Sir Andrew John Wiles is an English mathematician and a Royal Society Research Professor at the University of Oxford, specializing in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal by the Royal Society. He was appointed Knight Commander of the Order of the British Empire in 2000, and in 2018, was appointed the first Regius Professor of Mathematics at Oxford. Wiles is also a 1997 MacArthur Fellow.
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's Last Theorem, have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.
Diophantus of Alexandria was an Alexandrian mathematician, who was the author of a series of books called Arithmetica, many of which are now lost. His texts deal with solving algebraic equations. Diophantine equations and Diophantine approximations are important areas of mathematical research. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality. This term was rendered as adaequalitas in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought.
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers or defined as generalizations of the integers.
Marie-Sophie Germain was a French mathematician, physicist, and philosopher. Despite initial opposition from her parents and difficulties presented by society, she gained education from books in her father's library, including ones by Euler, and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss. One of the pioneers of elasticity theory, she won the grand prize from the Paris Academy of Sciences for her essay on the subject. Her work on Fermat's Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against her sex, she was unable to make a career out of mathematics, but she worked independently throughout her life. Before her death, Gauss had recommended that she be awarded an honorary degree, but that never occurred. On 27 June 1831, she died from breast cancer. At the centenary of her life, a street and a girls’ school were named after her. The Academy of Sciences established the Sophie Germain Prize in her honor.
Luitzen Egbertus Jan Brouwer, usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and complex analysis. Regarded as one of the greatest mathematicians of the 20th century, he is known as the founder of modern topology, particularly for establishing his fixed-point theorem and the topological invariance of dimension.
Paul Richard Halmos was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis. He was also recognized as a great mathematical expositor. He has been described as one of The Martians.
Mathematical beauty is the aesthetic pleasure typically derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians often express this pleasure by describing mathematics as beautiful. They might also describe mathematics as an art form or, at a minimum, as a creative activity. Comparisons are often made with music and poetry.
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and 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 infinitely many solutions.
The Princeton Companion to Mathematics is a book providing an extensive overview of mathematics that was published in 2008 by Princeton University Press. Edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, it has been noted for the high caliber of its contributors. The book was the 2011 winner of the Euler Book Prize of the Mathematical Association of America, given annually to "an outstanding book about mathematics".
Chike Obi was a Nigerian politician, mathematician and professor.
Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were almost universally considered inaccessible to prove by contemporaneous mathematicians, meaning that they were believed to be impossible to prove using current knowledge.
Harold Mortimer Edwards, Jr. was an American mathematician working in number theory, algebra, and the history and philosophy of mathematics.
Kenneth Alan Ribet is an American mathematician working in algebraic number theory and algebraic geometry. He is known for the Herbrand–Ribet theorem and Ribet's theorem, which were key ingredients in the proof of Fermat's Last Theorem, as well as for his service as President of the American Mathematical Society from 2017 to 2019. He is currently a professor of mathematics at the University of California, Berkeley.
This is a timeline of women in mathematics.
Jacqueline Anne "Jackie" Stedall was a British mathematics historian. She wrote nine books, and appeared on radio on BBC Radio 4's In Our Time programme.
Closing the Gap: The Quest to Understand Prime Numbers is a book on prime numbers and prime gaps by Vicky Neale, published in 2017 by the Oxford University Press (ISBN 9780198788287). The Basic Library List Committee of the Mathematical Association of America has suggested that it be included in undergraduate mathematics libraries.
Primality Testing for Beginners is an undergraduate-level mathematics book on primality tests, methods for testing whether a given number is a prime number, centered on the AKS primality test, the first method to solve this problem in polynomial time. It was written by Lasse Rempe-Gillen and Rebecca Waldecker, and originally published in German as Primzahltests für Einsteiger: Zahlentheorie, Algorithmik, Kryptographie. It was translated into English as Primality Testing for Beginners and published in 2014 by the American Mathematical Society, as volume 70 of their Student Mathematical Library book series. A second German-language edition was publisher by Springer in 2016.
Fermat's Last Tango is a 2000 off-Broadway musical about the proof of Fermat's Last Theorem, written by husband and wife Joshua Rosenblum and Joanne Sydney Lessner. The musical presents a fictionalized version of the real life story of Andrew Wiles, and has been praised for the accuracy of the mathematical content. The original production at the York Theatre received mixed reviews, but the musical was well received by mathematical audiences. A video of the original production has been distributed by the Clay Mathematics Institute and shown at several mathematical conferences and similar occasions. The musical has also been translated into Portuguese.
