren and three great-grandchildren, the memories about I. Gelfand are collected at the special site handled by his family. Gelfand held several degrees and was awarded the Order of Lenin three times for his research. In 1977 he was elected a Foreign Member of the Royal Society and he won the Wolf Prize in 1978, Kyoto Prize in 1989 and MacArthur Foundation Fellowship in 1994. Israel Gelfand died at the Robert Wood Johnson University Hospital near his home in Highland Park and he was less than five weeks past his 96th birthday. His death was first reported on the blog of his former collaborator Andrei Zelevinsky and confirmed a few hours later by an obituary in the Russian online newspaper Polit. ru. Gelfand, I. M. Lectures on linear algebra, Courier Dover Publications, ISBN 978-0-486-66082-0 Gelfand, I. M. Fomin, Sergei V. Silverman, Richard A. ed. Calculus of variations, Englewood Cliffs, ISBN 978-0-486-41448-5, MR0160139 Gelfand, I. Raikov, D. Shilov, G. Commutative normed rings, Translated from the Russian, with a chapter, New York. ISBN 978-0-8218-2022-3, MR0205105 Gelfand, I. M. Shilov, G. E. Generalized functions. Vol. I, Properties and operations, Translated by Eugene Saletan, Boston, MA, Academic Press, ISBN 978-0-12-279501-5, MR0166596 Gelfand, I. M. Shilov, G. E. Generalized functions
Israel Gelfand
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Israïl Moiseevich Gelfand
19.
Carl Ludwig Siegel
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Carl Ludwig Siegel was a German mathematician specialising in number theory and celestial mechanics. He is known for, amongst other things, his contributions to the Thue–Siegel–Roth theorem in Diophantine approximation and he was named as one of the most important mathematicians of the 20th century. André Weil, without hesitation, named Siegel as the greatest mathematician of the first half of the 20th century. Atle Selberg said of Siegel and his work, Siegel was born in Berlin, where he enrolled at the Humboldt University in Berlin in 1915 as a student in mathematics, astronomy, and physics. Amongst his teachers were Max Planck and Ferdinand Georg Frobenius, whose influence made the young Siegel abandon astronomy and his best student was Jürgen Moser, one of the founders of KAM theory, which lies at the foundations of chaos theory. Another notable student was Kurt Mahler, the number theorist, Siegel was an antimilitarist, and in 1917, during World War I he was committed to a psychiatric institute as a conscientious objector. According to his own words, he withstood the experience only because of his support from Edmund Landau, after the end of World War I, he enrolled at the Georg-August University of Göttingen, studying under Landau, who was his doctoral thesis supervisor. He stayed in Göttingen as a teaching and research assistant, many of his results were published during this period. In 1922, he was appointed professor at the Johann Wolfgang Goethe-Universität of Frankfurt am Main as the successor of Arthur Moritz Schönflies. Siegel, who was opposed to Nazism, was a close friend of the docents Ernst Hellinger and Max Dehn. This attitude prevented Siegels appointment as a successor to the chair of Constantin Carathéodory in Munich, in Frankfurt he took part with Dehn, Hellinger, Paul Epstein, and others in a seminar on the history of mathematics, which was conducted at the highest level. In the seminar they read only original sources, Siegels reminiscences about the time before World War II are in an essay in his collected works. In 1936 he was a Plenary Speaker at the ICM in Oslo and he returned to Göttingen only after World War II, when he accepted a post as professor in 1951, which he kept until his retirement in 1959. Siegels work on theory, diophantine equations, and celestial mechanics in particular won him numerous honours. In 1978, he was awarded the first Wolf Prize in Mathematics, when the prize committee decided to select the greatest living mathematician, the discussion centered around Siegel and Israel Gelfand as the leading candidates. The prize was split between them. He worked on L-functions, discovering the Siegel zero phenomenon and his work, derived from the Hardy–Littlewood circle method on quadratic forms, appeared in the later, adele group theories encompassing the use of theta-functions. The Siegel modular forms are recognised as part of the theory of abelian varieties
Carl Ludwig Siegel
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Carl Ludwig Siegel in 1975
20.
Jean Leray
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Jean Leray was a French mathematician, who worked on both partial differential equations and algebraic topology. He studied at École Normale Supérieure from 1926 to 1929 and he received his Ph. D. in 1933. Leray wrote an important paper that founded the study of solutions of the Navier–Stokes equations. From 1938 to 1939 he was professor at the University of Nancy and he did not join the Bourbaki group, although he was close with its founders. His main work in topology was carried out while he was in a prisoner of war camp in Edelbach and he concealed his expertise on differential equations, fearing that its connections with applied mathematics could lead him to be asked to do war work. Lerays work of this period proved seminal to the development of spectral sequences and sheaves and these were subsequently developed by many others, each separately becoming an important tool in homological algebra. He returned to work on differential equations from about 1950. He was professor at the University of Paris from 1945 to 1947 and he was awarded the Malaxa Prize, the Grand Prix in mathematical sciences, the Feltrinelli Prize, the Wolf Prize in Mathematics, and the Lomonosov Gold Medal. Leray spectral sequence Leray cover Lerays theorem Leray–Hirsch theorem OConnor, John J. Robertson, Jean Leray, MacTutor History of Mathematics archive, University of St Andrews. Jean Leray at the Mathematics Genealogy Project Jean Leray, by Armand Borel, Gennadi M. Henkin, and Peter D. Lax, Notices of the American Mathematical Society, vol
Jean Leray
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Jean Leray in 1961
21.
Henri Cartan
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Henri Paul Cartan was a French mathematician with substantial contributions in algebraic topology. He was the son of the French mathematician Élie Cartan and the brother of composer Jean Cartan, Cartan studied at the Lycée Hoche in Versailles, then at the École Normale Supérieure in Paris, receiving his doctorate in mathematics. Cartan is known for work in topology, in particular on cohomology operations, the method of killing homotopy groups. The number of his students was small, but includes Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre. Cartan also was a member of the Bourbaki group and one of its most active participants. His book with Samuel Eilenberg Homological Algebra was an important text, Cartan used his influence to help obtain the release of some dissident mathematicians, including Leonid Plyushch and Jose Luis Massera. For his humanitarian efforts, he received the Pagels Award from the New York Academy of Sciences, the Cartan model in algebra is named after Cartan. Cartan died on 13 August 2008 at the age of 104 and his funeral took place the following Wednesday on 20 August in Die, Drome. Cartan received numerous honours and awards including the Wolf Prize in 1980 and he was an Invited Speaker at the ICM in 1932 in Zurich and a Plenary Speaker at the ICM in 1950 in Cambridge, Massachusetts and in 1958 in Edinburgh. From 1974 until his death he had been a member of the French Academy of Sciences, Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications, thèse,1928 Sur les groupes de transformations analytiques,1935. Sur les classes de fonctions définies par des inégalités portant sur leurs dérivées successives,1940, cohomologie des groupes, suite spectrale, faisceaux, 1950-1951. Algèbres dEilenberg - Mac Lane et homotopie, 1954-1955, Homological Algebra, Princeton Univ Press,1956 ISBN 978-0-69104991-5 Séminaires de lÉcole normale supérieure, Secr. IHP, 1948-1964, New York, W. A. Benjamin ed.1967, théorie élémentaire des fonctions analytiques, Paris, Hermann,1961. Differential Forms, Dover 2006 Œuvres — Collected Works,3 vols, ed. Reinhold Remmert & Jean-Pierre Serre, Springer Verlag, Heidelberg,1967. Relations dordre en théorie des permutations des ensembles finis, Neuchâtel,1973, théorie élémentaire des fonctions analytiques dune ou plusieurs variables complexes, Paris, Hermann,1975. Elementary theory of functions of one or several complex variables, Dover 1995 Cours de calcul différentiel, Paris. Correspondance entre Henri Cartan et André Weil, Paris, SMF,2011, oConnor, John J. Robertson, Edmund F. Henri Cartan, MacTutor History of Mathematics archive, University of St Andrews. A17, retrieved 2008-08-25 Cartan, Henri, Eilenberg, Samuel, notices of the American Mathematical Society, Sept.2010, vol
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Henri Cartan
22.
