1.
Lecce
–
It is over 2,000 years old. Because of the rich Baroque architectural monuments found in the city, Lecce is commonly nicknamed "The Florence of the South". In the Grecìa Salentina, a group of towns not far from Lecce, the griko language is still spoken. Lecce is also an agricultural centre, chiefly for its olive oil and wine production, as well as an industrial centre specializing in ceramic production. According to legend, a city called Sybar existed at the time of the Trojan War, founded by the Messapii. It was conquered in the 3rd century BC receiving the new name of Lupiae. Under the Hadrian the city was moved 3 kilometres to the northeast, taking the name of Licea or Litium. Lecce was connected to the Hadrian Port. Orontius of Lecce, locally called Sant ` Oronzo, is Lecce's patron saint. After the fall of the Western Roman Empire, Lecce was sacked by the Ostrogoth Totila in the Gothic Wars. After the Norman conquest in the 11th century, Lecce regained commercial importance, flourishing in the subsequent Hohenstaufen and rule. , starting in 1630, it was enriched with precious Baroque monuments. In 1656, a plague broke out in the city, killing a thousand inhabitants. In 1943, aircraft based in Lecce helped support isolated Italian garrisons in the Aegean Sea during World War 2. Because they were delayed by the Allies, they couldn't prevent a defeat.
Lecce
–
Top left:Church of Santa Croce, Top right:Lecce Teatro Romano, Bottom left:Lecce Porta Napoli in Universita Street, Bottom middle:Saint Giovanni Cathedral in Perroni area, Bottom right:Lecce Cathedral in Duomo Square
Lecce
–
Piazza del Duomo
Lecce
–
The Roman Amphitheatre
2.
Italy
–
Italy, officially the Italian Republic, is a unitary parliamentary republic in Europe. Located in the heart of the Mediterranean Sea, Italy shares open land borders with Vatican City. With million inhabitants, it is the fourth most populous EU member state. Rome ultimately emerged as the dominant power, becoming the leading cultural, political, religious centre of Western civilisation. The legacy of the Roman Empire can be observed in the global distribution of civilian law, republican governments, Christianity and the Latin script. Italian culture flourished at this time, producing famous scholars, polymaths such as Leonardo da Vinci, Galileo, Michelangelo, Machiavelli. However, the southern areas of the country remained largely excluded from industrialisation, fuelling a large and influential diaspora. Italy has eighth largest economy in the world. It enjoys the highest life expectancy in the EU. The corpus of the solutions proposed by historians and linguists is very wide. Greek historian Dionysius of Halicarnassus states this account together with the legend that Italy was named after Italus, mentioned also by Aristotle and Thucydides. But by his time the name also applied to most of Lucania as well. Excavations throughout Italy revealed a Neanderthal presence dating back to the Palaeolithic period, some 200,000 years ago, modern Humans arrived about 40,000 years ago. Other Italian peoples of undetermined language families but of possible non-Indo-European origins include the Rhaetian people and Cammuni, known for their rock carvings. Also the Phoenicians established colonies on the coasts of Sardinia and Sicily.
Italy
–
The Colosseum in Rome, built c. 70 – 80 AD, is considered one of the greatest works of architecture and engineering of ancient history.
Italy
–
Flag
Italy
–
The Iron Crown of Lombardy, for centuries symbol of the Kings of Italy.
Italy
–
Castel del Monte, built by German Emperor Frederick II, UNESCO World Heritage site
3.
Pisa
–
Pisa is a city in Tuscany, Central Italy, straddling the River Arno just before it empties into the Tyrrhenian Sea. It is the city of the Province of Pisa. Much of the city's architecture was financed as one of the Italian maritime republics. The origin of Pisa, is a mystery. Archaeological remains from the 5th century BC confirmed the existence of a city at the sea, trading with Greeks and Gauls. The presence of an Etruscan necropolis, discovered in 1991, confirmed its Etruscan origins. Ancient Roman authors referred as an old city. Strabo referred Pisa's origins after the fall of Troy. The maritime role of Pisa should have been already prominent if the ancient authorities ascribed to it the invention of the naval ram. Pisa took advantage of being the only port along the western coast from Genoa to Ostia. Pisa served against Ligurians, Gauls and Carthaginians. In 180 BC, it became a Roman colony as Portus Pisanus. In 89 BC, Portus Pisanus became a municipium. Emperor Augustus changed the name in Colonia Iulia obsequens. It is supposed that Pisa was founded on the shore.
Pisa
–
Pisa
Pisa
–
Coat of arms
Pisa
–
Hypothetical map of Pisa in the 5th century AD
Pisa
–
Hypothetical map of Pisa in the 11th century AD
4.
Partial differential equation
–
In mathematics, a partial differential equation is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are either solved by hand, or used to create a relevant computer model. PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid dynamics, quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in partial differential equations. Partial differential equations are equations that involve rates of change with respect to continuous variables. The dynamics for the rigid body take place in a finite-dimensional space; the dynamics for the ﬂuid occur in an infinite-dimensional conﬁguration space. Here again, there will be simple solutions for linear problems. Classic domains where PDEs are used include acoustics, fluid dynamics, heat transfer. A partial equation for the function u is an equation of the form f = 0. If f is a linear function of its derivatives, then the PDE is called linear. Common examples of linear PDEs include the heat equation, the wave equation, Laplace's equation, Helmholtz equation, Poisson's equation. A relatively simple PDE is ∂ u ∂ x = 0. This relation implies that the u is independent of x.
Partial differential equation
–
Navier–Stokes differential equations used to simulate airflow around an obstruction.
5.
Scuola Normale Superiore di Pisa
–
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 Sant'Anna School of Advanced Studies, is a part of the Pisa University System. Ces écoles doivent être en effet la règle de les autres." 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. There was to be an organic division into two Faculties, of Arts and Sciences. In 1863, was appointed a new Director of the Scuola Normale, the respected Pasquale Villari. 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 and as director in 1932. 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 many practical difficulties; however, besides the restoration of Palazzo dei Cavalieri. The new institution, while still committed to the model established by the Scuola Normale Superiore di Pisa, was administered by the University of Pisa. 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.
Scuola Normale Superiore di Pisa
–
A detail of the main building, Palazzo della Carovana
Scuola Normale Superiore di Pisa
–
Scuola Normale of Pisa
Scuola Normale Superiore di Pisa
–
The first statute of the Scuola Normale Superiore
Scuola Normale Superiore di Pisa
–
Palazzo della Carovana, Scuola Normale's main building
6.
Alma mater
–
Alma mater is an allegorical Latin phrase for a university or college. In modern usage, it is a university which an individual has attended. The phrase is variously translated as "nourishing mother", "fostering mother", suggesting that a school provides intellectual nourishment to its students. It is related to the alumnus, denoting a university graduate, literally meaning a "nursling" or "one, nourished". The phrase can also denote a hymn associated with a school. Although alma was a common epithet for other mother goddesses, it was not frequently used in conjunction with mater in classical Latin. "Alma Redemptoris Mater" is a 11th century antiphon devoted to Mary. Many European universities have adopted Alma Mater as part of the Latin translation of their official name. Alma Mater Studiorum, refers to its status as the oldest continuously operating university in the world. The ancient Roman world had many statues of the Alma Mater, some still extant. Modern sculptures are found in prominent locations on American university campuses. There is a well-known statue of Alma Mater by Daniel Chester French situated on the steps of Columbia University's Low Library. The University of Illinois at Urbana–Champaign also has an Alma Mater statue by Lorado Taft. 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. The statue was cast in 1919 with Feliciana Villalón Wilson as the inspiration for Alma Mater.
Alma mater
–
The Alma Mater statue by Mario Korbel, at the entrance of the University of Havana in Cuba.
Alma mater
–
John Legate's Alma Mater for Cambridge in 1600
Alma mater
–
Alma Mater (1929, Lorado Taft), University of Illinois at Urbana–Champaign
7.
Sapienza University of Rome
–
The Sapienza University of Rome, also called simply Sapienza or the "University of Rome", is a collegiate research university located in Rome, Italy. The University is also the most prestigious Italian university and also the best ranked in Southern Europe. La Sapienza educated notable alumni, including presidents of the European Parliament, heads of several nations, astronauts. Pope Paul III restored the university shortly after his ascension to the pontificate in 1534. In the 1650s the university became known as Sapienza, meaning wisdom, a title it retains. 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 some satellite campuses outside Rome, the main of, in Latina. In 2011 a project was launched to build a campus with residence halls near Pietralata station, in collaboration with the Lazio region. 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 and administrative staff, is the largest university in Italy. The university has significant research programmes in the fields of engineering, natural sciences, biomedical sciences and humanities.
Sapienza University of Rome
–
Palazzo della Sapienza, former home of the University until 1935.
Sapienza University of Rome
–
Sapienza University of Rome
Sapienza University of Rome
–
Church of Sant'Ivo alla Sapienza, originally the chapel and seat of the university library (until 1935).
Sapienza University of Rome
–
The new campus of Rome University, built in 1935 by Marcello Piacentini, in a 1938 picture.
8.
Mauro Picone
–
Mauro Picone was an Italian mathematician. He was also an outstanding teacher of mathematical analysis: some of the best Italian mathematicians were among his pupils. Attraverso le sue ricerche di analisi matematica, Mauro Picone ha contribuito notevolmente allo sviluppo matematica del nostro secolo. Egli è stato un pioniere delle matematiche applicate. Picone, Mauro, Lezioni di analisi infinitesimale, Volume 1, Parte Seconda – L'Integrazione, Catania: Circolo matematico di Catania, pp. v+352–742, JFM 50.0150.04. Picone, Mauro; Viola, Tullio, Lezioni sulla teoria moderna dell'integrazione, Manuali Einaudi. The entry about Mauro Picone at the Edizione Nazionale Matematica Italiana. O'Connor, John J.; Robertson, Edmund F. "Mauro Picone", MacTutor History of Mathematics archive, University of St Andrews. Mauro Picone at the Mathematics Genealogy Project Istituto per le Applicazioni del Calcolo "Mauro Picone": the institute he founded in 1922.
Mauro Picone
–
Mauro Picone
9.
