- Robert Langlands
Robert Phelan Langlands (born October 6, 1936 in New Westminster, British Columbia, Canada) is one of the most significant mathematicians of the 20th century, with profound insights in number theory and representation theory. Langlands attended the University of British Columbia as an undergraduate and received his PhD from Yale University in 1960. During the early 1960s he developed the general theory of Eisenstein series for discrete groups, …
- Paul Vojta
Paul Vojta is an American mathematician, known for his work in number theory on diophantine geometry and diophantine approximation. In formulating a number of striking conjectures, he pointed out the possible existence of parallels between the Nevanlinna theory of complex analysis, and diophantine analysis. This was a novel contribution to the circle of ideas around the Mordell conjecture and abc conjecture, …
- Andrzej Schinzel
Andrzej Schinzel is a Polish mathematician, studying mainly number theory. He is a professor at the Institute of Mathematics of the Polish Academy of Sciences (IM PAN). A conjecture of his on the prime values of polynomials, known as Schinzel's hypothesis H, has attracted attention from other number theorists. Schinzel received his Ph.D. in 1960 from Warsaw University.
- Siemion Fajtlowicz
Siemion Fajtlowicz is a Polish mathematician, currently a professor at the University of Houston. He is known for developing the conjecture-making computer program Graffiti. Fajtlowicz received his Ph.D. in 1967 from the Polish Academy of Sciences.
- David Masser
David William Masser is Professor of Mathematics at the University of Basel, in Basel, Switzerland. He obtained his PhD from Cambridge University in 1974 on the topic of "Elliptic Functions and Transcendence". Before his appointment at the Mathematics Institute in Basel, Masser taught at the University of Michigan. He is known for his work in number theory, and was elected to the Royal Society in 2005.
- Rami Grossberg
Rami Grossberg is an associate professor of mathematics at Carnegie Mellon University and a leading researcher in model theory. Grossberg's recent work has revolved around the classification theory of non-elementary classes, …
- Stephen Schanuel
Stephen Schanuel is an American mathematician working in the fields of abstract algebra and number theory, more specifically category theory and measure theory. While he was a graduate student at University of Chicago, he discovered Schanuel's Lemma, an essential lemma in homological algebra. Schanuel received his Ph.D. in mathematics from Columbia University in 1963, under the supervision of Serge Lang.
- Dimitrie Pompeiu
Dimitrie Pompeiu was a well-known Romanian mathematician.
- Stephen Smale
Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan, and winner of the Fields Medal in 1966. He entered the University of Michigan in 1948. Initially, Smale was a good student, placing into an honors calculus sequence taught by Bob Thrall and earning himself A's. However, his sophomore and junior years were marred with mediocre grades, mostly Bs, Cs and even an F in nuclear physics.
- Michael Freedman
Michael Hartley Freedman is a mathematician at Microsoft Research. In 1986, he was awarded a Fields Medal for his work on the Poincaré conjecture, one of the most famous problems of the 20th century. The Poincaré conjecture asserts that a simply connected closed 3-dimensional manifold is a 3-dimensional sphere.
- Andrew Casson
Andrew John Casson FRS (born 1943) is a British mathematician, an expert on geometric topology and currently the chair of the Department of Mathematics at Yale University in the United States. Casson's Ph.D. advisor at the University of Liverpool was C. T. C. Wall, but he never completed his Ph.D. What would have been his Ph.D. thesis became his fellowship dissertation as a research fellow at Trinity College, Cambridge, …
- Valentin Poénaru
Valentin Poénaru is a Professor of Mathematics at Université de Paris-Sud. He specializes in low-dimensional topology. Born in Romania, he did his undergraduate studies at the University of Bucharest. In 1962, he was an invited speaker at the International Congress of Mathematicians in Stockholm, Sweden. While at the congress, he defected, subsequently leaving for France. He defended his Thèse d'État at the University of Paris on March 23, 1963.
- Christos Papakyriakopoulos
Christos Dimitriou Papakyriakopoulos, commonly known as "Papa" was a Greek mathematician specializing in geometric topology. He worked in isolation from most of the mathematical community until 1948, when he was invited by Ralph Fox to come as his guest at the Princeton mathematics department. Fox had been impressed by a letter from Papakyriakoupolos which purported to prove Dehn's lemma. The proof, as it turned out was faulty, …
- Martin Dunwoody
Professor Martin J. Dunwoody is professor of mathematics at the University of Southampton, England. Dunwoody is working on geometric group theory and low dimensional topology. He received some public attention as he claimed to have a proof for one of the Millennium Prize Problems, the Poincaré conjecture, on April 7 2002, but he had to admit a gap in the proof five days later.