Andrey Kolmogorov
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Andrey Kolmogorov was born in Tambov, about 500 kilometers south-southeast of Moscow, in 1903. Kolmogorova, died giving birth to him, Andrey was raised by two of his aunts in Tunoshna at the estate of his grandfather, a well-to-do nobleman. Little is known about Andreys father and he was supposedly named Nikolai Matveevich Kataev and had been an agronomist. Nikolai had been exiled from St. Petersburg to the Yaroslavl province after his participation in the movement against the czars. He disappeared in 1919 and he was presumed to have killed in the Russian Civil War. Andrey Kolmogorov was educated in his aunt Veras village school, and his earliest literary efforts, Andrey was the editor of the mathematical section of this journal. In 1910, his aunt adopted him, and they moved to Moscow, later that same year, Kolmogorov began to study at the Moscow State University and at the same time Mendeleev Moscow Institute of Chemistry and Technology. Kolmogorov writes about this time, I arrived at Moscow University with a knowledge of mathematics. I knew in particular the beginning of set theory, I studied many questions in articles in the Encyclopedia of Brockhaus and Efron, filling out for myself what was presented too concisely in these articles. Kolmogorov gained a reputation for his wide-ranging erudition, during the same period, Kolmogorov worked out and proved several results in set theory and in the theory of Fourier series. In 1922, Kolmogorov gained international recognition for constructing a Fourier series that diverges almost everywhere, around this time, he decided to devote his life to mathematics. In 1925, Kolmogorov graduated from the Moscow State University and began to study under the supervision of Nikolai Luzin, Kolmogorov became interested in probability theory. In 1929, Kolmogorov earned his Doctor of Philosophy degree, from Moscow State University, in 1930, Kolmogorov went on his first long trip abroad, traveling to Göttingen and Munich, and then to Paris. He had various contacts in Göttingen. His pioneering work, About the Analytical Methods of Probability Theory, was published in 1931, also in 1931, he became a professor at the Moscow State University. In 1935, Kolmogorov became the first chairman of the department of probability theory at the Moscow State University, around the same years Kolmogorov contributed to the field of ecology and generalized the Lotka–Volterra model of predator-prey systems. In 1936, Kolmogorov and Alexandrov were involved in the persecution of their common teacher Nikolai Luzin, in the so-called Luzin affair. In a 1938 paper, Kolmogorov established the basic theorems for smoothing and predicting stationary stochastic processes—a paper that had military applications during the Cold War
Andrey Kolmogorov
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Andrey Kolmogorov
Andrey Kolmogorov
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Kolmogorov (left) delivers a talk at a Soviet information theory symposium. (Tallinn, 1973).
Andrey Kolmogorov
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Kolmogorov works on his talk (Tallinn, 1973).
23.
Lars Ahlfors
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Lars Valerian Ahlfors was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his text on complex analysis. Ahlfors was born in Helsinki, Finland and his mother, Sievä Helander, died at his birth. His father, Axel Ahlfors, was a professor of engineering at the Helsinki University of Technology, the Ahlfors family was Swedish-speaking, so he first attended a private school where all classes were taught in Swedish. Ahlfors studied at University of Helsinki from 1924, graduating in 1928 having studied under Ernst Lindelöf and he assisted Nevanlinna in 1929 with his work on Denjoys conjecture on the number of asymptotic values of an entire function. In 1929 Ahlfors published the first proof of this conjecture, now known as the Denjoy–Carleman–Ahlfors theorem and it states that the number of asymptotic values approached by an entire function of order ρ along curves in the complex plane going toward infinity is less than or equal to 2ρ. He completed his doctorate from the University of Helsinki in 1930, Ahlfors worked as an associate professor at the University of Helsinki from 1933 to 1936. In 1936 he was one of the first two people to be awarded the Fields Medal, in 1935 Ahlfors visited Harvard University. He returned to Finland in 1938 to take up a professorship at the University of Helsinki, the outbreak of war led to problems although Ahlfors was unfit for military service. He was offered a post at the Swiss Federal Institute of Technology at Zurich in 1944, Ahlfors was a visiting scholar at the Institute for Advanced Study in 1962 and again in 1966. He was awarded the Wihuri Prize in 1968 and the Wolf Prize in Mathematics in 1981 and his book Complex Analysis is the classic text on the subject and is almost certainly referenced in any more recent text which makes heavy use of complex analysis. Ahlfors wrote several significant books, including Riemann surfaces and Conformal invariants. He made decisive contributions to meromorphic curves, value distribution theory, Riemann surfaces, conformal geometry, quasiconformal mappings, in 1933, he married Erna Lehnert, an Austrian who with her parents had first settled in Sweden and then in Finland. FUNDAMENTAL POLYHEDRONS AND LIMIT POINT SETS OF KLEINIAN GROUPS, proceedings of the National Academy of Sciences. Lars Ahlfors at the Mathematics Genealogy Project Ahlfors entry on Harvard University Mathematics department web site, lars Valerian Ahlfors, Notices of the American Mathematical Society, vol. Lars Valerian Ahlfors, a biographical memoir, National Academy of Sciences Biographical Memoir Author profile in the database zbMATH
Lars Ahlfors
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Lars Ahlfors
24.
Mark Krein
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Mark Grigorievich Krein was a Soviet Jewish mathematician, one of the major figures of the Soviet school of functional analysis. He is known for works in theory, the problem of moments, classical analysis. He was born in Kiev, leaving home at age 17 to go to Odessa and he had a difficult academic career, not completing his first degree and constantly being troubled by anti-Semitic discrimination. He was awarded the Wolf Prize in Mathematics in 1982, but was not allowed to attend the ceremony, david Milman, Mark Naimark, Izrail Glazman, Moshe Livshits and other known mathematicians were his students. On 14 January 2008, the plaque of Mark Krein was unveiled on the main administration building of I. I. Mark Krein at the Mathematics Genealogy Project INTERNATIONAL CONFERENCE Modern Analysis, dedicated to the centenary of Mark Krein
Mark Krein
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The memorial plaque of Mark Krein
25.