Luigi Ambrosio
–
Luigi Ambrosio is a professor at Scuola Normale Superiore in Pisa, Italy. His main fields of research are the calculus of variations and geometric theory. Ambrosio entered the Scuola Normale Superiore di Pisa in 1981. He obtained his degree at University of Pisa, the Diploma at Scuola Normale. He obtained his PhD in 1988. He is member of the editorial boards of scientific journals. In 1998 Ambrosio won the Caccioppoli Prize of the Italian Mathematical Union. In 2003 he has been awarded with the Fermat Prize. From 2005 he is a corresponding member of Accademia Nazionale dei Lincei. Ambrosio is listed as an ISI highly cited researcher. Ambrosio, L.. A compactness theorem for a new class of functions of bounded variation. Boll. Un. Mat.
Luigi Ambrosio
–
Luigi Ambrosio
10.
Gianni Dal Maso
Gianni Dal Maso
–
Gianni Dal Maso
11.
Minimal surface
–
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature. The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. However the term is used for more general surfaces that may self-intersect or do not have constraints. Minimal surfaces can be defined in several equivalent ways in R3. Note that this property is local: there might exist other surfaces that minimize area better with the same global boundary. This definition makes minimal surfaces a 2-dimensional analogue to geodesics. Mean curvature definition: A surface M ⊂ R3 is minimal if and only if its mean curvature vanishes identically. A direct implication of this definition is that every point on the surface is a point with opposite principal curvatures. This definition ties minimal surfaces to harmonic functions and potential theory. A direct implication of the maximum principle for harmonic functions is that there are no compact minimal surfaces in R3. This definition uses that the mean curvature is half of the trace of the shape operator, linked to the derivatives of the Gauss map. Mean curvature flow definition: Minimal surfaces are the critical points for the mean curvature flow. Variational definitions allow extending minimal surfaces than R3. While these were successfully used by Heinrich Scherk in 1830 to derive his surfaces, they were generally regarded as practically unusable.
Minimal surface
–
A helicoid minimal surface formed by a soap film on a helical frame
12.
House of Giorgi
–
The family is listed in the Almanach de Gotha and is currently one of the oldest European continuous noble lineage and aristocratic families. Its main branch still survives in Italy. The family established strong ties with the House of the ruling family of Monaco, ever since. The family was also the most loyal ally of the House of Hunyadi. The island of Curzola has been a fiefdom of the family since 1254. Over the centuries, the Giorgi were divided into several branches in Italy and abroad, merging with noble families of Dubrovnik and continental Europe. A branch of the family joined his name and arms to those of the House of Bona, creating a new branch as Bona-Giorgi. Between 1640 the House of Giorgi had 109 members of the Great Council, representing 4.95 % of the total. One of the minor cadet branches of the family ceased in 1897, the cadet branch of the counts Bona-Giorgi in 1902. The De Giorgi family still lives in Rome, Italy where some members hold public service positions. The current head of Diego Massimiliano De Giorgi, took the position following his father's abdication in 2014. Donato Giorgi, Dominican, professor of theology at the University of Padua, vicar general of the Dominican province of Dalmatia, Bishop of Trebinje-Mrkan. Governor of the Republic of Ragusa, 50th Doge of the Republic of Venice. Giovanni de Giorgi, Governor of the Republic of Ragusa. Matteo de Giorgi, Rector of the Republic of Ragusa.
House of Giorgi
–
House of Giorgi De Giorgi, Đurđević
13.
Accademia Nazionale dei Lincei
–
The Accademia dei Lincei is an Italian science academy, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy. The academy was named after the lynx, an animal whose sharp vision symbolizes the observational prowess that science requires. "The Lincei did not long survive the death in 1630 of Cesi, patron", "disappeared in 1651". It was revived in the 1870s to become the national academy of Italy, encompassing both science among its concerns. The first Accademia dei Lincei was founded by Federico Cesi, an aristocrat from Umbria, passionately interested in natural history - particularly botany. Cesi's father disapproved of the career that Federico was pursuing. Olimpia Orsini, supported him both financially and morally. After the death of Frederico's father he had enough money to allow the academy to flourish. At the time of the Accademia's founding Cesi was the others only 8 years older. His friends aimed to understand all of the natural sciences. The antiquarian emphasis set the "Lincei" apart from the host of sixteenth and seventeenth century Italian Academies. While originally a private association, the Academy became a semi-public establishment during the Napoleonic domination of Rome. This shift allowed scientific elite to carve out a place for themselves in larger scientific networks. However, as a semi-public establishment, the Academy's focus was directed by Napoleonic politics. This focus directed the member's efforts towards stimulating industry, secularizing the country.
Accademia Nazionale dei Lincei
–
Palazzo Corsini
Accademia Nazionale dei Lincei
–
Federico Cesi
14.
Annali di Matematica Pura ed Applicata
–
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 Francesco Brioschi. The editor-in-chief is Graziano Gentili. The journal is indexed in: According to the Journal Citation Reports, the journal has a 2012 impact factor of 0.680. Bacciotti, Andrea, "Periodici di matematica italiani: passato e futuro", Bollettino dell'Unione Matematica Italiana. Sezione A. La Matematica nella Società e nella Cultura, Serie VII, 1–A: 307–315, MR 1719425. Official website
Annali di Matematica Pura ed Applicata
–
Annali di Matematica Pura ed Applicata
15.
Bounded variation
–
Functions of bounded variation are precisely those with respect to which one may find Riemann–Stieltjes integrals of all continuous functions. After him, several authors applied BV functions to study Fourier series in several variables, geometric measure theory, mathematical physics. Ennio de Giorgi used them to define measure of nonsmooth boundaries of sets. His chain formula was later extended by Luigi Ambrosio and Gianni Dal Maso in the paper. Definition 1.1. Where the supremum is taken over the set P = of all partitions of the interval considered. Definition 1.2. 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 theorem states that every bounded linear functional arises uniquely in this way. Probability measures correspond to positive non-decreasing lower semicontinuous functions. This point of view has been important in spectral theory, to ordinary differential equations. BV functions, are functions whose distributional derivative is a finite Radon measure. More precisely: Definition 2.1. Let Ω be an open subset of ℝn. An definition is the following.
Bounded variation
–
The function f (x)=sin(1/ x) is not of bounded variation on the interval.
16.
Edoardo Amaldi
–
Edoardo Amaldi was an Italian physicist. Amaldi was born in Carpaneto Piacentino, son of Ugo Amaldi, Luisa Basini. Amaldi was his main collaborator until 1938, when Fermi left Italy for the United States. In 1939, Amaldi was returned to physics in 1941. He was the general secretary of CERN at its early stages when operations were still provisional, before September's 1954 foundation. He pioneered in Europe the search for gravitational waves. He also wrote historical-scientific books, for example, the biography of his missing friend Ettore Majorana. He was elected a Foreign Honorary Member of the Soviet Academy of American Academy of Arts and Sciences in 1962. In 1963 he became foreign member of the Royal Netherlands Academy of Arts and Sciences. The third Automated Transfer Vehicle of the European Space Agency bears his name.
Edoardo Amaldi
–
Edoardo Amaldi in 1960
Edoardo Amaldi
–
The Via Panisperna Boys, including Edoardo Amaldi (center), circa 1934
17.
Gaetano Fichera
–
Gaetano Fichera was an Italian mathematician, working in mathematical analysis, linear elasticity, partial differential equations and several complex variables. Classe died in Rome. Classe was born in Acireale, the elder of the four sons of Giuseppe Fichera and Marianna Abate. His Giuseppe was a professor of mathematics and influenced the young Gaetano starting his lifelong passion. In his young years Classe was a talented player. After the war Classe was first in Rome and then in Trieste, where he met Matelda Colautti, which become his wife in 1952. 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. His lifelong friendship with his teacher Mauro Picone is remembered in several occasions. The young, in 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. The close friendship between Angelo Pescarini and Fichera has not his roots in their scientific interests: it is another story. Gaetano quickly answered: "Non solo ti darò la condizione sufficiente, ma ti darò anche la condizione necessaria e pure per insiemi non limitati" --. One of 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 18 books: his work concerns mainly the fields of pure and applied mathematics listed below. His work in elasticity theory includes the paper, where Fichera proves his work on variational inequalities.
Gaetano Fichera
–
Gaetano Fichera in 1976 (photo by Konrad Jacobs)
18.
Enzo Martinelli
–
He was born 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 working career as the Director-general of the Italian Ministry of Public Education. In 1939 he became "Libero Docente" of Mathematical analysis: he taught also courses as associate professor. Martinelli held that chair to 1954 teaching also mathematical analysis, function theory, differential geometry and algebraic analysis as associate professor. He attended to various meetings. According to Rizza, Enzo's talent for mathematics was already evident when he was only a 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, awarded the title of professor emeritus. Another episode illustrating this aspect of Martinelli's personality is recalled by Gaetano Fichera. Martinelli, very tactfully, told him that the idea was already been developed by Georges de Rham. His doctoral advisor was Francesco Severi: other Italian mathematicians where among his teachers. Scriveva più volte ogni suo lavoro, curandone fin nei minimi particolari sostanza e forma, fino a renderli di piacevole lettura. È difficile trovare suoi scritti un concetto che possa essere espresso in modo migliore. Martinelli, Enzo, "Alcuni teoremi integrali per le funzioni analitiche di più variabili complesse", Atti della Reale Accademia d'Italia. Memorie della Classe di Scienze Fisiche, Matematiche e Naturali, 9: 269–283, JFM 64.0322.04, Zbl 0022.24002.
Enzo Martinelli
–
Enzo Martinelli around 1960
19.
International Standard Serial Number
–
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 cataloging, interlibrary loans, other practices in connection with serial literature. The ISSN system was first published as ISO 3297 in 1975. 46/SC 9 is responsible for maintaining the standard. When a serial with the same content is published in more than one media type, a different ISSN is assigned to each media type. For example, many serials are published both in electronic media. The ISSN system refers as print ISSN and electronic ISSN, respectively. The format of the ISSN is an eight code, divided by a hyphen into two four-digit numbers. As an number, it can be represented by the first seven digits. The last digit, which may be 0-9 or an X, is a check digit. The ISSN of the journal Hearing Research, for example, is 0378-5955, where the final 5 is the digit, C = 5. For calculations, an upper X in the check digit position indicates a check digit of 10. To calculate the sum of all eight digits of the ISSN multiplied by its position in the number, counting from the right. The modulus 11 of the sum must be 0.
