University of Oxford
The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the world's second-oldest university in continuous operation, it grew from 1167 when Henry II banned English students from attending the University of Paris. After disputes between students and Oxford townsfolk in 1209, some academics fled north-east to Cambridge where they established what became the University of Cambridge; the two'ancient universities' are jointly called'Oxbridge'. The history and influence of the University of Oxford has made it one of the most prestigious universities in the world; the university is made up of 38 constituent colleges, a range of academic departments, which are organised into four divisions. All the colleges are self-governing institutions within the university, each controlling its own membership and with its own internal structure and activities, it does not have a main campus, its buildings and facilities are scattered throughout the city centre.
Undergraduate teaching at Oxford is organised around weekly tutorials at the colleges and halls, supported by classes, lectures and laboratory work provided by university faculties and departments. It operates the world's oldest university museum, as well as the largest university press in the world and the largest academic library system nationwide. In the fiscal year ending 31 July 2018, the university had a total income of £2.237 billion, of which £579.1 million was from research grants and contracts. The university is ranked first globally by the Times Higher Education World University Rankings as of 2019 and is ranked as among the world's top ten universities, it is ranked second in all major national league tables, behind Cambridge. Oxford has educated many notable alumni, including 27 prime ministers of the United Kingdom and many heads of state and government around the world; as of 2019, 69 Nobel Prize winners, 3 Fields Medalists, 6 Turing Award winners have studied, worked, or held visiting fellowships at the University of Oxford, while its alumni have won 160 Olympic medals.
Oxford is the home of numerous scholarships, including the Rhodes Scholarship, one of the oldest international graduate scholarship programmes. The University of Oxford has no known foundation date. Teaching at Oxford existed in some form as early as 1096, but it is unclear when a university came into being, it grew from 1167 when English students returned from the University of Paris. The historian Gerald of Wales lectured to such scholars in 1188 and the first known foreign scholar, Emo of Friesland, arrived in 1190; the head of the university had the title of chancellor from at least 1201, the masters were recognised as a universitas or corporation in 1231. The university was granted a royal charter in 1248 during the reign of King Henry III. After disputes between students and Oxford townsfolk in 1209, some academics fled from the violence to Cambridge forming the University of Cambridge; the students associated together on the basis of geographical origins, into two'nations', representing the North and the South.
In centuries, geographical origins continued to influence many students' affiliations when membership of a college or hall became customary in Oxford. In addition, members of many religious orders, including Dominicans, Franciscans and Augustinians, settled in Oxford in the mid-13th century, gained influence and maintained houses or halls for students. At about the same time, private benefactors established colleges as self-contained scholarly communities. Among the earliest such founders were William of Durham, who in 1249 endowed University College, John Balliol, father of a future King of Scots. Another founder, Walter de Merton, a Lord Chancellor of England and afterwards Bishop of Rochester, devised a series of regulations for college life. Thereafter, an increasing number of students lived in colleges rather than in halls and religious houses. In 1333–34, an attempt by some dissatisfied Oxford scholars to found a new university at Stamford, was blocked by the universities of Oxford and Cambridge petitioning King Edward III.
Thereafter, until the 1820s, no new universities were allowed to be founded in England in London. The new learning of the Renaissance influenced Oxford from the late 15th century onwards. Among university scholars of the period were William Grocyn, who contributed to the revival of Greek language studies, John Colet, the noted biblical scholar. With the English Reformation and the breaking of communion with the Roman Catholic Church, recusant scholars from Oxford fled to continental Europe, settling at the University of Douai; the method of teaching at Oxford was transformed from the medieval scholastic method to Renaissance education, although institutions associated with the university suffered losses of land and revenues. As a centre of learning and scholarship, Oxford's reputation declined in the Age of Enlightenment. In 1636 William Laud, the chancellor and Archbishop of Canterbury, codified the university's statutes. These, to a large extent, remained its gove
Paul Friedrich Wolfskehl, was a physician with an interest in mathematics. He bequeathed 100,000 marks to the first person to prove Fermat's Last Theorem, he was the younger of two sons of Joseph Carl Theodor Wolfskehl. His older brother, the jurist Wilhelm Otto Wolfskehl, took over the family bank after the death of his father. Paul became a doctor of medicine. At about this time, he began to suffer from multiple sclerosis, which forced him to pursue another career, he chose mathematics. There are a number of theories concerning the prize's origin; the most romantic is that he was spurned by a young lady and decided to commit suicide, but was distracted by what he thought was an error in a paper by Ernst Kummer, who had detected a flaw in Augustin Cauchy's attempted proof of Fermat's famous problem. This rekindled his will to live and, in gratitude, he established the prize; this story was traced by Philip Davis and William Chinn in their 1969 book 3.1416 and All That to renowned mathematician Alexander Ostrowski, who heard it from another, unidentified source.