- Henri Poincaré
Jules Henri Poincaré was one of France's greatest mathematicians and theoretical physicists, and a philosopher of science. Poincaré is often described as a polymath, and in mathematics as 'The Last Universalist', since he excelled in all fields of the discipline as it existed during his lifetime. As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics.
- Richard Hamilton
Richard Streit Hamilton is professor of mathematics at Columbia University. He received his Ph.D. in 1966 from Princeton University. Robert Gunning supervised his thesis. Hamilton has taught at UC Irvine, UC San Diego, and Cornell University. Hamilton is best known for having invented the Ricci flow, which Grigori Perelman employed in his proof of the Thurston geometrization conjecture and the Poincaré conjecture.
- Bruce Kleiner
Bruce Kleiner is an American mathematician, working in differential geometry and topology and geometric group theory. He received his Ph.D. in 1990 from the University of California, Berkeley. His advisor was Wu-Yi Hsiang. He is now Professor of Mathematics at Yale University. Kleiner is currently working on Ricci flow.
- Huai-Dong Cao
Huai-Dong Cao is A. Everett Pitcher Professor of Mathematics in Lehigh University. He collaborated with Xi-Ping Zhu of Zhongshan University in verifying Grigori Perelman's proof of the Poincaré conjecture. The Cao-Zhu team is one of three teams formed for this purpose.
- Grigori Perelman
Grigori Yakovlevich Perelman, born 13 June 1966 in Leningrad, USSR (now St. Petersburg, Russia), sometimes known as Grisha Perelman, is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology. In particular, he has proved Thurston's geometrization conjecture. This solves in the affirmative the famous Poincaré conjecture, …
- John Edensor Littlewood
John Edensor Littlewood (9 June 1885 - 6 September 1977) was a British mathematician, best known for his long collaboration with G. H. Hardy
- Richard Arenstorf
Richard F. Arenstorf is an American mathematician who worked at NASA, where he received the NASA Exceptional Achievement Medal in 1966. Arenstorf retired as a full professor from Vanderbilt University. At Vanderbilt he specialized in celestial mechanics and analytic number theory. He provided potential proofs of the twin prime conjecture and the Hardy-Littlewood conjecture in May 2004. After finding an error in Lemma 8, however, he withdrew his paper in June 2004.
- Daniel Goldston
Daniel Alan Goldston is an American mathematician who specializes in number theory. He is currently a professor of mathematics at San Jose State University. Goldston is best known for the following result that he, János Pintz, and Cem Yildirim proved in 2005 : :<math>liminf_{n oinftyfrac{p_{n+1}-p_n}{log p_n}=0</math> where <math>p_n </math> denotes the nth prime number.
- Helmut Maier
Helmut Maier is an American mathematician who made significant progress in the study of Twin prime conjecture. His Erdős number is 1.
- Michel Balazard
Michel Balazard is a French mathematician. On June 3, 2004, he pointed out a flaw in a proposed proof of the Twin prime conjecture submitted by Richard Arenstorf, namely that lemma 8 on page 35 is false. His Erdős number is 2.
- Alphonse de Polignac
Alphonse de Polignac (1817 - 1890) was a French mathematician. In 1849 he made Polignac's conjecture: :For every natural number "k", there are infinitely many prime gaps of size 2"k". The case "k" = 1 is the twin prime conjecture.
- Peter Swinnerton-Dyer
Sir Henry Peter Francis Swinnerton-Dyer, 16th Baronet (born 2 August 1927), commonly known as Peter Swinnerton-Dyer, is an English mathematician specialising in number theory at Cambridge University. He was a Fellow of Trinity College, Master of St Catharine's College and vice-chancellor of Cambridge University from 1979 to 1981. He was elected Fellow of the Royal Society in 1967 and awarded the Sylvester Medal in 2006.
- Yuri I. Manin
Yuri Ivanovitch Manin is a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics. Manin was born in Simferopol. He gained a doctorate in 1960 at the Steklov Mathematics Institute as a student of Igor Shafarevich. He is now a Professor and Director of the Max-Planck-Institut für Mathematik in Bonn, and a professor at Northwestern University.
- Louis Mordell
Louis Joel Mordell (28 January 1888 - 12 March 1972) was a British mathematician, known for pioneering research in number theory. He was born in Philadelphia, USA, in a Jewish family of Lithuanian extraction. He came in 1906 to Cambridge to take the scholarship examination for entrance to St John's College, and was successful in gaining a place and support. Having taken third place in the Mathematical Tripos, …
- Don Zagier
Don Bernhard Zagier is a German mathematician. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany, and a professor at the "Collège de France" in Paris, France. He was born in Heidelberg, Germany. He grew up in the United States, and studied for three years at M.I.T., completing his bachelor's and master's degree and being named a Putnam Fellow in 1967 at the age of 16.