International Standard Serial Number
–
ISSN encoded in an EAN-13 barcode with sequence variant 0 and issue number 5
20.
Springer-Verlag
–
Springer Science+Business Media or Springer is a global publishing company that publishes books, e-books and peer-reviewed journals in science, technical and medical publishing. Springer also hosts a number including SpringerLink, Springer Protocols, SpringerImages. Book publications include major reference works, textbooks, book series; more than 168,000 titles are available as e-books in 24 subject collections. Springer has major offices in New York City. On January 2015, Holtzbrinck Publishing Group / Nature Publishing Group and Springer Science + Business Media announced a merger. In 1964, Springer expanded its business internationally, opening an office in New York City. Offices in Delhi soon followed. The academic publishing BertelsmannSpringer was formed after Bertelsmann bought a majority stake in Springer-Verlag in 1999. Cinven and Candover bought BertelsmannSpringer from Bertelsmann in 2003. They merged the company in 2004 with the Dutch publisher Kluwer Academic Publishers which they bought from Wolters Kluwer in 2002, to form Springer Science+Business Media. Springer acquired the open-access publisher BioMed Central for an undisclosed amount. In 2009, Cinven and Candover sold Springer to two private equity firms, Government of Singapore Investment Corporation. The closing of the sale was confirmed after the competition authorities in the USA and in Europe approved the transfer. In 2011, Springer acquired Publishing Services from Wolters Kluwer. In 2013, the private equity firm BC Partners acquired a majority stake in Springer from EQT and GIC for $4.4 billion.
Springer-Verlag
–
Springer Science+Business Media
21.
International Standard Book Number
–
The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each variation of a book. For example, an e-book, a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned after 1 January 2007, 10 digits long if assigned before 2007. The method of assigning an ISBN 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 based upon the 9-digit Standard Book Numbering created in 1966. The 10-digit ISBN format was published in 1970 as international standard ISO 2108. The International Standard Serial Number, identifies periodical publications such as magazines; and the International Standard Music Number covers for musical scores. The ISBN configuration of recognition was generated in 1967 in the United Kingdom by Emery Koltay. The 10-digit ISBN format was published as international standard ISO 2108. 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 by prefixing the digit "0". This can be converted to ISBN 0-340-01381-8; the digit does not need to be re-calculated. Since 1 ISBNs have contained 13 digits, a format, compatible with "Bookland" European Article Number EAN-13s.
International Standard Book Number
–
A 13-digit ISBN, 978-3-16-148410-0, as represented by an EAN-13 bar code
22.
Adobe Systems
–
Adobe Systems Incorporated /əˈdoʊbiː/ is an American multinational computer software company. The company is headquartered in California, United States. Adobe has historically focused with a more recent foray towards rich Internet application software development. In 1985, Apple Computer licensed PostScript for use in its LaserWriter printers, which helped spark the desktop revolution. As of 2015, Adobe Systems has about 40 % of whom work in San Jose. The name of Adobe, comes from Adobe Creek in Los Altos, California, which ran behind the houses of both of the company's founders. Adobe's corporate logo was designed by the wife of John Warnock, Marva Warnock, a graphic designer. Adobe's first products after PostScript were digital fonts, which they released in a proprietary format called Type 1. In the mid-1980s, Adobe entered the consumer market with Adobe Illustrator, a vector-based drawing program for the Apple Macintosh. Illustrator, which grew from the firm's 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 in 2012. Adobe's fiscal years run to November. For example, the 2007 fiscal year ended on November 2007. In 1989, Adobe introduced what was to become its product, a graphics editing program for the Macintosh called Adobe Photoshop.
Adobe Systems
–
Adobe Systems headquarters in San Jose, California
Adobe Systems
–
Adobe Systems Incorporated
Adobe Systems
–
Adobe Systems Canada in Ottawa, Ontario (not far from archrival Corel).
23.
Scuola Normale Superiore
–
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 Sant'Anna School of Advanced Studies, is a part of the Pisa University System. Ces écoles doivent être en effet la règle de toutes les autres." 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. There was to be an organic division into two Faculties, of Arts and Sciences. In 1863, was appointed a new Director of the Scuola Normale, the respected Pasquale Villari. 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 and as director in 1932. 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 many practical difficulties; however, besides the restoration of Palazzo dei Cavalieri. The new institution, while still committed to the model established by the Scuola Normale Superiore di Pisa, was administered by the University of Pisa. 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.
Scuola Normale Superiore
–
A detail of the main building, Palazzo della Carovana
Scuola Normale Superiore
–
Scuola Normale of Pisa
Scuola Normale Superiore
–
The first statute of the Scuola Normale Superiore
Scuola Normale Superiore
–
Palazzo della Carovana, Scuola Normale's main building
24.
Notices of the AMS
–
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 an editorial board of mathematical experts. Since 2016, the editor-in-chief is Frank Morgan. The cover regularly features mathematical visualizations. The Notices is the world's most widely read mathematical journal. 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 professional issues facing mathematicians, well as reviews of books and other works. American Mathematical Monthly, another "most widely read mathematics journal in the world" Official website
Notices of the AMS
–
March 2005 issue
25.
Heidelberg
–
It is a city situated on the river Neckar in south-west Germany. The fifth-largest town in the State of Baden-Württemberg after Stuttgart, Karlsruhe, Mannheim and Freiburg im Breisgau, Heidelberg is part of the densely populated Rhine-Neckar Metropolitan Region. In 2015, over 156,000 people lived in the city. A former residence of the Electorate of the Palatinate, Heidelberg is the location among its most reputable universities. It is a popular destination due to its romantic and picturesque cityscape, including Heidelberg Castle and the baroque style Old Town. It is on the left bank of the lower part of the Neckar in a steep valley in the Odenwald. Heidelberg is bordered by 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 along the Bergstraße, a road running through the Odenwald hills. It is on European walking E1. Alongside the Philosophenweg on the opposite side of the Old Town, winegrowing was restarted in 2000. It is a unitary authority within the Regierungsbezirk Karlsruhe. The Rhein-Neckar-Kreis rural district has its seat in the town, although the town is not a part of the district.
Heidelberg
–
Heidelberg, with Heidelberg Castle on the hill and the Old Bridge over river Neckar
Heidelberg
–
Heidelberg with suburbs
Heidelberg
–
The Altstadt from the Castle
Heidelberg
–
The River Neckar at night
26.
Jacques-Louis Lions
–
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 SIAM's John von Neumann prize in numerous other distinctions. Lions is listed as an ISI highly cited researcher. After being part of the French Résistance in 1944, J.-L. Lions entered the École Normale Supérieure in 1947. He was a professor of mathematics at the Université of Nancy, the École polytechnique. He joined the prestigious Collège de France well as the French Academy of Sciences in 1973. This eventually led him to be appointed director of the Centre National d'Etudes Spatiales to 1992. Lions was elected President of the International Mathematical Union in 1991 and also received that same year. In 1992, the University of Houston awarded an honorary doctoral degree. His son Pierre-Louis Lions is also a well-known mathematician, awarded a Fields Medal in 1994. In fact both Father and Son received recognition in the form of Honorary Doctorates from Heriot-Watt University in 1986 and 1995 respectively. With Enrico Magenes: Problèmes aux limites applications. 3 vols. 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.
Jacques-Louis Lions
–
Jacques-Louis Lions
27.
Basel
–
Basel is a city in northwestern Switzerland on the river Rhine. The Basel region culturally extends into French Alsace. Basel joined the Swiss Confederacy in 1501. It emerged as a centre for the chemical and pharmaceutical industry in the 20th century. Basel is Switzerland's third-most-populous city with about inhabitants. Located where the Swiss, German borders meet, Basel also has suburbs in France and Germany. The Basel metropolitan area has around 830,000 inhabitants in 226 municipalities. The main spoken language is the local variant of the Alemannic Swiss German dialect. Basel German belongs to the Low Alemannic group, linking it more closely than with the other varieties of Swiss German. Basel has been the Age of Enlightenment. It has the oldest university of the Swiss Confederation. There are settlement traces on the Rhine knee from the early La Tène period. 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.
Basel
–
Basel, as seen from the Elisabethenkirche
Basel
–
Map of Basel in 1642, engraved by Matthäus Merian, oriented with SW at the top and NE at the bottom.
Basel
–
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
–
The synagogue of Basel
28.
Boston
–
Boston is the capital and most populous city of the Commonwealth of Massachusetts in the United States. Boston is also the seat of Suffolk County, although the government was disbanded on July 1, 1999. One of the oldest cities in the United States, Boston was founded on the Shawmut Peninsula in 1630 from England. Upon U.S. independence from Great Britain, the city continued to be manufacturing hub, as well as a center for education and culture. Through municipal annexation, Boston has expanded beyond the original peninsula. Its rich history attracts many tourists, with Faneuil Hall alone drawing over million visitors per year. Boston's many firsts include Boston Latin School, first subway system, first public park. Boston's economic base also includes finance, professional and business services, biotechnology, government activities. Boston's early European settlers had later renamed it Boston after Boston, Lincolnshire, England, the origin of several prominent colonists. The renaming, on September 1630, was by Puritan colonists from England, who had moved over from Charlestown earlier that year in quest of fresh water. The peninsula is known to have been inhabited early as 5000 BC. In 1629, John Winthrop, led the signing of the Cambridge Agreement, a key founding document of the city. Their focus on education influenced its early history; America's first public school was founded in Boston in 1635. Boston was the largest town in British North America until Philadelphia grew larger in the 18th century. The Embargo Act of the War of 1812 significantly curtailed Boston's harbor activity.