Another, more prosaic story claims that Wolfskehl wanted to leave as little as possible to his shrewish wife. Yet another story, told in "The man who loved only numbers" by Paul Hoffman, tells that Wolfskehl missed his supposed suicide time because he was in the library studying the Theorem. Upon realizing that, he concluded that the contemplation of mathematics was more rewarding than a beautiful woman so he decided not to kill himself, he bankrolled the Theorem because it "saved his life". On June 27, 1997, the prize was won by Andrew Wiles. By due in part to the hyperinflation Germany suffered after the end of World War I, the award had dwindled to £30,000; the play From Abstraction by Robert Thorogood is based on the life of Paul Wolfskehl. It was broadcast on BBC Radio 4 on 1 November 2006 and 29 August 2008. Andrew Beal, a Dallas banker who has offered $1,000,000 for a proof or disproof of Beal's conjecture Wiles' proof of Fermat's Last Theorem Millennium Prize Problems Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed.
New York: Dover, pp. 69–73, 1987. Barner, K. "Paul Wolfskehl and the Wolfskehl Prize." Not. Amer. Math. Soc. 44, 1294-1303, 1997. Hoffman, P; the Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth, New York: Hyperion, pp. 193–199, 1998. Details about Wolfskehl from Simon Singh, author of the book Fermat's Last Theorem
The Abel Prize is a Norwegian prize awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after Norwegian mathematician Niels Henrik Abel and directly modeled after the Nobel Prizes, it comes with a monetary award of 6 million Norwegian Kroner. The Abel Prize's history dates back to 1899, when its establishment was proposed by the Norwegian mathematician Sophus Lie when he learned that Alfred Nobel's plans for annual prizes would not include a prize in mathematics. In 1902 King Oscar II of Sweden and Norway indicated his willingness to finance a mathematics prize to complement the Nobel Prizes, but the establishment of the prize was prevented by the dissolution of the union between Norway and Sweden in 1905, it took a century before the prize was established by the Government of Norway in 2001, it was intended "to give the mathematicians their own equivalent of a Nobel Prize." The laureates are selected by the Abel Committee, the members of which are appointed by the Norwegian Academy of Science and Letters.
The award ceremony takes place in the Aula of the University of Oslo, where the Nobel Peace Prize was awarded between 1947 and 1989. The Abel Prize board has established an Abel symposium, administered by the Norwegian Mathematical Society; the prize was first proposed in 1899, to be part of the celebration of the 100th anniversary of Niels Henrik Abel's birth in 1802. Shortly before his death in 1899, the Norwegian mathematician Sophus Lie proposed establishing an Abel Prize when he learned that Alfred Nobel's plans for annual prizes would not include a prize in mathematics. King Oscar II was willing to finance a mathematics prize in 1902, the mathematicians Ludwig Sylow and Carl Størmer drew up statutes and rules for the proposed prize. However, Lie's influence waned after his death, the dissolution of the union between Sweden and Norway in 1905 ended the first attempt to create an Abel Prize. After interest in the concept of the prize had risen in 2001, a working group was formed to develop a proposal, presented to the Prime Minister of Norway in May.