- Alexander Beilinson
Alexander A. Beilinson is the David and Mary Winton Green University Professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1981 Beilinson announcement a proof of the Kazhdan-Lusztig conjectures and Jantzen conjectures with Joseph Bernstein. In 1982 Beilinson stated very deep conjectures about the existence of motivic cohomology groups for schemes, …
- Viggo Brun
Viggo Brun was a Norwegian mathematician. He studied at the University of Oslo and began research at the University of Gottingen in 1910. In 1923, Brun became a professor at the Technical University in Trondheim and in 1946 a professor at the University of Oslo. He retired in 1955 at the age of 70. In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the "Brun sieve", …
- William A. Stein
William Stein (born February 21, 1974 in Santa Barbara, California) is an associate professor of mathematics at the University of Washington. He is best known as the lead developer of Software for Algebra and Geometry Experimentation. Stein is currently doing computational and theoretical research into the problem of computing with modular forms and the Birch and Swinnerton-Dyer conjecture.
- Bryan John Birch
Bryan John Birch F.R.S. (born 1931) is a British mathematician. His name has been given to the Birch and Swinnerton-Dyer conjecture. As a doctoral student at the University of Cambridge, he was officially working under J. W. S. Cassels. More influenced by Harold Davenport, he proved Birch's theorem, …
- Suren Arakelov
Suren Yurievich Arakelov is a mathematician, best known for the influential theory that bears his name. Arakelov theory was exploited by Gerd Faltings in his proof of the Mordell conjecture. From 1965 onwards he attended the Mathematics department of Moscow State University, where he graduated in 1971. He obtained his "candidate of science" title in 1974 at the Steklov Institute in Moscow, under the supervision of Igor Shafarevich.
- Lev Schnirelmann
Lev Genrikhovich Schnirelmann, also Shnirelman, Shnirel'man (born January 2, 1905 in Gomel, died September 24, 1938 in Moscow) was a Soviet mathematician who sought to prove Goldbach's conjecture. In 1931, using the Brun sieve, he proved that any natural number greater than 1 can be written as the sum of not more than 300,000 prime numbers. His other fundamental work is joint with Lazar Lyusternik.
- Gerd Faltings
Gerd Faltings is a German mathematician known for his work in arithmetic algebraic geometry. From 1972 to 1978, he studied mathematics and physics at the University of Münster. In 1978 he received his PhD in mathematics and in 1981 he got the "venia legendi" (Habilitation) in mathematics, both from the University of Münster. During this time he was an assistant professor at the University of Münster.
- Victor Kolyvagin
Victor Kolyvagin is an Russian mathematician. He wrote a series of papers on Euler systems, leading to breakthroughs on the Birch and Swinnerton-Dyer conjecture, and Iwasawa's conjecture for cyclotomic fields. Kolyvagin received his Ph.D. in Mathematics in 1981 from Moscow State University, where his advisor was Yuri I. Manin. He then worked at Steklov Institute of Mathematics in Moscow until 1994.
- Olivier Ramaré
Olivier Ramaré is a French mathematician who teaches at the Université des Sciences et Technologies de Lille. In 1995, he proved that every even number is a sum of at most six primes. This result may be compared with Goldbach's conjecture, which states that every even number except 2 is the sum of two primes. The truth of Ramaré's result for all sufficiently large even numbers is a consequence of Vinogradov's theorem, …
- H.A. Pogorzelski
Henry Andrew Pogorzelski was a mathematician who circulated a proof of Goldbach's conjecture that is not accepted among mathematicians. According to his claim in Crelle's Journal, 292, 1977, 1–12, the proof depends upon the "Consistency Hypothesis", the "Extended Wittgenstein Thesis", and "Church's Thesis", all of which, no doubt, contributed to its dubious reputation among his peers. He published several paperbacks on the "Transtheoretic Foundations of Mathematics", …
- Lothar Collatz
Lothar Collatz was a German mathematician. In 1937 he posed the famous Collatz conjecture, which remains unsolved. Collatz studied at the University of Berlin under Alfred Klose, receiving his doctorate in 1935 for a dissertation entitled "Das Differenzenverfahren mit höherer Approximation für lineare Differentialgleichungen" (The finite difference method with higher approximation for linear differential equations).