Shiing-Shen Chern
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Shiing-Shen Chern was a Chinese-American mathematician. Shiing-Shen Chern co-founded the world-renowned Mathematical Sciences Research Institute at Berkeley in 1982, Chern was born in Xiushui County, Jiaxing, in Zhejiang province. The year after his birth, China changed its regime from the Qing Dynasty to the Republic of China and he graduated from Xiushui Middle School and subsequently moved to Tianjin in 1922 to accompany his father. In 1926, after spending four years in Tianjin, Chern graduated from Fulun High School, at age 15, Chern entered the Faculty of Sciences of the Nankai University in Tianjin, studied mathematics there, and graduated with a Bachelor of Science degree in 1930. At Nankai, Cherns mentor was Li-Fu Chiang, a Harvard-trained geometer, also at Nankai, he was heavily influenced by the physicist Rao Yutai. Rao is today considered to be one of the fathers of modern Chinese informatics. Chern went to Beiping to work at the Tsinghua University Department of Mathematics as a teaching assistant, at the same time he also registered at Tsinghua Graduate School as a student. He studied projective geometry under Prof. Sun Guangyuan, a University of Chicago-trained geometer and logician who was also from Zhejiang, Sun is another mentor of Chern who is considered a founder of modern Chinese mathematics. In 1932, Chern published his first research article in the Tsinghua University Journal, in the summer of 1934, Chern graduated from Tsinghua with a masters degree, the first ever masters degree in mathematics issued in China. Chen-Ning Yangs father — Yang Ko-Chuen, another Chicago-trained professor at Tsinghua, at the same time, Chern was Chen-Ning Yangs teacher of undergraduate maths at Tsinghua. At Tsinghua, Hua Luogeng, also a mathematician, was Cherns colleague, in 1932, Wilhelm Blaschke from the University of Hamburg visited Tsinghua and was impressed by Chern and his research. In 1934, co-funded by Tsinghua and the Chinese Foundation of Culture and Education, Chern studied at the University of Hamburg and worked under Blaschkes guidance first on the geometry of webs then on the Cartan-Kähler theory. Blaschke recommended Chern to study in Paris, in August 1936, Chern watched summer Olympics in Berlin together with Hua Luogeng who paid Chern a brief visit. During that time, Hua was studying at the University of Cambridge in Britain, in September 1936, Chern went to Paris and worked with Élie Cartan. Chern spent one year at the Sorbonne in Paris, in 1937, Chern accepted Tsinghuas invitation and was promoted to professor of mathematics at Tsinghua. However, at the time the Marco Polo Bridge Incident happened. Three universities including Peking University, Tsinghua, and Nankai formed the National Southwestern Associated University, in the same year, Hua Luogeng was promoted to professor of mathematics at Tsinghua
Shiing-Shen Chern
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Shiing-Shen Chern, 1976
26.
Kunihiko Kodaira
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Kunihiko Kodaira was a Japanese mathematician known for distinguished work in algebraic geometry and the theory of complex manifolds, and as the founder of the Japanese school of algebraic geometers. He was awarded a Fields Medal in 1954, being the first Japanese national to receive this honour and he graduated from the University of Tokyo in 1938 with a degree in mathematics and also graduated from the physics department at the University of Tokyo in 1941. During the war years he worked in isolation, but was able to master Hodge theory as it then stood and he obtained his Ph. D. from the University of Tokyo in 1949, with a thesis entitled Harmonic fields in Riemannian manifolds. He was involved in work from about 1944, while holding an academic post in Tokyo. In 1949 he travelled to the Institute for Advanced Study in Princeton, at this time the foundations of Hodge theory were being brought in line with contemporary technique in operator theory. Kodaira rapidly became involved in exploiting the tools it opened up in algebraic geometry and this work was particularly influential, for example on Hirzebruch. In a second phase, Kodaira wrote a long series of papers in collaboration with D. C. Spencer, founding the theory of complex structures on manifolds. This gave the possibility of constructions of moduli spaces, since in such structures depend continuously on parameters. This theory is still foundational, and also had an influence on the theory of Grothendieck. Spencer then continued work, applying the techniques to structures other than complex ones. In a third part of his work, Kodaira worked again from around 1960 through the classification of algebraic surfaces from the point of view of birational geometry of complex manifolds. This resulted in a typology of seven kinds of two-dimensional compact complex manifolds, recovering the five algebraic types known classically and this work also included a characterisation of K3 surfaces as deformations of quartic surfaces in P4, and the theorem that they form a single diffeomorphism class. Again, this work has proved foundational, Kodaira left the Institute for Advanced Study in 1961, and briefly served as chair at the Johns Hopkins University and Stanford University. In 1967, returned to the University of Tokyo and he was awarded a Wolf Prize in 1984/5. He died in Kofu on 26 July 1997, ISBN 978-0-691-08158-8, MR0366598 Kodaira, Kunihiko, Baily, Walter L. ed. Kunihiko Kodaira, collected works, II, Iwanami Shoten, Publishers, Tokyo, Princeton University Press, Princeton, N. J. ISBN 978-0-691-08163-2, MR0366599 Kodaira, Kunihiko, Baily, Walter L. ed. Kunihiko Kodaira, collected works, III, Iwanami Shoten, Publishers, Tokyo, Princeton University Press, Princeton, N. J. Robertson, Edmund F. Kunihiko Kodaira, MacTutor History of Mathematics archive, spencer, Kunihiko Kodaira, Notices of the AMS,45, 388–389
Kunihiko Kodaira
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Kunihiko Kodaira
27.
Hans Lewy
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Hans Lewy was a German born American mathematician, known for his work on partial differential equations and on the theory of functions of several complex variables. Lewy was born in Breslau, Germany, on October 20,1904, at Göttingen, he studied both mathematics and physics, his teachers there included Max Born, Richard Courant, James Franck, David Hilbert, Edmund Landau, Emmy Noether, and Alexander Ostrowski. He earned his doctorate in 1926, at time he. After Hitlers election as chancellor in 1933, Lewy was advised by Herbert Busemann to leave Germany again and he was offered a position in Madrid, but declined it, fearing for the future there under Francisco Franco. At the end of term, in 1935, he moved to the University of California. During World War II, Lewy obtained a license. He married Helen Crosby in 1947, in 1950, Lewy was fired from Berkeley for refusing to sign a loyalty oath. He taught at Harvard University and Stanford University in 1952 and 1953 before being reinstated by the California Supreme Court case Tolman v. Underhill and he retired from Berkeley in 1972, and in 1973 became one of two Ordway Professors of Mathematics at the University of Minnesota. He died on August 23,1988, in Berkeley, Lewy was elected to the National Academy of Sciences in 1964, and was also a member of the American Academy of Arts and Sciences. He became a member of the Accademia dei Lincei in 1972. He was awarded a Leroy P. Steele Prize in 1979, in 1986, the University of Bonn gave him an honorary doctorate. A priori limitations for Monge-Ampère equations, on the non-vanishing of the Jacobian in certain one-to-one mappings. Proc Natl Acad Sci U S A.22, 377–381, a priori limitations for Monge-Ampère equations. On the existence of a convex surface realizing a given Riemannian metric. Proc Natl Acad Sci U S A.24, 104–106, on differential geometry in the large. Aspects of the Calculus of Variations, Berkeley, U. of California Press, notes by J. W. Green from lectures by Hans Lewy, vi+96 pp. Lewy, Hans. On the boundary behavior of minimal surfaces, proc Natl Acad Sci U S A.37, 103–110. A note on harmonic functions and a hydrodynamical application, on the reflection laws of second order differential equations in two independent variables
Hans Lewy
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Hans Lewy in 1975 (photo by George Bergman)
28.