In August 2001, the Norwegian government announced that the prize would be awarded beginning in 2002, the two-hundredth anniversary of Abel's birth. Atle Selberg received an honorary Abel Prize in 2002, but the first actual Abel Prize was awarded in 2003. A book series presenting Abel Prize laureates and their research was commenced in 2010; the first two volumes cover 2008 -- 2012 respectively. In 2019 Karen Uhlenbeck became the first woman to win the Abel Prize, with the award committee citing “the fundamental impact of her work on analysis and mathematical physics. Anyone may submit a nomination for the Abel Prize, self-nominations are not permitted; the nominee must be alive. The Norwegian Academy of Science and Letters declares the winner of the Abel Prize each March after recommendation by the Abel Committee, which consists of five leading mathematicians. Both Norwegians and non-Norwegians may serve on the Committee, they are elected by the Norwegian Academy of Science and Letters and nominated by the International Mathematical Union and the European Mathematical Society.
The committee is of 2018 chaired by Norwegian mathematician Hans Munthe-Kaas, was before that, headed by Professor John Rognes. The Norwegian Government gave the prize an initial funding of NOK 200 million in 2001; the funding came from the Abel foundation, but today the prize is financed directly through the national budget. The funding is controlled by the Board, which consists of members elected by the Norwegian Academy of Science and Letters; the current leader of the Board is John Grue. List of prizes known as the Nobel of a field List of mathematics prizes Official website Official website of the Abel Symposium Barile and Weisstein, Eric W. "Abel Prize". MathWorld. CS1 maint: Multiple names: authors list
A Regius Professor is a university professor with royal patronage or appointment. They are a unique feature of academia in the British Isles; the first Regius Professorship was in the field of medicine, founded by the Scottish King James IV at the University of Aberdeen in 1497. Regius chairs have since been instituted in various universities, in disciplines judged to be fundamental and for which there is a continuing and significant need; each was established by an English, Scottish, or British monarch, following proper advertisement and interview through the offices of the university and the national government, the current monarch still appoints the professor. This royal imprimatur, the relative rarity of these professorships, means a Regius chair is prestigious and sought-after. Regius Professors are traditionally addressed as "Regius" and not "Professor"; the University of Glasgow has the highest number of extant Regius chairs, at thirteen. Traditionally, Regius Chairs only existed in the ancient universities of the British Isles.
In October 2012 it was announced that Queen Elizabeth II would create up to six new Regius Professorships, to be announced in early 2013, to mark her Diamond Jubilee. In January 2013 the full list was announced, comprising twelve new chairs the largest number created in one year, more than created in most centuries. In July 2015 it was announced that further Regius Professorships would be created to mark the Queen's 90th birthday. Regius Professor of Anatomy Regius Professor of Botany Regius Professor of English Literature Regius Professor of Greek Regius Professor of Humanity Regius Professor of Classics Regius Professor of Logic Regius Professor of Mathematics Regius Professor of Medicine Regius Professor of Materia Medica Regius Professor of Moral Philosophy Regius Professor of Natural History Regius Professor of Obstetrics and Gynaecology Regius Professor of Midwifery Regius Professor of Physiology Regius Professor of Surgery Regius Professor of Pharmacy Regius Professor of Chemistry Regius Professor of Botany Regius Professor of Civil Law Regius Professor of Divinity Regius Professor of Engineering Regius Professor of Greek Regius Professor of Hebrew Regius Professor of History Regius Professor of Physic Regius Professor of Physic Regius Professor of Laws Regius Professor of Greek Regius Professor of Surgery Regius Professor of Life Sciences Regius Professor of Public Law and the Law of Nature and Nations Regius Professor of Rhetoric and English Literature Regius Professor of Astronomy Regius Professor of Clinical Surgery Regius Professor of Medical Science Regius Professor of Forensic Medicine Regius Professor of Sanskrit Regius Professor of Engineering Regius Professor of Geology Regius Professor of Political Science Regius Professor of Medicine and Therapeutics Regius Professor of Materia Medica Regius Professor of Law Regius Professor of Anatomy Regius Professor of Astronomy Regius Professor of Zoology Regius Professor of Obstetrics and Gynaecology Regius Professor of