Boston
–
From top to bottom, left to right: the Boston skyline viewed from the Bunker Hill Monument; the Museum of Fine Arts; Faneuil Hall; Massachusetts State House; The First Church of Christ, Scientist; Boston Public Library; the John F. Kennedy Presidential Library and Museum; South Station; Boston University and the Charles River; Arnold Arboretum; Fenway Park; and the Boston Common
Boston
–
State Street, 1801
Boston
–
View of Boston from Dorchester Heights, 1841
Boston
–
Scollay Square in the 1880s
29.
Stuttgart
–
Stuttgart is also the capital of the greater Stuttgart Metropolitan Region, making the center of political goings for a population of 5.3 million people. It is the metropolitan after the Rhine-Ruhr area, Berlin/Brandenburg and Frankfurt/Rhine-Main. Stuttgart is an Independent city that controls 23 City districts that form the center of a densely populated area, surrounded by a ring of smaller towns. This area has a population of million. Stuttgart is a very important economic zone within the European Union. Such companies as Porsche, Mercedes-Benz, Dinkelacker, Neoplan, Horváth & Partners are headquartered here. Stuttgart is unusual in the scheme of German cities. It is spread across a variety of parks. This is often a source of surprise to visitors who associate the city with its reputation as the'Cradle of the Automobile'. The city's tourism slogan is "Stuttgart offers more". For business, it describes itself as "Standort Zukunft", "Where business meets the future"). In July 2010, Stuttgart unveiled a new logo, designed to entice more business people to enjoy breaks in the area. Stuttgart has often been nicknamed Schwabenmetropole in reference in the local dialect spoken by some natives. In that dialect, the city's name is pronounced Schtugert or Schtuagerd. Because of this, the city is often described as lying "zwischen Wald und Reben".
Stuttgart
–
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
–
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
–
Stuttgart at night, looking northwest
Stuttgart
–
Schlossplatz
30.
Web page
–
A web page is a document, suitable for the World Wide Web and web browsers. A browser displays a web page on a monitor or mobile device. The term also refers to a computer file, usually written in HTML or comparable markup language. Web browsers to present the web page. Typical web pages provide hypertext that includes a sidebar menu to other web pages via hyperlinks, often referred to as links. On a network, a browser can retrieve a web page from a remote web server. On a lower level, the browser uses the Hypertext Transfer Protocol to make such requests. Dynamic website pages help the browser to enhance the web page to the server. An HTTP 1.1 server will maintain a connection with the browser until all related resources have been requested and provided. Web browsers usually render images along with the text and other material on the displayed page. These scripts may run on the computer, if the user allows. A browser can have a Graphical User Interface, like Internet Explorer, Mozilla Firefox, Google Chrome, Opera, or can be text-based, like Lynx or Links. Web users with disabilities often use assistive technologies and adaptive strategies to access web pages. Users of mobile devices often have restricted displays and bandwidth. Web Accessibility Initiative recommend that all web pages should be designed with all of these options in mind.
Web page
–
A screenshot of Wikimedia Commons, a web page
31.
Web site
–
Web pages, which are the building blocks of websites, are documents, typically composed in plain text interspersed with formatting instructions of Hypertext Markup Language. They may incorporate elements from other websites with suitable markup anchors. Web pages are transported with the Hypertext Transfer Protocol, which may optionally employ encryption to provide privacy for the user. Often a browser, renders the page content according to its HTML markup instructions onto a display terminal. Some websites require subscription to access content. As of 2016, end users can access websites on a range including desktop and laptop computers, tablet computers, smart TVs. The World Wide Web was created in 1990 by the British CERN physicist Tim Berners-Lee. On 30 April 1993, CERN announced that the World Wide Web would be free to use for anyone. These protocols offer a simple structure which the user chooses files to download. Documents were encoded in processor formats. Websites are typically dedicated to purpose. Any website can contain a hyperlink to any other website, so the distinction between individual sites, as perceived by the user, can be blurred. Websites are accessed using a interface classified as a user agent. A website is hosted on a computer system known as a web server, also called an HTTP server. Apache is the most commonly used web server software and Microsoft's IIS is also commonly used.
Web site
–
NASA.gov homepage as it appeared in April 2015
32.
University of St Andrews
–
The University of St Andrews is a British public research university in St Andrews, Fife, Scotland. It is the oldest of the four ancient universities of Scotland and the third oldest university in the English-speaking world. St Andrews was founded between 1413, when the Avignon Antipope Benedict XIII issued a papal bull to a small group of Augustinian clergy. St Andrews is made up including 18 academic schools organised into four faculties. The university occupies historic and modern buildings located throughout the town. The academic year is divided into Candlemas. In time, over one-third of the town's population is either a staff student of the university. It is ranked behind Oxbridge. The Times Higher Education World Universities Ranking names St Andrews among the world's Top 50 universities for Social Sciences, Arts and Humanities. St Andrews has the highest student satisfaction amongst all multi-faculty universities in the United Kingdom. St Andrews has affiliated faculty, including eminent mathematicians, scientists, theologians, politicians. Six Nobel Laureates are amongst St Andrews' alumni and former staff: two in Chemistry and Physiology or Medicine, one each in Peace and Literature. A charter of privilege was bestowed by the Bishop of Henry Wardlaw, on 28 February 1411. King James I of Scotland confirmed the charter of the university in 1432. Subsequent kings supported the university with King James V "confirming privileges of the university" in 1532.
University of St Andrews
–
College Hall, within the 16th century St Mary's College building
University of St Andrews
–
University of St Andrews shield
University of St Andrews
–
St Salvator's Chapel in 1843
University of St Andrews
–
The "Gateway" building, built in 2000 and now used for the university's management department
33.
Leonida Tonelli
–
Tonelli graduated in 1907. His reply was a question: "Can you use semicontinuity?" The Italian was Leonida Tonelli. Semicontinuity was then still a recent concept, known only to a few. In the hands of Tonelli, it became an important tool to the calculus of variations. A cura dell ` Unione matematica italiana e col contributo del Consiglio nazionale delle richerche, 1900 Fondamenti di Calcolo delle Variazioni. Zanichelli, Bologna, vol. 1: 1922, vol. 2: 1923 "The Calculus of Variations". Bull. Amer. Math. Soc. 31: 163–172. 1925. Doi:10.1090/s0002-9904-1925-04002-1. MR 1561014. Serie trigonometriche.
Leonida Tonelli
–
Leonida Tonelli
34.
Israel Gelfand
–
Gelfand made significant contributions including group theory, functional analysis. He taught students through his seminar at Moscow State University. A native of Kherson Governorate of Gelfand was born into a Jewish family in the small 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 postgraduate 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 postgraduate study at the age of 19. Gelfand also published works on biology and medicine. For a long time Gelfand organized a seminar on the subject. Gelfand worked extensively in education, particularly with education. In 1994, he was awarded a MacArthur Fellowship for this work. Gelfand was married to Zorya Shapiro, 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. Gelfand and Tatiana became the parents of a daughter, Tatiana. The family also includes four grandchildren and three great-grandchildren.
Israel Gelfand
–
Israïl Moiseevich Gelfand
35.
Carl Ludwig Siegel
–
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 Siegel mass formula for quadratic forms. 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. Amongst his teachers were Ferdinand Georg Frobenius, whose influence made the young Siegel abandon astronomy and turn towards number theory instead. His best student was one of the founders of KAM theory, which lies at the foundations of chaos theory. Another notable student was the number theorist. 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 because of his support from Edmund Landau, whose father had a clinic in the neighborhood. After the end of World War I, he enrolled at the Georg-August University of Göttingen, studying under Landau, his doctoral supervisor. He stayed as a teaching and research assistant; many of his groundbreaking 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, deeply opposed to Nazism, used his influence to help them. This attitude prevented Siegel's appointment to the chair of Constantin Carathéodory in Munich. In the seminar they read only original sources.
Carl Ludwig Siegel
–
Carl Ludwig Siegel in 1975
36.
Jean Leray
–
Jean Leray was a French mathematician, who worked on both partial differential equations and algebraic topology. He was born in Chantenay-sur-Loire. He studied to 1929. He received his Ph.D. in 1933. Leray wrote an important paper that founded the study of weak solutions of the Navier–Stokes equations. From 1938 to 1939 he was professor at the University of Nancy. 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 from 1940 to 1945. He concealed his expertise on differential equations, fearing that its connections with applied mathematics could lead him to be asked to do work. Leray's work of this period proved seminal to the development of spectral sheaves. These were subsequently developed by many others, each separately becoming an important tool in homological algebra. He returned to work from about 1950. He was professor at the University of Paris until 1978. He was awarded the Malaxa Prize, the Grand Prix in mathematical sciences, the Feltrinelli Prize, the Lomonosov Gold Medal. Leray spectral sequence Leray cover Leray's theorem Leray -- Hirsch theorem O'Connor, John J.; Robertson, Edmund F. "Jean Leray", University of St Andrews.
Jean Leray
–
Jean Leray in 1961
37.
Henri Cartan
–
Henri Paul Cartan was a French mathematician with substantial contributions in algebraic topology. He was the brother of composer Jean Cartan. Cartan studied at the École Normale Supérieure in Paris receiving his doctorate in mathematics. Cartan is known for work in particular on cohomology operations, the method of "killing homotopy groups", group cohomology. The number of his official students includes Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom. Cartan also was one of its most active participants. His book with Samuel Eilenberg Homological Algebra was an important text, treating the subject with the help of category theory. Cartan used his influence to 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. His funeral took the following Wednesday on 20 August in Die, Drome. Cartan received numerous awards including the Wolf Prize in 1980. Until his death he had been a member of the French Academy of Sciences. Holomorphes à variétés linéaires lacunaires et leurs applications, thèse, 1928 Sur les groupes de transformations analytiques, 1935.
Henri Cartan
–
Henri Cartan
38.
Andrey Kolmogorov
–
Andrey Kolmogorov was born in 1903. His unmarried mother, Maria Y. Kolmogorova, died giving birth to him. Andrey was raised by two of his aunts at the estate of his grandfather, a well-to-do nobleman. Little is known about Andrey's father. He had been an agronomist. Nikolai had been exiled after his participation in the revolutionary movement against the czars. He was presumed to have been killed in the Russian Civil War. Andrey was the "editor" of the mathematical section of this journal. In 1910, they moved to Moscow, where he graduated from high school in 1920. Later 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 fair knowledge of mathematics. I knew in particular the beginning of theory. I studied many questions in articles 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.