Atle Selberg
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Atle Selberg was a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory. He was awarded the Fields Medal in 1950, Selberg was born in Langesund, Norway, the son of teacher Anna Kristina Selberg and mathematician Ole Michael Ludvigsen Selberg. Two of his brothers went on to become mathematicians as well. During the war he fought against the German invasion of Norway and he studied at the University of Oslo and completed his Ph. D. in 1943. During World War II, Selberg worked in isolation due to the German occupation of Norway, after the war his accomplishments became known, including a proof that a positive proportion of the zeros of the Riemann zeta function lie on the line ℜ =12. After the war, he turned to sieve theory, a previously neglected topic which Selbergs work brought into prominence. In a 1947 paper he introduced the Selberg sieve, a well adapted in particular to providing auxiliary upper bounds. In 1948 Selberg submitted two papers in Annals of Mathematics in which he proved by means the theorems for primes in arithmetic progression. This challenged the widely held view of his time that certain theorems are only obtainable with the methods of complex analysis. For his fundamental accomplishments during the 1940s, Selberg received the 1950 Fields Medal, Selberg moved to the United States and settled at the Institute for Advanced Study in Princeton, New Jersey in the 1950s where he remained until his death. During the 1950s he worked on introducing spectral theory into number theory, culminating in his development of the Selberg trace formula and he was awarded the 1986 Wolf Prize in Mathematics. He was also awarded an honorary Abel Prize in 2002, its founding year, Selberg received many distinctions for his work in addition to the Fields Medal, the Wolf Prize and the Gunnerus Medal. He was elected to the Norwegian Academy of Science and Letters, the Royal Danish Academy of Sciences and Letters, in 1972 he was awarded an honorary degree, doctor philos. Honoris causa, at the Norwegian Institute of Technology, later part of Norwegian University of Science, Selberg had two children, Ingrid Selberg and Lars Selberg. Ingrid Selberg is married to playwright Mustapha Matura and he died at home in Princeton on 6 August 2007 of heart failure. Baas, Nils A. Skau, Christian F, the lord of the numbers, Atle Selberg. Doi,10. 1090/S0273-0979-08-01223-8 Interview with Selberg Hejhal, Dennis, notices of the American Mathematical Society. Atle Selberg Archive webpage Obituary at IAS Obituary in The Times Atle Selbergs private archive exists at NTNU University Library Dorabiblioteket
Atle Selberg
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Atle Selberg
29.
Peter Lax
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Peter David Lax is a Hungarian-born American mathematician working in the areas of pure and applied mathematics. Lax is listed as an ISI highly cited researcher, Lax was born in Budapest, Hungary to a Jewish family. His parents Klara Kornfield and Henry Lax were both physicians, and his uncle, Albert Kornfeld, was a mathematician and a friend of Leó Szilárd, Lax began displaying an interest in mathematics at age twelve, and soon his parents hired Rózsa Péter as a tutor for him. The family left Hungary on November 15,1941, and traveled via Lisbon to the United States, as he was still 17 when he finished high school, he could avoid military service, and was able to study for three semesters at New York University. In a complex analysis class that he had begun in the role of a student, before being able to complete his studies, Lax was drafted into the U. S. Army. After basic training, the Army sent him to Texas A&M University for more studies, then Oak Ridge National Laboratory, at Los Alamos, he began working as a calculator operator, but eventually moved on to higher-level mathematics. Lax returned to NYU for the 1946-1947 academic year, and by pooling credits from the four universities at which he had studied, he graduated that year. He stayed at NYU for his studies, marrying Anneli in 1948. In a 1958 paper Lax stated a conjecture about matrix representations for third order hyperbolic polynomials which remained unproven for over four decades. Interest in the Lax conjecture grew as mathematicians working in different areas recognized the importance of its implications in their field. Lax holds a faculty position in the Department of Mathematics, Courant Institute of Mathematical Sciences and he is a member of the Norwegian Academy of Science and Letters and the National Academy of Sciences, USA. He won a Lester R. Ford Award in 1966 and again in 1973 and he was awarded the National Medal of Science in 1986, the Wolf Prize in 1987, the Abel Prize in 2005 and the Lomonosov Gold Medal in 2013. The American Mathematical Society selected him as its Gibbs Lecturer for 2007, in 2012 he became a fellow of the American Mathematical Society. Some of the present, possibly members of the Weathermen, threatened to destroy the computer with incendiary devices. Complex Proofs of Real Theorems, with Lawrence Zalcman, University Lecture Series,2012,90 pp, softcover, Volume,58, ISBN 978-0-8218-7559-9 Functional Analysis, Wiley-Interscience, linear Algebra and Its Applications, 2nd ed. Wiley-Interscience, New York. Hyperbolic Partial Differential Equations, American Mathematical Society/Courant Institute of Mathematical Sciences, scattering Theory, with R. S. Phillips, Academic Press. Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, decay of Solutions of Systems of Nonlinear Hyperbolic Conservation Laws, with J. Glimm, American Mathematical Society. Recent Mathematical Methods in Nonlinear Wave Propagation, with G. Boillat, C. M. Dafermos, scattering Theory for Automorphic Functions with R. S. Phillips, Princeton Univ
Peter Lax
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Peter Lax in Tokyo, 1969
30.
Friedrich Hirzebruch
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Friedrich Ernst Peter Hirzebruch ForMemRS was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. He has been described as the most important mathematician in Germany of the postwar period, Hirzebruch was born in Hamm, Westphalia in 1927. He studied at the University of Münster from 1945–1950, with one year at ETH Zürich, Hirzebruch then held a position at Erlangen, followed by the years 1952–54 at the Institute for Advanced Study in Princeton, New Jersey. After one year at Princeton University 1955–56, he was made a professor at the University of Bonn, more than 300 people gathered in celebration of his 80th birthday in Bonn in 2007. Hirzebruchs book Neue topologische Methoden in der algebraischen Geometrie was a text for the new methods of sheaf theory. He went on to write the foundational papers on topological K-theory with Michael Atiyah, in his later work he provided a detailed theory of Hilbert modular surfaces, working with Don Zagier. In March 1945, Hirzebruch became a soldier, and in April, in the last weeks of Hitlers rule, when a British soldier found that he was studying mathematics, he drove him home and released him, and told him to continue studying. Hirzebruch died at the age of 84 on 27 May 2012, amongst many other honours, Hirzebruch was awarded a Wolf Prize in Mathematics in 1988 and a Lobachevsky Medal in 1989. The government of Japan awarded him the Order of the Sacred Treasure in 1996, Hirzebruch won an Einstein Medal in 1999, and received the Cantor medal in 2004. In 1980–81 he delivered the first Sackler Distinguished Lecture in Israel
Friedrich Hirzebruch
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Friedrich Hirzebruch in 1980 (picture courtesy MFO)
31.
John Milnor
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John Willard Milnor is an American mathematician known for his work in differential topology, K-theory and dynamical systems. Milnor is a professor at Stony Brook University and one of the four mathematicians to have won the Fields Medal, the Wolf Prize. Milnor was born on February 20,1931 in Orange, New Jersey and his father was J. Willard Milnor and his mother was Emily Cox Milnor. As an undergraduate at Princeton University he was named a Putnam Fellow in 1949 and 1950, upon completing his doctorate he went on to work at Princeton. He was a professor at the Institute for Advanced Study from 1970 to 1990 and his students have included Tadatoshi Akiba, Jon Folkman, John Mather, Laurent C. His wife, Dusa McDuff, is a professor of mathematics at Barnard College, one of his published works is his proof in 1956 of the existence of 7-dimensional spheres with nonstandard differential structure. Later, with Michel Kervaire, he showed that the 7-sphere has 15 differentiable structures, an n-sphere with nonstandard differential structure is called an exotic sphere, a term coined by Milnor. Milnors 1968 book on his theory inspired the growth of a huge, in 1961 Milnor disproved the Hauptvermutung by illustrating two simplicial complexes which are homeomorphic but combinatorially distinct. In 1984 Milnor introduced a definition of attractor, the objects generalize standard attractors, include so-called unstable attractors and are now known as Milnor attractors. Milnors current interest is dynamics, especially holomorphic dynamics, Milnor cast his eye on dynamical systems theory in the mid-1970s. By that time the Smale program in dynamics had been completed, milnors approach was to start over from the very beginning, looking at the simplest nontrivial families of maps. The first choice, one-dimensional dynamics, became the subject of his joint paper with Thurston, even the case of a unimodal map, that is, one with a single critical point, turns out to be extremely rich. This work may be compared with Poincarés work on circle diffeomorphisms, milnors work has opened several new directions in this field, and has given us many basic concepts, challenging problems and nice theorems. He was an editor of the Annals of Mathematics for a number of years after 1962 and he has written a number of books. In 1962 Milnor was awarded the Fields Medal for his work in differential topology. He later went on to win the National Medal of Science, in 1991 a symposium was held at Stony Brook University in celebration of his 60th birthday. Milnor was awarded the 2011 Abel Prize, for his discoveries in topology, geometry. Reacting to the award, Milnor told the New Scientist It feels very good, in 2013 he became a fellow of the American Mathematical Society, for contributions to differential topology, geometric topology, algebraic topology, algebra, and dynamical systems
John Milnor
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John Willard Milnor
32.