Surgery Regius Professor of Chemistry Regius Professor of Botany Regius Professor of Forensic Medicine Regius Professor of Physiology Regius Professor of Civil Engineering and Mechanics Regius Professor of English Language and Literature Regius Professor of Ecclesiastical History Regius Professor of Precision Medicine Regius Professor of Chemistry Regius Professor of Cancer Research Regius Professor of Psychiatry Regius Professor of Economics Regius Professor of Music Regius Professor of Engineering Regius Professor of Infectious Disease Regius Professor of Physics Regius Professor of Materials Regius Professor of Ageing Regius Professor of Open Education Regius Professor of Civil Law Regius Professor of Divinity Regius Professor of Moral and Pastoral Theology Regius Professor of Ecclesiastical History Regius Professor of Hebrew Regius Professor of Medicine Regius Professor of Greek Regius Professor of Modern History Regius Professor of Mathematics Regius Professor of Electronics & Computer Engineering Regius Professor of Meteorology and Climate Science Regius Professor of Mathematics Regius Professor of Computer Science Regius Professorship in Ocean Sciences Regius Professor of Electronic Engineering Regius Professor of Mathematics Regius Professor of Manufacturing
Richard Taylor (mathematician)
Richard Lawrence Taylor is a British and American mathematician working in the field of number theory. He is a professor of mathematics at Stanford University and the Institute for Advanced Study. Taylor received the 2014 Breakthrough Prize in Mathematics "for numerous breakthrough results in the theory of automorphic forms, including the Taniyama–Weil conjecture, the local Langlands conjecture for general linear groups, the Sato–Tate conjecture." He received the 2007 Shaw Prize in Mathematical Sciences for his work on the Langlands program with Robert Langlands. He received his BA from Cambridge. During his time at Cambridge, he was president of The Archimedeans in 1981 and 1982, following the impeachment of his predecessor, he earned his PhD from Princeton University in 1988. From 1995 to 1996 he held the Savilian chair of geometry at Oxford University and Fellow of New College and became the Herchel Smith Professor of Mathematics at Harvard University, he holds Robert and Luisa Fernholz Professorship at the Institute for Advanced Study.
He received the Whitehead Prize in 1990, the Fermat Prize, the Ostrowski Prize in 2001, the Cole Prize of the American Mathematical Society in 2002, the Shaw Prize for Mathematics in 2007. He was elected a Fellow of the Royal Society in 1995. In 2012 he became a fellow of the American Mathematical Society. In 2015 he was inducted into the National Academy of Sciences, he was elected to the American Philosophical Society in 2018. One of the two papers containing the published proof of Fermat's Last Theorem is a joint work of Taylor and Andrew Wiles. In subsequent work, Taylor proved the local Langlands conjectures for GL over a number field. A simpler proof was suggested at the same time by Guy Henniart, ten years by Peter Scholze. Taylor, together with Christophe Breuil, Brian Conrad and Fred Diamond, completed the proof of the Taniyama–Shimura conjecture, by performing quite heavy technical computations in the case of additive reduction. In 2008, following the ideas of Michael Harris and building on his joint work with Laurent Clozel, Michael Harris, Nick Shepherd-Barron, announced a proof of the Sato–Tate conjecture, for elliptic curves with non-integral j-invariant.
This partial proof of the Sato–Tate conjecture uses Wiles's theorem about modularity of semistable elliptic curves. Taylor is the son of British physicist John C. Taylor, he is married, has two children. His home page at the Institute for Advanced Study Richard Taylor at the Mathematics Genealogy Project Autobiography upon Shaw Prize acceptance
Fermat's Last Theorem
In number theory Fermat's Last Theorem states that no three positive integers a, b, c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have an infinite number of solutions; the proposition was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica. However, there were first doubts about it since the publication was done by his son without his consent, after Fermat's death. After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles, formally published in 1995, it proved much of the modularity theorem and opened up entire new approaches to numerous other problems and mathematically powerful modularity lifting techniques. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century, it is among the most notable theorems in the history of mathematics and prior to its proof was in the Guinness Book of World Records as the "most difficult mathematical problem" in part because the theorem has the largest number of unsuccessful proofs.