Andrey Kolmogorov
–
Andrey Kolmogorov
Andrey Kolmogorov
–
Kolmogorov (left) delivers a talk at a Soviet information theory symposium. (Tallinn, 1973).
Andrey Kolmogorov
–
Kolmogorov works on his talk (Tallinn, 1973).
39.
Lars Ahlfors
–
Lars Valerian Ahlfors was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his text on complex analysis. He was born in Helsinki, Finland. Sievä Helander, died at his birth. 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. He studied from 1924 graduating in 1928 having studied under Ernst Lindelöf and Rolf Nevanlinna. Ahlfors assisted Nevanlinna in 1929 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. Ahlfors completed his doctorate in 1930. He worked from 1933 to 1936. In 1936 Ahlfors was one of the first two people to be awarded the Fields Medal. In 1935 Ahlfors visited Harvard University. Ahlfors returned 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. Ahlfors was offered a post at the Swiss Federal Institute of Technology in 1944 and finally managed to travel there in March 1945.
Lars Ahlfors
–
Lars Ahlfors
40.
Oscar Zariski
–
Oscar Zariski (born Oscher Zaritsky was a Russian-born American mathematician and one of the most influential algebraic geometers of the 20th century. Zariski was born Oscher Zaritsky in 1918 studied at the University of Kiev. Zariski wrote a doctoral dissertation on a topic in Galois theory, proposed to him by Castelnuovo. At the time of his publication, he changed his name to Oscar Zariski. Zariski emigrated in 1927 supported by Solomon Lefschetz. He had a position at Johns Hopkins University where he became professor in 1937. During this period, he wrote Algebraic Surfaces as a summation of the work of the Italian school. It is still an important reference. It seems to have been this work that set the seal of Zariski's discontent to birational geometry. He addressed by recourse to commutative algebra. The Zariski topology, as it was later known, is adequate for geometry, where varieties are mapped by polynomial functions. That theory is too limited for algebraic surfaces, even for curves with singular points. A rational map is to a regular map as a rational function is to a polynomial: it may be indeterminate at some points. In geometric terms, one has to work with functions defined on some dense set of a given variety. The description of the behaviour on the complement may require infinitely near points to be introduced to account for limiting behaviour along different directions.
Oscar Zariski
–
Oscar Zariski (1899–1986)
41.
Mark Krein
–
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 the problem of moments, classical analysis and representation theory. He was born in Kiev, leaving home at age 17 to go to Odessa. He had a academic career, not completing his first degree and constantly being troubled by anti-Semitic discrimination. His supervisor was Nikolai Chebotaryov. He was not allowed to attend the ceremony. David Milman, Mark Naimark, Izrail Glazman, other known mathematicians were his students. He died in Odessa. On 14 January 2008, the memorial plaque of Mark Krein was unveiled on the main administration building of I.I. Mechnikov Odessa National University. Mark Krein at the Mathematics Genealogy Project INTERNATIONAL CONFERENCE Applications. Dedicated to the centenary of Mark Krein
Mark Krein
–
The memorial plaque of Mark Krein
42.
Shiing-Shen Chern
–
Shiing-Shen Chern was a Chinese-American mathematician. Chern is regarded in differential geometry of the twentieth century. He was born in Zhejiang province. The year after his birth, China changed its regime to the Republic of China. Chern subsequently moved to Tianjin in 1922 to accompany his father. After spending four years in Tianjin, he graduated from Fulun High School. At Nankai, Chern's mentor was a Harvard-trained geometer. Also at Nankai, Chern was heavily influenced by the physicist RaoYuTai. Rao is today considered to be one of the founding fathers of Chinese informatics. He went to Beiping to work as a teaching assistant. At the same time Chern also registered as a student. He studied projective differential geometry under Prof. Sun Guangyuan, a University of Chicago-trained geometer and logician, also from Zhejiang. Sun is another mentor of Chern, considered a founder of Chinese mathematics. In 1932, he published his first article in the Tsinghua University Journal.
Shiing-Shen Chern
–
Shiing-Shen Chern, 1976
43.
Kunihiko Kodaira
–
He was awarded a Fields Medal in 1954, being the first Japanese national to receive this honour. He was born in Tokyo. During the war years he was able to master Hodge theory as it then stood. He obtained his Ph.D. degree from the University of Tokyo with a thesis entitled Harmonic fields in Riemannian manifolds. He was involved in cryptographic work while holding an academic post in Tokyo. In 1949 he travelled to the Institute at the invitation of Hermann Weyl. At this time the foundations of Hodge theory were being brought with contemporary technique in operator theory. Kodaira rapidly became involved in exploiting the tools it opened up in algebraic geometry, adding theory as it became available. This work was particularly influential, for example on Hirzebruch. In a second research phase, Kodaira wrote a long series of papers in collaboration with D. C. Spencer, founding the deformation theory of complex structures on manifolds. This gave the possibility of constructions of moduli spaces, in general such structures depend continuously on parameters. This theory is still foundational, also had an influence on the theory of Grothendieck. Spencer then continued this work, applying the techniques to structures such as G-structures. This resulted in a typology of seven kinds of two-dimensional complex manifolds, recovering the five algebraic types known classically; the other two being non-algebraic.
Kunihiko Kodaira
–
Kunihiko Kodaira
44.
Hans Lewy
–
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 on October 20, 1904. He earned his doctorate in 1926, at which time his friend Kurt Otto Friedrichs both became assistants to Courant and privatdozents at Göttingen. After Hitler's election as chancellor in 1933, Lewy was advised by Herbert Busemann to leave Germany again. He was offered a position in Madrid, but declined it, fearing there under Francisco Franco. In 1935, he moved to the University of California, Berkeley. During World War II, Lewy then worked at the Aberdeen Proving Ground. He married Helen Crosby in 1947. In 1950, Lewy was fired for refusing to sign a loyalty oath. He taught at Harvard University and Stanford University before being reinstated by the California Supreme Court case Tolman v. Underhill. He in 1973 became one of two Ordway Professors of Mathematics at the University of Minnesota. He died in Berkeley. Lewy was also a member of the American Academy of Arts and Sciences. He became a foreign member of the Accademia dei Lincei in 1972. He was awarded a Leroy P. Steele Prize in 1979, a Wolf Prize in Mathematics for his work on partial differential equations.
Hans Lewy
–
Hans Lewy in 1975 (photo by George Bergman)
45.
Samuel Eilenberg
–
Samuel Eilenberg was a Polish-born American mathematician. He earned his Ph.D. in 1936. His advisor was Karol Borsuk. His main interest was algebraic topology. He worked with Norman Steenrod, on homological algebra with Saunders Mac Lane. In the process, Eilenberg and Mac Lane created theory. Eilenberg was a member of Bourbaki and with Henri Cartan, wrote the 1956 book Homological Algebra, which became a classic. Later in life he worked mainly in pure theory, being one of the founders of the field. The Eilenberg swindle is a construction applying the telescoping idea to projective modules. Eilenberg also wrote an important book on theory. A form of automaton, was introduced by Eilenberg in 1974. Eilenberg was also a prominent collector of Asian art. His collection mainly consisted from India, Indonesia, Nepal, Thailand, Cambodia, Sri Lanka and Central Asia. Samuel Eilenberg, Automata, Languages and Machines. ISBN 0-12-234001-9.
Samuel Eilenberg
–
Samuel Eilenberg (1970)
46.
Atle Selberg
–
He was awarded the Fields Medal in 1950. Selberg was born in the son of teacher Anna Kristina Selberg and mathematician Ole Michael Ludvigsen Selberg. The remaining one became a professor of engineering. During the war he was imprisoned several times. He completed his Ph.D. in 1943. During World War II, Selberg worked due to the German occupation of Norway. After the war, he turned to sieve a previously neglected topic which Selberg's work brought into prominence. This challenged the widely held view of his time that certain theorems are only obtainable with the advanced methods of complex analysis. Circumstances leading up to the proofs, well as publication disagreements, led to a bitter dispute between the two mathematicians. For his fundamental accomplishments during the 1940s, Selberg received the 1950 Fields Medal. He was awarded the 1986 Wolf Prize in Mathematics. He was also awarded an honorary Abel Prize in its founding year, before the awarding of the regular prizes began. Selberg received many distinctions to the Fields Medal, the Wolf Prize and the Gunnerus Medal. In 1972 he was awarded doctor philos. Honoris causa, at the Norwegian Institute of Technology, later part of Norwegian University of Science and Technology.
Atle Selberg
–
Atle Selberg
47.
Peter Lax
–
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 to a Jewish family. His uncle, Albert Kornfeld, was a mathematician and a friend of Leó Szilárd. Soon his parents hired Rózsa Péter as a tutor for him. The family traveled via Lisbon to the United States. Before being able to complete his studies, Lax was drafted into the U.S. Army. At Los Alamos, he eventually moved on to higher-level mathematics. By pooling credits from the four universities at which he had studied, he graduated that year. He stayed for his graduate studies marrying Anneli in 1948 and earning a Ph.D. in 1949 under the supervision of Kurt O. Friedrichs. In a 1958 paper Lax stated a conjecture for third order hyperbolic polynomials which remained unproven for over four decades. Lax holds a position in the Department of Mathematics, Courant Institute of Mathematical Sciences, New York University. He is a member of the National Academy of Sciences, USA. He won a Lester R. Ford Award in 1966 and again in 1973. The American Mathematical Society selected him for 2007.
Peter Lax
–
Peter Lax in Tokyo, 1969
48.
Friedrich Hirzebruch
–
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 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. More than 300 people gathered in 2007. Hirzebruch's Neue topologische Methoden in der algebraischen Geometrie was a basic text for the ` new methods' of sheaf theory, in complex algebraic geometry. He went on to collaborate with Armand Borel on the theory of characteristic classes. In his later work he provided a detailed theory of Hilbert modular surfaces, working with Don Zagier. When a British soldier found that he was studying mathematics, he drove him home and told him to continue studying. Hirzebruch died on 27 May 2012. Amongst other honours, Hirzebruch was awarded a Wolf Prize in Mathematics in 1988 and a Lobachevsky Medal in 1989. The government of Japan awarded the Order of the Sacred Treasure in 1996. Hirzebruch received the Cantor medal in 2004. In 1980 -- 81 he delivered Distinguished Lecture in Israel.