Lennart Carleson
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Lennart Axel Edvard Carleson is a Swedish mathematician, known as a leader in the field of harmonic analysis. One of his most famous achievements is his proof of Lusins conjecture and he was a student of Arne Beurling and received his Ph. D. from Uppsala University in 1950. Between 1978 and 1982 he served as president of the International Mathematical Union, Carleson married Butte Jonsson in 1953, and they had two children, Caspar and Beatrice. His work has included the solution of some outstanding problems, using techniques from combinatorics, in the theory of Hardy spaces, Carlesons contributions include the corona theorem and establishing the almost everywhere convergence of Fourier series for square-integrable functions. He is also known for the theory of Carleson measures, in the theory of dynamical systems, Carleson has worked in complex dynamics. He is a member of the Norwegian Academy of Science and Letters, in 2012 he became a fellow of the American Mathematical Society. Selected Problems on Exceptional Sets, Van Nostrand,1967 Matematik för vår tid, Prisma 1968 with T. W. Gamelin, Complex Dynamics, Springer,1993
Lennart Carleson
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Lennart Carleson in May 2006.
33.
Jacques Tits
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Jacques Tits is a Belgium-born French mathematician who works on group theory and incidence geometry, and who introduced Tits buildings, the Tits alternative, and the Tits group. Tits was born in Uccle to Léon Tits, a professor, Jacques attended the Athénée of Uccle and the Free University of Brussels. His thesis advisor was Paul Libois, and Tits graduated with his doctorate in 1950 with the dissertation Généralisation des groupes projectifs basés sur la notion de transitivité. His academic career includes professorships at the Free University of Brussels, the University of Bonn and he changed his citizenship to French in 1974 in order to teach at the Collège de France, which at that point required French citizenship. Because Belgian nationality law did not allow dual nationality at the time and he has been a member of the French Academy of Sciences since then. Tits received the Wolf Prize in Mathematics in 1993, the Cantor Medal from the Deutsche Mathematiker-Vereinigung in 1996, and the German distinction Pour le Mérite. In 2008 he was awarded the Abel Prize, along with John Griggs Thompson, “for their profound achievements in algebra and he is a member of the Norwegian Academy of Science and Letters. He became a member of the Royal Netherlands Academy of Arts. He introduced the theory of buildings, which are structures on which groups act. The related theory of pairs is a tool in the theory of groups of Lie type. Of particular importance is his classification of all buildings of spherical type. In the rank-2 case spherical building are generalized n-gons, and in joint work with Richard Weiss he classified these when they admit a group of symmetries. In collaboration with François Bruhat he developed the theory of affine buildings, the Tits group and the Tits–Koecher construction are named after him. Buildings of spherical type and finite BN-pairs, lecture Notes in Mathematics, Vol.386. MR0470099 Tits, Jacques, Weiss, Richard M. Moufang polygons, MR1938841 J. Tits, Oeuvres - Collected Works,4 vol. J. Tits, Résumés des cours au Collège de France, Jacques Tits at the Mathematics Genealogy Project OConnor, John J. Robertson, Edmund F. Jacques Tits, MacTutor History of Mathematics archive, University of St Andrews. Biography at the Abel Prize site List of publications at the Université libre de Bruxelles
Jacques Tits
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Jacques Tits in May 2008
34.
Andrew Wiles
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Sir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is most notable for proving Fermats Last Theorem, for which he received the 2016 Abel Prize, Wiles has received numerous other honours. Wiles was born in 1953 in Cambridge, England, the son of Maurice Frank Wiles, the Regius Professor of Divinity at the University of Oxford and his father worked as the Chaplain at Ridley Hall, Cambridge, for the years 1952–55. Wiles attended Kings College School, Cambridge, and The Leys School, Wiles states that he came across Fermats Last Theorem on his way home from school when he was 10 years old. He stopped by his local library where he found a book about the theorem. Fascinated by the existence of a theorem that was so easy to state that he, a ten-year-old, could understand it, Wiles earned his bachelors degree in mathematics in 1974 at Merton College, Oxford, and a PhD in 1980 at Clare College, Cambridge. After a stay at the Institute for Advanced Study in New Jersey in 1981, in 1985–86, Wiles was a Guggenheim Fellow at the Institut des Hautes Études Scientifiques near Paris and at the École Normale Supérieure. From 1988 to 1990, Wiles was a Royal Society Research Professor at the University of Oxford and he rejoined Oxford in 2011 as Royal Society Research Professor. Wiless graduate research was guided by John Coates beginning in the summer of 1975, together these colleagues worked on the arithmetic of elliptic curves with complex multiplication by the methods of Iwasawa theory. He further worked with Barry Mazur on the conjecture of Iwasawa theory over the rational numbers. The modularity theorem involved elliptic curves, which was also Wiless own specialist area, the conjecture was seen by contemporary mathematicians as important, but extraordinarily difficult or perhaps impossible to prove. Despite this, Wiles, with his fascination with Fermats Last Theorem, decided to undertake the challenge of proving the conjecture. In June 1993, he presented his proof to the public for the first time at a conference in Cambridge and he gave a lecture a day on Monday, Tuesday and Wednesday with the title Modular Forms, Elliptic Curves and Galois Representations. There was no hint in the title that Fermats last theorem would be discussed, finally, at the end of his third lecture, Dr. Wiles concluded that he had proved a general case of the Taniyama conjecture. Then, seemingly as an afterthought, he noted that that meant that Fermats last theorem was true, in August 1993, it was discovered that the proof contained a flaw in one area. Wiles tried and failed for over a year to repair his proof, according to Wiles, the crucial idea for circumventing, rather than closing this area, came to him on 19 September 1994, when he was on the verge of giving up. Together with his former student Richard Taylor, he published a paper which circumvented the problem. Both papers were published in May 1995 in a volume of the Annals of Mathematics
Andrew Wiles
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Wiles at the 61st Birthday conference for P. Deligne (Institute for Advanced Study, 2005).
Andrew Wiles
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Andrew Wiles before the statue of Pierre de Fermat in Beaumont-de-Lomagne (October 1995)
35.