The Pythagorean equation, x2 + y2 = z2, has an infinite number of positive integer solutions for x, y, z. Around 1637, Fermat wrote in the margin of a book that the more general equation an + bn = cn had no solutions in positive integers if n is an integer greater than 2. Although he claimed to have a general proof of his conjecture, Fermat left no details of his proof, no proof by him has been found, his claim was discovered some 30 years after his death. This claim, which came to be known as Fermat's Last Theorem, stood unsolved for the next three and a half centuries; the claim became one of the most notable unsolved problems of mathematics. Attempts to prove it prompted substantial development in number theory, over time Fermat's Last Theorem gained prominence as an unsolved problem in mathematics; the special case n = 4 - proved by Fermat himself - is sufficient to establish that if the theorem is false for some exponent n, not a prime number, it must be false for some smaller n, so only prime values of n need further investigation.
Over the next two centuries, the conjecture was proved for only the primes 3, 5, 7, although Sophie Germain innovated and proved an approach, relevant to an entire class of primes. In the mid-19th century, Ernst Kummer extended this and proved the theorem for all regular primes, leaving irregular primes to be analyzed individually. Building on Kummer's work and using sophisticated computer studies, other mathematicians were able to extend the proof to cover all prime exponents up to four million, but a proof for all exponents was inaccessible. Separately, around 1955, Japanese mathematicians Goro Shimura and Yutaka Taniyama suspected a link might exist between elliptic curves and modular forms, two different areas of mathematics. Known at the time as the Taniyama–Shimura–Weil conjecture, as the modularity theorem, it stood on its own, with no apparent connection to Fermat's Last Theorem, it was seen as significant and important in its own right, but was considered inaccessible to proof. In 1984, Gerhard Frey noticed an apparent link between these two unrelated and unsolved problems.
An outline suggesting this could be proved was given by Frey. The full proof that the two problems were linked was accomplished in 1986 by Ken Ribet, building on a partial proof by Jean-Pierre Serre, who proved all but one part known as the "epsilon conjecture"; these papers by Frey and Ribet showed that if the Modularity Theorem could be proven for at least the semi-stable class of elliptic curves, a proof of Fermat's Last Theorem would follow automatically. The connection is described below: any solution that could contradict Fermat's Last Theorem could be used to contradict the Modularity Theorem. So if the modularity theorem were found to be true by definition no solution contradicting Fermat's Last Theorem could exist, which would therefore have to be true as well. Although both problems were daunting and considered to be "completely inaccessible" to proof at the time, this was the first suggestion of a route by which Fermat's Last Theorem could be extended and proved for all numbers, not just some numbers.
Important for researchers choosing a research topic was the fact that unlike Fermat's Last Theorem the Modularity Theorem was a major active research area for which a proof was desired and not just a historical oddity, so time spent working on it could be justified professionally. However, general opinion was that this showed the impracticality of proving the Taniyama–Shimura conjecture. Mathematician John Coates' quoted reaction was a common one: "I myself was sceptical that the beautiful link between Fermat’s Last Theorem and the Taniyama–Shimura conjecture would lead to anything, because I must confess I did not think that the Taniyama–Shimura conjecture was accessible to proof. Beautiful though this problem was, it seemed impossible to prove. I must confess I thought I wouldn’t see it proved in my lifetime." On hearing that Ribet had proven Frey's li
Princeton University Department of Mathematics
The Princeton University Department of Mathematics is an academic department at Princeton University. Founded in 1760, the department has trained some of the world's most renowned and internationally recognized scholars of mathematics. Notable individuals affiliated with the department include John Nash, Senior Research Mathematician and winner of the 1994 Nobel Prize. Since 2012, the chair of the department has been David Gabai, awarded the Oswald Veblen Prize in Geometry in 2004 and was elected into the United States National Academy of Sciences in 2011; the first courses in mathematics were offered in 1760 when undergraduates enrolled in classes such as algebra, trigonometry and conic sections. Walter Minto was one of the earliest teachers of mathematics beginning in 1787. By the beginning of the twentieth century, the department became "one of the world's great centers of mathematical teaching and research." President Woodrow Wilson appointed Henry Burchard Fine as dean of the faculty in 1903 and as the first chairman of the Department of Mathematics in 1905.