Friedrich Hirzebruch
–
Friedrich Hirzebruch in 1980 (picture courtesy MFO)
49.
John Milnor
–
John Willard Milnor is an American mathematician known for his work in differential topology, K-theory and dynamical systems. Milnor was born in Orange, New Jersey. His mother was Emily Cox Milnor. As an undergraduate at Princeton University he also proved the Fary -- Milnor theorem. 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. His students have included Tadatoshi Akiba, Jon Folkman, John Mather, Laurent C. Siebenmann, Michael Spivak. Dusa McDuff, is a professor of mathematics at Barnard College. One of his published works is his proof 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 structure is called an exotic sphere, a term coined by Milnor. Milnor's 1968 book on his theory inspired the growth of a huge and rich area which continues to mature to this day. 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.
John Milnor
–
John Willard Milnor
50.
Ilya Piatetski-Shapiro
–
Ilya Piatetski-Shapiro was a Soviet-born Israeli mathematician. During a career that spanned 60 years Ilya made major contributions to applied science well as theoretical mathematics. In the forty years his research focused on pure mathematics; in particular, analytic number theory, group representations and algebraic geometry. Impact was in the area of automorphic forms and L-functions. For the last 30 years of his life Ilya suffered from Parkinson's disease. He was born in Moscow, Soviet Union. Both mother, Sofia Arkadievna, were from traditional Jewish families, but which had become assimilated. His father was from a small city in the Ukraine, with a largely Jewish population. His mother was from a similar small city in Belorussia. They sank into poverty after the October revolution of 1917. In 1952, Piatetski-Shapiro won the Moscow Mathematical Society Prize for a Young Mathematician for work done while still an undergraduate at Moscow University. His winning paper contained a solution on sets of uniqueness of trigonometric series. The award was especially remarkable in Soviet Union at that time. He was ultimately admitted to the Moscow Pedagogical Institute, where he received his Ph.D. under the direction of Alexander Buchstab. His early work was in analytic number theory.
Ilya Piatetski-Shapiro
–
Ilya Piatetski-Shapiro
51.
Lennart Carleson
–
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 Lusin's conjecture. 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, they had two children: Caspar and Beatrice. His work has included the solution of some outstanding problems, using techniques from combinatorics and probability theory. Establishing the 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
–
Lennart Carleson in May 2006.
52.
John G. Thompson
–
John Griggs Thompson is a mathematician at the University of Florida noted for his work in the field of finite groups. He was awarded the Fields Medal in 1970, the 2008 Abel Prize. He received his B.A. under the supervision of Saunders Mac Lane. He is currently professor of mathematics at the University of Florida. He received the Abel Prize 2008 together with Jacques Tits. At the time, this achievement was noted in The New York Times. Thompson became a figure toward the classification of finite simple groups. In 1963, Walter Feit proved that all nonabelian finite simple groups are of even order. This work was recognised in Algebra of the American Mathematical Society. His N-group papers classified all simple groups for which the normalizer of every non-identity solvable subgroup is solvable. This included, as a by-product, the classification of all minimal simple groups. The Thompson Th is one of the 26 sporadic finite simple groups. Thompson also made major contributions to the inverse Galois problem. He found a criterion for a finite group to be a Galois group, that in particular implies that the monster simple group is a Galois group. In 1971, Thompson was elected to the United States National Academy of Sciences.
John G. Thompson
–
John Thompson in 2007
53.
Mikhail Leonidovich Gromov
–
Mikhail Leonidovich Gromov, is a French-Russian mathematician known for important contributions in many different areas of mathematics, including geometry, analysis and group theory. He is a permanent member of a Professor of Mathematics at New York University. Gromov has won several prizes, including the Abel Prize in 2009 "for his revolutionary contributions to geometry". Mikhail Gromov was born on 23 December 1943 in Boksitogorsk, Soviet Union. His Jewish mother Lea Rabinovitz were pathologists. Gromov studied mathematics at Leningrad State University where he defended his Postdoctoral Thesis in 1973. His advisor was Vladimir Rokhlin. Gromov married in 1967. In 1970, invited to give a presentation in France, he was not allowed to leave the USSR. Still, his lecture was published in the conference proceedings. Disagreeing with the Soviet system, he had been thinking of emigrating since the age of 14. In the early 1970s he ceased publication, hoping that this would help his application to move to Israel. He changed his last name to that of his mother. When the request was granted in 1974, he moved directly to New York where a position had been arranged at Stony Brook. He adopted French citizenship in 1992.
Mikhail Leonidovich Gromov
–
Mikhail Gromov
54.
Jacques Tits
–
Tits was born to Léon Tits, a professor, Lousia André. Jacques attended the Free University of Brussels. He changed his citizenship in 1974 in order to teach at the Collège de France, which at that point required French citizenship. Because Belgian law did not allow dual nationality at the time, he renounced his Belgian citizenship. He has been a member of the French Academy of Sciences since then. Tits received the Wolf Prize in 1993, the Cantor Medal from the Deutsche Mathematiker-Vereinigung in 1996, the German distinction "Pour le Mérite". He is a member of several Academies of Sciences. He is a member of the Norwegian Academy of Science and Letters. He became a foreign member of the Royal Netherlands Academy of Arts and Sciences in 1988. He introduced the theory of buildings, which are combinatorial structures on which groups act, particularly in algebraic theory. The related theory of pairs is a basic tool in the theory of groups of type. The Tits -- Koecher construction are named after him. He introduced the Kneser–Tits conjecture. Tits, Jacques. "abstract simple groups".
Jacques Tits
–
Jacques Tits in May 2008
55.
Robert Langlands
–
Robert Phelan Langlands is a Canadian mathematician. He occupies Albert Einstein's office at the Institute for Advanced Study in Princeton. Langlands received an undergraduate degree from the University of British Columbia in 1957, continued on there to receive an M. Sc. in 1958. He then went to Yale University where he received a Ph.D. in 1960. The years 1967 -- 72 at Yale University. He was a Miller Research Fellow at the University of California Berkeley from 1964-65. He was appointed Hermann Weyl Professor at the Institute for Advanced Study in 1972, becoming Professor Emeritus in January 2007. Previously this had been known only for certain classical groups where it could be shown by induction. This work led in the winter of 1966 -- 67, to the now well known conjectures making up what is often called the Langlands program. These conjectures were first posed in relatively complete form in a famous letter to Weil, written in January 1967. It was in this letter that he introduced what has since become along with it, the notion of functoriality. Langlands's introduction of these notions broke up large and to some extent intractable problems into more manageable pieces. For example, they made the infinite-dimensional theory of reductive groups into a major field of mathematical activity. Functoriality is the conjecture that automorphic forms on different groups should be related in terms of their L-groups. In its application to Artin's conjecture, functoriality associated to every N-dimensional representation of a Galois group an automorphic representation of the adelic group of GL.
Robert Langlands
–
Robert Langlands
56.
Andrew Wiles
–
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 Fermat's Last Theorem, for which he received the 2016 Abel Prize. Wiles has received numerous other honours. His father worked for the years 1952 -- 55. He attended Cambridge. Wiles states that he came across Fermat's 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. He earned his bachelor's degree at Clare College, Cambridge. After a stay at the Institute for Advanced Study in New Jersey in 1981, Wiles became a professor at Princeton University. 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, then he returned to Princeton. He rejoined Oxford in 2011 as Royal Society Research Professor. Wiles's graduate research was guided by John Coates beginning in the summer of 1975. Together these colleagues worked by the methods of Iwasawa theory. The modularity theorem involved elliptic curves, also Wiles's own specialist area.
Andrew Wiles
–
Wiles at the 61st Birthday conference for P. Deligne (Institute for Advanced Study, 2005).
Andrew Wiles
–
Andrew Wiles before the statue of Pierre de Fermat in Beaumont-de-Lomagne (October 1995)
57.
Yakov Sinai
–
Yakov Grigorevich Sinai is a mathematician known for his work on dynamical systems. Sinai connected the world of deterministic systems with the world of probabilistic systems. Sinai has also worked on mathematical physics and theory. His efforts have provided the groundwork for advances in the physical sciences. He has won several awards, including the Nemmers Prize, the Abel Prize. Yakov Grigorevich Sinai was born in Moscow, Soviet Union. Nadezda Kagan and Gregory Sinai, were both microbiologists. Veniamin Kagan, headed the Department of Differential Geometry at Moscow State University and was a major influence on Sinai's life. He received master's degrees from Moscow State University. In 1960, he earned his Ph.D. also from Moscow State; his adviser was Andrey Kolmogorov. Together with Kolmogorov, Sinai showed that even for "unpredictable" dynamic systems, the level of unpredictability of motion can be described mathematically. In 1963, he introduced the idea of dynamical billiards, also known as "Sinai Billiards". In this idealized system, a particle bounces around without loss of energy. Inside the square is a circular wall, of which the particle also bounces off. It was the first anyone proved a dynamic system was ergodic.
Yakov Sinai
–
Yakov G. Sinai
58.
Elias M. Stein
–
Elias Menachem Stein is a mathematician active in the field of harmonic analysis. He is a emeritus of Mathematics at Princeton University. Stein was born from Belgium. After the German invasion in 1940, the Stein family fled to the United States, first arriving in New York City. In 1955, Stein earned a Ph.D. under the direction of Antoni Zygmund. Stein has made contributions in both extending and clarifying Calderón -- Zygmund theory. He has written numerous books on harmonic analysis, which are often cited as the standard references on the subject. His Princeton Lectures in series were penned for his sequence of undergraduate courses on analysis at Princeton. Stein is also noted as having trained a high number of graduate students, so shaping modern Fourier analysis. They include two Fields medalists, Terence Tao. His honors include the Steele Prize, the Schock Prize in Mathematics, the National Medal of Science. In addition, he has fellowships to National Science Foundation, Sloan Foundation, National Academy of Sciences. In 2005, Stein was awarded the Stefan Bergman prize in recognition of his contributions in complex, harmonic analysis. In 2012 he became a fellow of the American Mathematical Society. In 1959, he married a former Jewish refugee during World War II.