Elias M. Stein
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Elias Menachem Stein is a mathematician. He is a figure in the field of harmonic analysis. He is an emeritus of Mathematics at Princeton University. Stein was born to Elkan Stein and Chana Goldman, Ashkenazi Jews from Belgium, after the German invasion in 1940, the Stein family fled to the United States, first arriving in New York City. He graduated from Stuyvesant High School in 1949, where he was classmates with future Fields Medalist Paul Cohen, in 1955, Stein earned a Ph. D. from the University of Chicago under the direction of Antoni Zygmund. He began teaching in MIT in 1955, moved to the University of Chicago in 1958 as an assistant professor, and in 1963 became a professor at Princeton. Stein has worked primarily in the field of analysis, and has made contributions in both extending and clarifying Calderón–Zygmund theory. He has written books on harmonic analysis, which are often cited as the standard references on the subject. His Princeton Lectures in Analysis series were penned for his sequence of courses on analysis at Princeton. Stein is also noted as having trained a number of graduate students. They include two Fields medalists, Charles Fefferman and Terence Tao and his honors include the Steele Prize, the Schock Prize in Mathematics, the Wolf Prize in Mathematics, and the National Medal of Science. In addition, he has fellowships to National Science Foundation, Sloan Foundation, Guggenheim Foundation, in 2005, Stein was awarded the Stefan Bergman prize in recognition of his contributions in real, complex, and harmonic analysis. In 2012 he became a fellow of the American Mathematical Society, in 1959, he married Elly Intrator, a former Jewish refugee during World War II. They had two children, Karen Stein and Jeremy C, Stein, and grandchildren named Alison, Jason, and Carolyn. Singular Integrals and Differentiability Properties of Functions, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Introduction to Fourier Analysis on Euclidean Spaces, Lectures on Pseudo-differential Operators, Regularity Theorems and Applications to Non-elliptic Problems. Harmonic Analysis, Real-variable Methods, Orthogonality and Oscillatory Integrals, Stein, Elias, Shakarchi, R. Fourier Analysis, An Introduction. Stein, Elias, Shakarchi, R. Complex Analysis, real Analysis, Measure Theory, Integration, and Hilbert Spaces
Elias M. Stein
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Elias M. Stein
36.
Vladimir Arnold
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Vladimir Igorevich Arnold was a Soviet and Russian mathematician. Arnold was also known as a popularizer of mathematics, through his lectures, seminars, and as the author of several textbooks and popular mathematics books, he influenced many mathematicians and physicists. Many of his books were translated into English, Vladimir Igorevich Arnold was born on 12 June 1937 in Odessa, Soviet Union. His father was Igor Vladimirovich Arnold, a mathematician and his mother was Nina Alexandrovna Arnold, an art historian. This is the Kolmogorov–Arnold representation theorem, after graduating from Moscow State University in 1959, he worked there until 1986, and then at Steklov Mathematical Institute. He became an academician of the Academy of Sciences of the Soviet Union in 1990, Arnold can be said to have initiated the theory of symplectic topology as a distinct discipline. The Arnold conjecture on the number of fixed points of Hamiltonian symplectomorphisms, Arnold worked at the Steklov Mathematical Institute in Moscow and at Paris Dauphine University up until his death. As of 2006 he was reported to have the highest citation index among Russian scientists, to his students and colleagues Arnold was known also for his sense of humour. In accordance with this principle I shall formulate some problems. ”Arnold died of pancreatitis on 3 June 2010 in Paris. He was buried on June 15 in Moscow, at the Novodevichy Monastery, in a telegram to Arnolds family, Russian President Dmitry Medvedev stated, “The death of Vladimir Arnold, one of the greatest mathematicians of our time, is an irretrievable loss for world science. It is difficult to overestimate the contribution made by academician Arnold to modern mathematics, teaching had a special place in Vladimir Arnolds life and he had great influence as an enlightened mentor who taught several generations of talented scientists. The memory of Vladimir Arnold will forever remain in the hearts of his colleagues, friends and students, as well as everyone who knew and admired this brilliant man. ”Arnold is well known for his writing style, combining mathematical rigour with physical intuition. His defense is that his books are meant to teach the subject to those who wish to understand it. Arnold was a critic of the trend towards high levels of abstraction in mathematics during the middle of the last century. Arnold was very interested in the history of mathematics and he liked to study the classics, most notably the works of Huygens, Newton and Poincaré, and many times he reported to have found in their works ideas that had not been explored yet. Arnold worked on systems theory, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics. Moser and Arnold expanded the ideas of Kolmogorov and gave rise to what is now known as KAM Theory, KAM theory shows that, despite the perturbations, such systems can be stable over an infinite period of time, and specifies what the conditions for this are. In 1965, Arnold attended René Thoms seminar on catastrophe theory, after this event, singularity theory became one of the major interests of Arnold and his students
Vladimir Arnold
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Vladimir Arnold in 2008
37.
John Tate
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John Torrence Tate, Jr. is an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry. He is professor emeritus at Harvard University and he was awarded the Abel Prize in 2010. His father, John Tate Sr. was a professor of physics at the University of Minnesota, and his mother, Lois Beatrice Fossler, was a high school English teacher. Tate Jr. received his bachelors degree in mathematics from Harvard University and he later transferred to the mathematics department and received his PhD in 1950 as a student of Emil Artin. Tate taught at Harvard for 36 years before joining the University of Texas in 1990 and he retired from the Texas mathematics department in 2009, and returned to Harvard as a professor emeritus. He currently resides in Cambridge, Massachusetts with his wife Carol and he has three daughters with his first wife Karin Tate. Together with his teacher Emil Artin, Tate gave a cohomological treatment of class field theory, using techniques of group cohomology applied to the idele class group. Subsequently, Tate introduced what are now known as Tate cohomology groups, in the decades following that discovery he extended the reach of Galois cohomology with the Poitou–Tate duality, the Tate–Shafarevich group, and relations with algebraic K-theory. With Jonathan Lubin, he recast local class field theory by the use of formal groups and he found a p-adic analogue of Hodge theory, now called Hodge–Tate theory, which has blossomed into another central technique of modern algebraic number theory. Other innovations of his include the Tate curve parametrization for certain p-adic elliptic curves, many of his results were not immediately published and some of them were written up by Serge Lang, Jean-Pierre Serre, Joseph H. Silverman and others. Tate and Serre collaborated on a paper on good reduction of abelian varieties, the classification of abelian varieties over finite fields was carried out by Taira Honda and Tate. The Tate conjectures are the equivalent for étale cohomology of the Hodge conjecture and they relate to the Galois action on the l-adic cohomology of an algebraic variety, identifying a space of Tate cycles that conjecturally picks out the algebraic cycles. A special case of the conjectures, which are open in the case, was involved in the proof of the Mordell conjecture by Gerd Faltings. Tate has also had a influence on the development of number theory through his role as a Ph. D. advisor. His students include Benedict Gross, Robert Kottwitz, Jonathan Lubin, Stephen Lichtenbaum, James Milne, V. Kumar Murty, Carl Pomerance, Ken Ribet, Joseph H. Silverman, in 1956 Tate was awarded the American Mathematical Societys Cole Prize for outstanding contributions to number theory. In 1995 he received the Leroy P. Steele Prize for Lifetime Achievement from the American Mathematical Society and he was awarded a Wolf Prize in Mathematics in 2002/03 for his creation of fundamental concepts in algebraic number theory. In 2012 he became a fellow of the American Mathematical Society, in 2010, the Norwegian Academy of Science and Letters, of which he is a member, awarded him the Abel Prize, citing his vast and lasting impact on the theory of numbers. He has truly left an imprint on modern mathematics
John Tate
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John Tate
38.