The university invited a number of leading mathematics to conduct research at Princeton including Luther P. Eisenhart, Solomon Lefschetz, James W. Alexander II, James Jeans, J. H. M. Wedderburn, George David Birkhoff, Oswald Veblen. In 1928, Princeton created the first research professorship in mathematics in the United States. Research in the field of mathematics continued to thrive when the Institute for Advanced Study was founded in Princeton, New Jersey in 1930. Although the IAS and Princeton remain separate, they have continued to maintain close relations and collaborative projects thanks to their proximity to one another. Students and faculty are able to attend IAS seminar series; the political situation in Europe caused an increased number of immigrants to enter the United States beginning in the 1930s. These scholars included Ralph Fox, Norman Steenrod, Emil Artin, John Tukey, Valentine Bargmann, Arthur Wightman, William Feller, Donald C. Spencer. Others worked with both the School of Mathematics and the Institute for Advanced Study to immigrate to the United States, including Albert Einstein, Hermann Weyl, Oskar Morgenstern, John von Neumann, Eugene Wigner, Paul Erdős.
Einstein, although never holding a position at the university, delivered a series of lectures on his theory of relativity in 1921 and continued to hold an office within the department of mathematics' building, Fine Hall. In 1968, the department moved to Fine Hall, named in honor of the first faculty teacher and Princeton's first dean of science, Henry Burchard Fine; the building features three stories of graduate student offices. Another ten floors contain faculty offices, a seminar room, a professors' lounge. Fine Hall has been described as the "anchor of mathematics" as it was the home of the School of Mathematics, it was that closer collaboration between the Institute for Advanced Study and Princeton University strengthened. Fine Hall connects to Jadwin Hall, home to additional classroom and academic facilities; the architects of Fine and Jadwin Hall won the Award Award of Merit in the Architectural Design Award Program in 1966. The Albert Einstein Memorial Lecture is held annually at Princeton on or around Einstein's birthday on March 14.
The lecture is open to the public. The 24th Annual Albert Einstein Memorial Lecture was dedicated to "Scientific Inquiry and Growth", it featured Nobel Prize Winner Jack Szostak giving a presentation on "The Origin of Life". The department runs the Program in Applied and Computational Mathematics, an interdisciplinary and interdepartmental program for scholars interested in the application of mathematics to other fields; the PACM faculty consists of 15 core members, in addition to an executive committee, 34 graduate students, 30 undergraduate certificate students. The PACM has been at the forefront of research within the field of high-energy physics, notably leading the NSF-funded Institute for Research and Innovation in Software for High Energy Physics, a coalition of 17 research universities that develops computing software for the Large Hadron Collider at CERN in Geneva, Switzerland; the department co-publishes a bimonthly academic journal, the Annals of Mathematics, with the Institute for Advanced Study.
Founded in 1884, the Annals is recognized as one of the top journals in mathematics. The Women and Mathematics program is co-directed by the department and the IAS; the initiative aims to "recruit and retain more women in mathematics" through its lectures and mentorship program. Sun-Yung Alice Chang, the previous chairperson and first female chair, has taken a personal interest in attracting more women into the field. A number of individuals affiliated with the department have won international prizes for their research in mathematics, including the Fields Medal, the Wolf Prize, the Henri Poincaré Prize, the Shaw Prize, Goldwater Scholars, the Fulbright Award. At the undergraduate level 70–75 students concentrate in the field. Students complete required courses in real analysis, complex analysis, algebra and topology. Like all A. B. candidates at Princeton, students are required to complete a senior thesis based on original and independent research. Students are permitted to study abroad for a semester or an academic year at one of several internationally recognized institutions including the University of Oxford, the University of Cambridge, Bonn University, the University of Moscow, the University of Budapest.
The department encourages tho