Elias M. Stein
–
Elias M. Stein
59.
Raoul Bott
–
Raoul Bott, ForMemRS was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. Bott is best known for his Bott periodicity theorem, the Morse -- the Borel -- Bott -- Weil theorem. He was born in the son of Margit Kovács and Rudolph Bott. His mother was of Hungarian Jewish descent; Bott was raised a Catholic by his mother and stepfather. He spent his working life in the United States. Subsequently he served in the Canadian Army in Europe during World War II. He later went at McGill University in Montreal where he studied electrical engineering. Bott then earned a Ph.D. in 1949. His thesis, titled Electrical Network Theory, was written under the direction of Richard Duffin. Afterward, Bott began teaching in Ann Arbor. He continued his study for Advanced Study in Princeton. Bott was a professor at Harvard University from 1959 to 1999. In 2005 he died in San Diego. With Richard Duffin at Carnegie Mellon, he studied existence of electronic filters corresponding to given positive-real functions. In 1949 they proved a fundamental theorem of synthesis.
Raoul Bott
–
Raoul Bott in 1986
60.
Jean-Pierre Serre
–
Jean-Pierre Serre is a French mathematician who has made contributions to algebraic topology, algebraic geometry, algebraic number theory. He was awarded the Fields Medal in 1954, the Abel Prize in 2003. He was awarded his doctorate from the Sorbonne in 1951. From 1948 to 1954 he held positions in Paris. In 1956 he was elected professor at a position he held until his retirement in 1994. Professor Josiane Heulot-Serre, was a chemist; she also was the director of the Ecole Normale Supérieure de Jeunes Filles. Their daughter is the former French diplomat, writer Claudine Monteil. The French mathematician Denis Serre is his nephew. Serre's thesis concerned the Leray -- spectral sequence associated to a fibration. Serre subsequently changed his focus. Two foundational papers by Serre were Faisceaux Algébriques Cohérents, on coherent cohomology, Géometrie Algébrique et Géométrie Analytique. Even at an early stage in his work Serre had perceived a need to construct more general and refined cohomology theories to tackle the Weil conjectures. The problem was that the cohomology of a coherent sheaf over a finite field couldn't capture as topology as singular cohomology with integer coefficients. Amongst Serre's early candidate theories of 1954–55 was one based on Witt vector coefficients. Around 1958 Serre suggested that principal bundles on algebraic varieties -- those that become trivial after pullback by a finite étale map -- are important.
Jean-Pierre Serre
–
Jean-Pierre Serre
Jean-Pierre Serre
–
Serre
61.
Vladimir Arnold
–
Vladimir Igorevich Arnold was a Soviet and Russian mathematician. Arnold was also known as a popularizer of mathematics. Through as the author of several 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. His mother was an historian. This is the Kolmogorov–Arnold representation theorem. After graduating from Moscow State University in 1959, he worked there until 1986, 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 and Lagrangian intersections were also a major motivation in the development of Floer homology. Arnold worked at Paris Dauphine University up until his death. As of 2006 he was reported to have the highest citation index among Russian scientists, h-index of 40. To his students and colleagues Arnold was known also for his sense of humour.
Vladimir Arnold
–
Vladimir Arnold in 2008
62.
Saharon Shelah
–
Saharon Shelah is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey. He was born on July 1945. He is the son of the Israeli poet and political activist Yonatan Ratosh. He received his PhD for his work on stable theories in 1969 from the Hebrew University. Shelah is married to Yael, has three children. He initially was attracted to biology, not mathematics. At the age of 15, he decided to become a mathematician, a choice cemented after reading Abraham Halevy Fraenkel's book "An Introduction to Mathematics". He was a Lecturer at Princeton University during 1969-70, then worked during 1970-71. Shelah became a professor in a position he continues to hold. He has been a Distinguished Visiting Professor at Rutgers University since 1986. According to the list of Shelah's papers, as of 2016 he had published 1095 mathematical papers including joint papers with over 220 co-authors. His main interests lie in theory in particular, in axiomatic set theory. In theory, Shelah developed theory, which led him to a solution of Morley's problem. In theory, Shelah discovered the notion of an important tool in iterated forcing arguments.
Saharon Shelah
–
Saharon Shelah in his office in Rutgers University, September 6, 2005. Photo by Andrzej Rosłanowski.
63.
John Tate
–
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 emeritus at Harvard University. He was awarded the Abel Prize in 2010. Tate was born in Minneapolis. John Tate Sr. was a professor of physics at the University of Minnesota, a longtime editor of Physical Review. Lois Beatrice Fossler, was a high school English teacher. Tate Jr. entered the doctoral program in physics at Princeton University. He later received his PhD in 1950 as a student of Emil Artin. Tate taught at Harvard before joining the University of Texas in 1990. He returned to Harvard as a professor emeritus. He currently resides in Cambridge, Massachusetts with his wife Carol. He has three daughters with his first wife Karin Tate. 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 relations with algebraic K-theory. With Jonathan Lubin, he recast local class theory by the use of formal groups, creating the Lubin -- Tate local theory of complex multiplication.
John Tate
–
John Tate
64.
Grigory Margulis
–
He was awarded a Fields Medal in 1978 and a Wolf Prize in Mathematics in 2005, becoming the seventh mathematician to receive both prizes. 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. He received his PhD from the Moscow State University starting research in ergodic theory under the supervision of Yakov Sinai. Early work with David Kazhdan produced the Kazhdan -- a basic result on discrete groups. His superrigidity theorem from 1975 clarified an area of classical conjectures amongst lattices in Lie groups. He was not permitted to travel to Helsinki to accept it in person. In 1991, Margulis accepted a professorial 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. It had been known since the 1950s that a simple-minded way of constructing subgroups of semisimple Lie groups produces examples of lattices, called arithmetic lattices. It is analogous to considering the SL of the real special linear group SL that consists of matrices with integer entries. Margulis proved that under suitable assumptions on G, any Γ in it is arithmetic, i.e. can be obtained in this way. Thus Γ is commensurable with the 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.
Grigory Margulis
–
Grigory Margulis
65.
Stephen Smale
–
Stephen Smale is an American mathematician from Flint, Michigan. His research concerns topology, mathematical economics. He was 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, earning himself A's. However, junior years were marred with mediocre grades, mostly Bs, Cs and even an F in nuclear physics. However, with some luck, Smale was accepted at the University of Michigan's mathematics department. Yet again, Smale performed poorly in his first years, earning a C average as a graduate student. It was only when Hildebrandt, threatened to kick Smale out that he began to work hard. Smale finally earned his Ph.D. under Raoul Bott. Smale began his career at the University of Chicago. In 1958, he astounded the mathematical world with a proof of a eversion. After having made great strides in topology, he then turned to the study of dynamical systems, where he made significant advances well. His first contribution is the Smale horseshoe that started significant research in dynamical systems. He also outlined a program carried out by many others.
Stephen Smale
–
Stephen Smale
66.
Hillel Furstenberg
–
He is known including number theory and Lie groups. He attended Marsha Stern Talmudical Academy and then Yeshiva University, where he concluded his BA and MSc studies in 1955. He obtained his Ph. D. under Salomon Bochner at Princeton University in 1958. After several years at the University of Minnesota he became a Professor of Mathematics at the Hebrew University of Jerusalem in 1965. He gained attention for producing an topological proof of the infinitude of prime numbers. He proved unique ergodicity of horocycle flows on compact hyperbolic Riemann surfaces in the early 1970s. In 1977, he gave an ergodic theory reformulation, subsequently proof, of Szemerédi's theorem. The Furstenberg compactification of a locally symmetric space are named after him, as is the Furstenberg -- Sárközy theorem in additive number theory. 1993 – Furstenberg received the Israel Prize, for exact sciences. 1993 – Furstenberg received the Harvey Prize from Technion. 2006/7 – He received the Wolf Prize in Mathematics. Furstenberg, Harry, N.J. Princeton University Press, 1960. Furstenberg, Harry, Recurrence in ergodic theory and combinatorial number theory, Princeton, N.J. Princeton Univ. Press, 1981. Compactification Ratner's theorems List of Israel Prize recipients O'Connor, John J.; Robertson, Edmund F. "Hillel Furstenberg", MacTutor History of Mathematics archive, University of St Andrews.
Hillel Furstenberg
–
Hillel Furstenberg in 1992 (photo by George Bergman)
67.
Pierre Deligne
–
Pierre René, Viscount Deligne is a Belgian mathematician. He is known on the Weil conjectures leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 1978 Fields Medal. He was born in Etterbeek, studied at the Université libre de Bruxelles. Deligne's also focused on topics in Hodge theory. He tested them on objects in complex geometry. He also collaborated on a new description of the moduli spaces for curves. Perhaps Deligne's most famous contribution was his proof of the Weil conjectures. This proof completed a programme largely developed by Alexander Grothendieck. As a corollary he proved the celebrated Ramanujan -- Petersson conjecture for modular forms of weight greater than one; weight one was proved with Serre. Until 1984 when he moved to the Institute for Advanced Study in Princeton, Deligne was a permanent member of the IHÉS staff. During this time he did much important outside of his work on algebraic geometry. He received a Fields Medal in 1978. This idea allows one to get around the lack of knowledge of the Hodge conjecture, for some applications. All this is part of the yoga of weights, the l-adic Galois representations.
Pierre Deligne
–
Pierre Deligne, March 2005
68.
Phillip Griffiths
–
He was a major developer in particular of the theory of variation of Hodge structure in Hodge theory and theory. He received his B.S. from his Ph.D. from Princeton University in 1962 working under Donald Spencer. Since then, he has held positions at Berkeley, Princeton, Duke University. From 1991 to 2003 he was the Director of the Institute for Advanced Study at Princeton, New Jersey. He has published on algebraic geometry, differential geometry, the geometry of partial differential equations. Griffiths serves as the Chair of the Science Initiative Group. He is co-author, with Joe Harris, of Principles of a well-regarded textbook on complex algebraic geometry. In 2008 he was awarded 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 devotion to mathematics and outstanding achievements. "On certain homogeneous complex manifolds". Proc Natl Acad Sci U S A. 48: 780–783. 1962. Doi:10.1073/pnas.48.5.780.