Grigory Margulis
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Gregori Aleksandrovich Margulis is a Russian-American mathematician known for his work on lattices in Lie groups, and the introduction of methods from ergodic theory into diophantine approximation. He was awarded a Fields Medal in 1978 and a Wolf Prize in Mathematics in 2005, in 1991, he joined the faculty of Yale University, where he is currently the Erastus L. DeForest Professor of Mathematics. Margulis was born in Moscow, Soviet Union and he received his PhD in 1970 from the Moscow State University, starting research in ergodic theory under the supervision of Yakov Sinai. Early work with David Kazhdan produced the Kazhdan–Margulis theorem, a result on discrete groups. His superrigidity theorem from 1975 clarified an area of classical conjectures about the characterisation of arithmetic groups amongst lattices in Lie groups and he was awarded the Fields Medal in 1978, but was not permitted to travel to Helsinki to accept it in person. In 1991, Margulis accepted a position at Yale University. Margulis was elected a member of the U. S. National Academy of Sciences in 2001, in 2012 he became a fellow of the American Mathematical Society. In 2005, Margulis received the Wolf Prize for his contributions to theory of lattices and applications to ergodic theory, representation theory, number theory, combinatorics, and measure theory. Marguliss early work dealt with Kazhdans property and the questions of rigidity and arithmeticity of lattices in semisimple algebraic groups of rank over a local field. It had been known since the 1950s that a certain simple-minded way of constructing subgroups of semisimple Lie groups produces examples of lattices and it is analogous to considering the subgroup SL of the real special linear group SL that consists of matrices with integer entries. Margulis proved that under suitable assumptions on G, any lattice Γ in it is arithmetic, thus Γ is commensurable with the subgroup G of G, i. e. they agree on subgroups of finite index in both. Unlike general lattices, which are defined by their properties, arithmetic lattices are defined by a construction, therefore, these results of Margulis pave a way for classification of lattices. Arithmeticity turned out to be related to another remarkable property of lattices discovered by Margulis. Superrigidity for a lattice Γ in G roughly means that any homomorphism of Γ into the group of invertible n × n matrices extends to the whole G. While certain rigidity phenomena had already known, the approach of Margulis was at the same time novel, powerful. Margulis solved the Banach–Ruziewicz problem that asks whether the Lebesgue measure is the only normalized rotationally invariant finitely additive measure on the n-dimensional sphere, Margulis gave the first construction of expander graphs, which was later generalized in the theory of Ramanujan graphs. In 1986, Margulis gave a resolution of the Oppenheim conjecture on quadratic forms. He has formulated a program of research in the same direction
Grigory Margulis
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Grigory Margulis
39.
Stephen Smale
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Stephen Smale is an American mathematician from Flint, Michigan. His research concerns topology, dynamical systems and mathematical economics and he was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty of the University of California, Berkeley. Smale entered the University of Michigan in 1948, initially, he was a good student, placing into an honors calculus sequence taught by Bob Thrall and earning himself As. However, his sophomore and junior years were marred with mediocre grades, mostly Bs, Cs, however, with some luck, Smale was accepted as a graduate student at the University of Michigans mathematics department. Yet again, Smale performed poorly in his first years, earning a C average as a graduate student and it was only when the department chair, Hildebrandt, threatened to kick Smale out that he began to work hard. Smale finally earned his Ph. D. in 1957, under Raoul Bott, Smale began his career as an instructor at the college at the University of Chicago. In 1958, he astounded the world with a proof of a sphere eversion. After having made great strides in topology, he turned to the study of dynamical systems. His first contribution is the Smale horseshoe that started significant research in dynamical systems and he also outlined a research program carried out by many others. Smale is also known for injecting Morse theory into mathematical economics, in 1998 he compiled a list of 18 problems in mathematics to be solved in the 21st century, known as Smales problems. This list was compiled in the spirit of Hilberts famous list of problems produced in 1900, in fact, Smales list contains some of the original Hilbert problems, including the Riemann hypothesis and the second half of Hilberts sixteenth problem, both of which are still unsolved. Earlier in his career, Smale was involved in controversy over remarks he made regarding his work habits while proving the higher-dimensional Poincaré conjecture and he said that his best work had been done on the beaches of Rio. This led to the withholding of his grant money from the NSF and he has been politically active in various movements in the past, such as the Free Speech movement and the movement against the Vietnam War. At one time he was subpoenaed by the House Un-American Activities Committee, in 1960 Smale was appointed an associate professor of mathematics at the University of California, Berkeley, moving to a professorship at Columbia University the following year. In 1964 he returned to a professorship at UC Berkeley where he has spent the part of his career. He retired from UC Berkeley in 1995 and took up a post as professor at the City University of Hong Kong and he also amassed over the years one of the finest private mineral collections in existence. Many of Smales mineral specimens can be seen in the book—The Smale Collection, since 2002 Smale is a Professor at the Toyota Technological Institute at Chicago, starting August 1,2009, he is also a Distinguished University Professor at the City University of Hong Kong. In 2007, Smale was awarded the Wolf Prize in mathematics, generalized Poincarés conjecture in dimensions greater than four
Stephen Smale
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Stephen Smale
40.
Phillip Griffiths
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Phillip Augustus Griffiths IV is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He was a developer in particular of the theory of variation of Hodge structure in Hodge theory. He received his B. S. from Wake Forest College in 1959, since then, he has held positions at Berkeley, Princeton, Harvard University, and Duke University. From 1991 to 2003 he was the Director of the Institute for Advanced Study at Princeton and he has published on algebraic geometry, differential geometry, geometric function theory, and the geometry of partial differential equations. Griffiths serves as the Chair of the Science Initiative Group and he is co-author, with Joe Harris, of Principles of Algebraic Geometry, a well-regarded textbook on complex algebraic geometry. In 2008 he was awarded the Wolf Prize and the Brouwer Medal, in 2012 he became a fellow of the American Mathematical Society. Moreover, in 2014 Griffiths was awarded the Leroy P. Steele Prize for Lifetime Achievement by the American Mathematical Society, also in 2014, Griffiths was awarded the Chern Medal for lifetime devotion to mathematics and outstanding achievements. Proc Natl Acad Sci U S A.48, 780–783, some remarks on automorphisms, analytic bundles, and embeddings of complex algebraic varieties. Proc Natl Acad Sci U S A.49, 817–820, on the differential geometry of homogeneous vector bundles. The residue calculus and some results in algebraic geometry, I. Proc Natl Acad Sci U S A.55, 1303–1309, the residue calculus and some transcendental results in algebraic geometry, II. Proc Natl Acad Sci U S A.55, 1392–1395, some results on locally homogeneous complex manifolds. Proc Natl Acad Sci U S A.56, 413–416, a transcendental method in algebraic geometry. Periods of integrals on algebraic manifolds, with Joe Harris, A Poncelet theorem in space. With S. S. Chern, Abels Theorem and Webs, introduction to Algebraic Curves, American Mathematical Society, Providence, RI,1989, ISBN0821845306 Differential Systems and Isometric Embeddings, with Gary R
Phillip Griffiths
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Phillip Griffiths in 2008 (photo from MFO)
41.
David Mumford
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David Bryant Mumford is an American mathematician known for distinguished work in algebraic geometry, and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow, in 2010 he was awarded the National Medal of Science. He is currently a University Professor Emeritus in the Division of Applied Mathematics at Brown University, Mumford was born in Worth, West Sussex in England, of an English father and American mother. His father William started a school in Tanzania and worked for the then newly created United Nations. In high school, he was a finalist in the prestigious Westinghouse Science Talent Search, after attending the Phillips Exeter Academy, Mumford went to Harvard, where he became a student of Oscar Zariski. At Harvard, he became a Putnam Fellow in 1955 and 1956 and he completed his Ph. D. in 1961, with a thesis entitled Existence of the moduli scheme for curves of any genus. He met his first wife, Erika Jentsch, at Radcliffe College, after Erika died in 1988, he married his second wife, Jenifer Gordon. He and Erika had four children, Mumfords work in geometry combined traditional geometric insights with the latest algebraic techniques. He published on moduli spaces, with a theory summed up in his book Geometric Invariant Theory, on the equations defining an abelian variety and his books Abelian Varieties and Curves on an Algebraic Surface combined the old and new theories. His lecture notes on scheme theory circulated for years in unpublished form, at a time when they were, beside the treatise Éléments de géométrie algébrique and they are now available as The Red Book of Varieties and Schemes. Other work that was less thoroughly written up were lectures on varieties defined by quadrics, and this work on the equations defining abelian varieties appeared in 1966–7. He published some books of lectures on the theory. He also was one of the founders of the toroidal embedding theory and these pathologies fall into two types, bad behavior in characteristic p and bad behavior in moduli spaces. This second example is developed further in Mumfords third paper on classification of surfaces in characteristic p, worse pathologies related to p-torsion in crystalline cohomology were explored by Luc Illusie. Further such examples arise in Zariski surface theory and he also conjectures that the Kodaira vanishing theorem is false for surfaces in characteristic p. In the third paper, he gives an example of a surface for which Kodaira vanishing fails. The first example of a surface for which Kodaira vanishing fails was given by Michel Raynaud in 1978. In the second Pathologies paper, Mumford finds that the Hilbert scheme parametrizing space curves of degree 14, in the fourth Pathologies paper, he finds reduced and irreducible complete curves which are not specializations of non-singular curves
David Mumford
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David Mumford in 2010
David Mumford
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David Mumford in 1975
42.