Phillip Griffiths
–
Phillip Griffiths in 2008 (photo from MFO)
69.
David Mumford
–
David Bryant Mumford is an American mathematician known for distinguished work in algebraic geometry, then for research into vision and pattern theory. He 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 West Sussex in England, of an English father and American mother. His father William 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 1956. He completed his Ph.D. with a thesis entitled Existence of the moduli scheme for curves of any genus. He met Erika Jentsch, at Radcliffe College. After Erika died in 1988, he married Jenifer Gordon. He and Erika had four children. Mumford's work in geometry combined geometric insights with the latest algebraic techniques. Abelian Varieties and Curves on an Algebraic Surface combined the old and new theories.
David Mumford
–
David Mumford in 2010
David Mumford
–
David Mumford in 1975
70.
Dennis Sullivan
–
Dennis Parnell Sullivan is an American mathematician. He is known for work in topology, both geometric, on dynamical systems. He is a professor at Stony Brook University. He received his B.A. in 1963 from Princeton University. His Ph.D. thesis, entitled Triangulating homotopy equivalences, 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. Wall. In homotopy theory, Sullivan put forward the radical concept that spaces could directly be localised, a hitherto applied to the algebraic constructs made from them. He founded rational theory. This area has generated further research. In 1985, he proved the No wandering theorem. The Parry–Sullivan invariant is named after him and the English mathematician Bill Parry. In 1987, he proved Thurston's conjecture about the approximation of the Riemann map together with Burton Rodin. I.H.E.S. 47: 269–331, MR 0646078 O'Connor, John J.; Robertson, Edmund F. "Dennis Sullivan", MacTutor History of Mathematics archive, University of St Andrews.
Dennis Sullivan
–
Dennis Parnell Sullivan
71.
Shing-Tung Yau
–
Shing-Tung Yau is a Hong Kong and naturalised American mathematician. He was awarded the Fields Medal in 1982. He is currently the William Caspar Graustein Professor of Mathematics at Harvard. Yau's work is mainly in geometry, especially in geometric analysis. He has been active at the interface between geometry and theoretical physics. His proof of the positive theorem in general relativity demonstrated -- sixty years after its discovery -- that Einstein's theory is consistent and stable. His proof of the Calabi conjecture allowed physicists to show, using Calabi -- Yau compactification, that theory is a viable candidate for a unified theory of nature. Calabi–Yau manifolds are part of the standard toolkit for string theorists today. Yau was born in a family of eight children. After graduating from Pui Ching Middle School, he studied mathematics from 1966 to 1969. He spent a year as a member of the Institute before joining Stony Brook University in 1972 as an assistant professor. In 1974, he became an associate professor at Stanford University. Yau has held American citizenship since 1990. Since 1987, he has been at Harvard University. He is also involved in Hong Kong and the Chinese mainland.
Shing-Tung Yau
–
Image of mathematician Shing Tung Yau
Shing-Tung Yau
72.
Michael Aschbacher
–
Michael George Aschbacher is an American mathematician best known for his work on finite groups. He was a leading figure in the completion of the classification of simple groups in the 1970s and 1980s. It later turned out that the classification was incomplete, because the case of quasithin groups had not been finished. This gap was fixed by Aschbacher and Stephen D. Smith in a pair of books comprising about 1300 pages. Aschbacher is currently the Shaler Arthur Hanisch Professor of Mathematics at the California Institute of Technology. Aschbacher received his B.S. at the California Institute of his Ph.D. at the University of Wisconsin -- Madison in 1969. He became a full professor in 1976. He was a visiting scholar for Advanced Study in 1978-79. He was elected to the National Academy of Sciences in 1990. In 1992, Aschbacher was elected a Fellow of the American Academy of Arts and Sciences. He was awarded the Rolf Schock Prize for Mathematics in 2011. In 1973, Aschbacher became a leading figure in the classification of simple groups. Aschbacher only became interested in simple groups as a postdoctorate. In particular, another leader of the classification of finite simple groups, said that Aschbacher's entrance was "dramatic." In fact, the rate of Aschbacher's results proved so astounding that other mathematicians decided to leave the field to pursue other problems.
Michael Aschbacher
–
Michael Aschbacher
73.
Michael Artin
–
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 brought up in Indiana. His parents were preeminent algebraist of the 20th century. Artin's parents had left Germany in 1937, because Michael Artin's maternal grandfather was Jewish. His work on the problem of characterising the representable functors in the category of schemes has led in local algebra. This work also has proved very influential in moduli theory. Additionally, he has made contributions to the theory of algebraic varieties. In 2002, Artin won the American Mathematical Society's annual Steele Prize for Lifetime Achievement. In 2005, he was awarded the Harvard Centennial Medal. In 2013 he won the Wolf Prize 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
–
Michael Artin (photo by George Bergman)
74.
Peter Sarnak
–
Peter Clive Sarnak is a South African-born mathematician with dual South-African and American nationalities. He is an editor of the Annals of Mathematics. He is known for his work in analytic theory. Sarnak is also on the permanent faculty at the School of Mathematics of the Institute for Advanced Study. He also sits given under the auspices of the Shaw Prize. Sarnak graduated University of the Witwatersrand and Stanford University, under the direction of Paul Cohen. Sarnak's highly cited work applied deep results in number theory with connections to combinatorics and computer science. He is the recipient of the 2014 Wolf Prize in Mathematics. He was also elected in 2002. He was awarded an honorary doctorate in 2010. He was also awarded an honorary doctorate in 2015. Sarnak, P.. "Spectral Behavior of Quasi Periodic Potentials". Commun. Math.
Peter Sarnak
–
Peter Sarnak
75.
Richard Schoen
–
Richard Melvin Schoen is an American mathematician. Born in Ohio, he received his PhD in 1977 from Stanford University. Schoen is currently an Excellence in Teaching Chair at the University of California, Irvine. His surname is pronounced "Shane," perhaps as a reflection of the regional dialect spoken by some of his German ancestors. Schoen has investigated the use of analytic techniques in global geometry. In 1979, together with Shing-Tung Yau, he proved the fundamental positive energy theorem in general relativity. In 1983, in 1984, he obtained a complete solution to the Yamabe problem on compact manifolds. This work combined new techniques with ideas developed in partial results by Thierry Aubin and Neil Trudinger. The resulting theorem asserts that any Riemannian metric on a closed manifold may be conformally rescaled as to produce a metric of constant scalar curvature. In 2007, Simon Brendle and Richard Schoen proved a fundamental result in the study of manifolds of positive sectional curvature. He has also made fundamental contributions to the theory of minimal surfaces and harmonic maps. For his work on the Yamabe problem, Schoen was awarded the Bôcher Memorial Prize in 1989. He 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.
Richard Schoen
–
Richard Schoen (photo by George Bergman)
76.
Charles Fefferman
–
Charles Louis Fefferman is an American mathematician at Princeton University. His primary field of research is mathematical analysis. Fefferman entered college by the age of 11 and had written his first scientific paper by the age of 15 in German. This made the youngest full professor ever appointed in the United States. At 24, he returned to Princeton to assume a full professorship there — a position he still holds. He won the Fields Medal in 1978 for his work in mathematical analysis. He was elected in 1979. He was appointed the Herbert Jones Professor at Princeton in 1984. Fefferman contributed several innovations that revised the study of complex analysis by finding fruitful generalisations of classical low-dimensional results. His early work included a study of the asymptotics of the Bergman kernel in C n. He has studied mathematical physics, harmonic analysis, fluid dynamics, neural networks, geometry, spectral analysis, amongst others. His wife Julie have two daughters, Nina and Lainie. She has an interest in Middle Eastern music. Nina is a computational biologist whose research is concerned to complex biological systems. Robert Fefferman, is also an accomplished mathematician and former Dean of the Physical Sciences Division at the University of Chicago.
Charles Fefferman
–
Charles Fefferman
77.
Virtual International Authority File
–
The Virtual International Authority File is an international authority file. It operated by the Online Computer Library Center. The project was initiated by the US Library of Congress. The aim is to link the national authority files to a virtual authority file. In this file, identical records from the different sets are linked together. The data are available for research and data exchange and sharing. Reciprocal updating uses the Open Archives Initiative protocol. The file numbers are incorporated into Wikidata. VIAF's clustering algorithm is run every month. Integrated Authority File International Standard Name Identifier Wikipedia's authority control template for articles Official website
Virtual International Authority File
–
Screenshot 2012
78.
Integrated Authority File
–
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 increasingly also by archives and museums. The GND is managed 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 sub-classes, useful in library classification, 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
–
GND screenshot
79.
Ennio de Giorgi
–
Ennio De Giorgi was an Italian mathematician, member of the House of Giorgi, who worked on partial differential equations and the foundations of mathematics. He solved Bernstein's problem about minimal surfaces. He solved the 19th Hilbert problem on the regularity of solutions of partial differential equations. "analytical expression of the perimeter of a set" is the first note published by De Giorgi on his approach to Caccioppoli sets. De Giorgi, Ennio; Colombini, Ferruccio; Piccinini, Livio, Frontiere orientate di misura minima e questioni collegate, Quaderni, Pisa: Edizioni della Normale, p. 180, MR 493669, Zbl 0296.49031. "A new kind in the calculus of variations" is the first paper about SBV functions and related variational problems. Michele, Ennio De Giorgi, retrieved 21 May 2011. O'Connor, John J.; Robertson, Edmund F. "Ennio de Giorgi", MacTutor History of Mathematics archive, University of St Andrews. 30 November 2006, retrieved 21 May 2011. Workshop "The Mathematics of Pisa: Scuola Normale Superiore, 24 -- 27 October 2001, retrieved 21 May 2011.
Ennio de Giorgi
–
Ennio De Giorgi