Dennis Sullivan
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Dennis Parnell Sullivan is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems and he holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University. He received his B. A. in 1963 from Rice University and his Ph. D. thesis, entitled Triangulating homotopy equivalences, was written under the supervision of William Browder, and was a contribution to surgery theory. He was a permanent member of the Institut des Hautes Études Scientifiques from 1974 to 1997, Sullivan is one of the founders of the surgery method of classifying high-dimensional manifolds, along with Browder, Sergei Novikov and C. T. C. In homotopy theory, Sullivan put forward the concept that spaces could directly be localised. This area has generated considerable further research, in 1985, he proved the No wandering domain theorem. The Parry–Sullivan invariant is named after him and the English mathematician Bill Parry, in 1987, he proved Thurstons conjecture about the approximation of the Riemann map by circle packings together with Burton Rodin. 47, 269–331, MR0646078 OConnor, John J. Robertson, Edmund F. Dennis Sullivan, MacTutor History of Mathematics archive, Dennis Sullivan at the Mathematics Genealogy Project Sullivans homepage at CUNY Sullivans homepage at SUNY Stony Brook Dennis Sullivan International Balzan Prize Foundation
Dennis Sullivan
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Dennis Parnell Sullivan
43.
Michael Artin
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Michael Artin is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry. Artin was born in Hamburg, Germany, and brought up in Indiana and his parents were Natalia Naumovna Jasny and Emil Artin, preeminent algebraist of the 20th century. Artins parents had left Germany in 1937, because Michael Artins maternal grandfather was Jewish, in the early 1960s Artin spent time at the IHÉS in France, contributing to the SGA4 volumes of the Séminaire de géométrie algébrique, on topos theory and étale cohomology. His work on the problem of characterising the representable functors in the category of schemes has led to the Artin approximation theorem and this work also gave rise to the ideas of an algebraic space and algebraic stack, and has proved very influential in moduli theory. Additionally, he has made contributions to the theory of algebraic varieties. Small, which prompted first foray into ring theory, in 2002, Artin won the American Mathematical Societys annual Steele Prize for Lifetime Achievement. In 2005, he was awarded the Harvard Centennial Medal, in 2013 he won the Wolf Prize in Mathematics, and in 2015 was awarded the National Medal of Science. Artin–Mazur zeta function Artin stacks Artin–Verdier duality Michael Artin at MIT Mathematics
Michael Artin
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Michael Artin (photo by George Bergman)
44.
Richard Schoen
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Richard Melvin Schoen is an American mathematician. Born in Celina, Ohio, and a 1968 graduate of Fort Recovery High School and he then received his PhD in 1977 from Stanford University and is currently an Excellence in Teaching Chair at the University of California, Irvine. His surname is pronounced Shane, perhaps as a reflection of the dialect spoken by some of his German ancestors. Schoen has investigated the use of techniques in global differential geometry. In 1979, together with his doctoral supervisor, Shing-Tung Yau. In 1983, he was awarded a MacArthur Fellowship, and in 1984 and this work combined new techniques with ideas developed in earlier work with Yau, and partial results by Thierry Aubin and Neil Trudinger. The resulting theorem asserts that any Riemannian metric on a manifold may be conformally rescaled so as to produce a metric of constant scalar curvature. In 2007, Simon Brendle and Richard Schoen proved the differentiable sphere theorem and he has also made fundamental contributions to the regularity theory of minimal surfaces and harmonic maps. For his work on the Yamabe problem, Schoen was awarded the Bôcher Memorial Prize in 1989 and he joined the American Academy of Arts and Sciences in 1988 and the National Academy of Sciences in 1991, and won a Guggenheim Fellowship in 1996. In 2012 he became a fellow of the American Mathematical Society, in 2015, he was elected Vice President of the American Mathematical Society. He received the Wolf Prize in Mathematics for 2017, shared with Charles Fefferman, Richard Schoen at the Mathematics Genealogy Project
Richard Schoen
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Richard Schoen (photo by George Bergman)
45.
Charles Fefferman
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Charles Louis Fefferman is an American mathematician at Princeton University. His primary field of research is mathematical analysis, a child prodigy, Fefferman entered college by the age of 11 and had written his first scientific paper by the age of 15 in German. He received his B. S. from University of Maryland in mathematics, which is part of the University of Maryland College of Computer, Mathematical, and Natural Sciences at age 17. Then, he received his PhD in mathematics at 20 from Princeton University under Elias Stein and this made him the youngest full professor ever appointed in the United States. At 24, he returned to Princeton to assume a professorship there — a position he still holds. He won the Alan T. Waterman Award in 1976 and the Fields Medal in 1978 for his work in mathematical analysis and he was elected to the National Academy of Sciences in 1979. He was appointed the Herbert Jones Professor at Princeton in 1984, Fefferman contributed several innovations that revised the study of multidimensional complex analysis by finding fruitful generalisations of classical low-dimensional results. His early work included a study of the asymptotics of the Bergman kernel off the boundaries of domains in C n. He has studied physics, harmonic analysis, fluid dynamics, neural networks, geometry, mathematical finance and spectral analysis. Charles Fefferman and his wife Julie have two daughters, Nina and Lainie, Lainie Fefferman is a composer, taught math at Saint Anns School and holds a degree in music from Yale University as well as a Ph. D. in music composition from Princeton. She has an interest in Middle Eastern music, Nina is a computational biologist whose research is concerned with the application of mathematical models to complex biological systems. Charles Feffermans brother, Robert Fefferman, is also an accomplished mathematician and his most cited papers include, in the order of citations, Hp spaces of several variables, Acta Mathematica. Weighted norm inequalities for maximal functions and singular integrals, Studia Mathematica, some maximal inequalities, American Journal of Mathematics. The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Inventiones mathematicae, the uncertainty principle, Bulletin of the American Mathematical Society. Inequalities for strongly singular convolution operators, Acta Mathematica, geometric constraints on potentially singular solutions for the 3-D Euler equations, Communications in Partial Differential Equations. The multiplier problem for the ball, Annals of Mathematics, oConnor, John J. Robertson, Edmund F. Charles Fefferman, MacTutor History of Mathematics archive, University of St Andrews. Charles Fefferman at the Mathematics Genealogy Project Charles Fefferman Curriculum Vitae
Charles Fefferman
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Charles Fefferman
46.
Integrated Authority File
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The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used mainly for documentation in libraries and increasingly also by archives, the GND is managed by the German National Library in cooperation with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero license, the GND specification provides a hierarchy of high-level entities and sub-classes, useful in library classification, and an approach to unambiguous identification of single elements. It also comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format
Integrated Authority File
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GND screenshot