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Alexander Grothendieck was a German-born mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century.

Go to ProfileAndré Weil was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was one of the most influential mathematicians of the twentieth century. His influence is due both to his original contributions to a remarkably broad spectrum of mathematical theories, and to the mark he left on mathematical practice and style, through some of his own works as well as through the Bourbaki group, of which he was one of the principal founders.

Go to ProfilePaul Erdős was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered around discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open...

Go to ProfileJean-Pierre Serre is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003.

Go to ProfileEugene Paul "E. P." Wigner was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles".

Go to ProfileChinese-born Shing-Tung Yau currently holds the title of William Caspar Graustein Professor of Mathematics at Harvard University, where he has worked since 1987. He is also the director of three mathematical institutes in China, including the Yau Mathematical Sciences Center at Tsinghua University. Yau completed his undergraduate education in mathematics at Chinese University of Hong Kong in 1969, then his PhD at the University of California, Berkeley in 1971. Yau is considered most influential for his work in differential geometry and geometric analysis. Early in his career, Yau proved the P...

Go to ProfileSir Roger Penrose was born in Colchester, England in 1931. He is best known for his significant contributions to the mathematical physics of general relativity and cosmology. Penrose attended University College London where he earned his bachelor’s in mathematics. He received a PhD studying algebraic geometry at St John’s College, Cambridge in 1958. In his free time at Cambridge, he attended a few lectures led by Hermann Bondi and Paul Dirac, which lent some of his curiosity in the direction of physics. Penrose went on to become an innovator in the field of mathematical physics, and is now widely regarded as among the greatest living mathematical physicists.

Go to ProfileTao is arguably the greatest living mathematician, and has been called the greatest mathematician of his generation. Born in South Australia, Tao was a child prodigy, the youngest person ever to win a medal in the International Mathematical Olympiad—he was ten. He has since won the Field Medal, the “Nobel Prize” for mathematicians. Terence Tao holds the James and Carol Collins Chair in Mathematics at the University of California at Los Angeles (UCLA). At the age of 14, Tao attended the Research Science Institute, a summer seminar for talented high school students hosted by the Massachusetts Institute of Technology (MIT).

Go to ProfileSir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004.

Go to ProfileHenri Paul Cartan was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of composer , physicist and mathematician , and the son-in-law of physicist Pierre Weiss.

Go to ProfileClaude Elwood Shannon was an American mathematician, electrical engineer, computer scientist and cryptographer known as the "father of information theory". As a 21-year-old master's degree student at the Massachusetts Institute of Technology , he wrote his thesis demonstrating that electrical applications of Boolean algebra could construct any logical numerical relationship. Shannon contributed to the field of cryptanalysis for national defense of the United States during World War II, including his fundamental work on codebreaking and secure telecommunications.

Go to ProfilePaul 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.

Go to ProfileDavid Bryant Mumford is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded the National Medal of Science. He is currently a University Professor Emeritus in the Division of Applied Mathematics at Brown University.

Go to ProfilePierre René, Viscount Deligne is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.

Go to ProfileSaunders Mac Lane was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville. He was christened "Leslie Saunders MacLane", but "Leslie" fell into disuse because his parents, Donald MacLane and Winifred Saunders, came to dislike it. He began inserting a space into his surname because his first wife found it difficult to type the name without a space. He was the oldest of three brothers; one of his brothers, Gerald MacLane, also became a mathematics professor at Rice University and Purdue University.

Go to ProfileGrigori Yakovlevich Perelman is a Russian mathematician who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. He is widely regarded as one of the greatest living mathematicians.

Go to ProfileJean Alexandre Eugène Dieudonné was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology. His work on the classical groups , and on formal groups, introducing what now are called Dieudonné modules, had a major effect on those fields.

Go to ProfileAlonzo Church was an American mathematician, computer scientist, logician, and philosopher who made major contributions to mathematical logic and the foundations of theoretical computer science. He is best known for the lambda calculus, the Church–Turing thesis, proving the unsolvability of the Entscheidungsproblem, the Frege–Church ontology, and the Church–Rosser theorem. He also worked on philosophy of language . Alongside his doctoral student Alan Turing, Church is considered one of the founders of computer science.

Go to ProfileDonaldson is a permanent member of the Simons Center for Geometry and Physics at Stony Brook University and Professor in Pure Mathematics at Imperial College, London. He is known for the eponymous Donaldson-Thomas theory of invariants in algebraic geometry (see also Andrei Akounkov above). Donaldson has a Bachelor of Arts degree in mathematics from Pembroke College in Cambridge University in 1979, and his Ph.D. from Oxford University in 1983. Donaldson published a paper while working on his Ph.D. that made him famous. The paper, titled “Self-dual connections and the topology of smooth 4-manifo...

Go to ProfileConway is the John Von Neumann Professor Emeritus of Mathematics at Princeton University. He has interests in diverse fields in mathematics, including number theory, combinatorial games theory, knot theory, and coding theory. Coding theory is a mathematical treatment of codes and their use in cryptography and other disciplines. Conway is perhaps best known as the inventor of the Game of Life, an Artificial Intelligence program whose agents (objects in code) evolve according to deterministic rules. The agents are known in mathematics as cellular automatons. Conway received his Bachelor of Arts degree in Mathematics from Cambridge University in England in 1959.

Go to ProfileSamuel Eilenberg was a Polish-American mathematician who co-founded category theory and homological algebra. Early life and education He was born in Warsaw, Kingdom of Poland to a Jewish family. He spent much of his career as a professor at Columbia University.

Go to ProfileShiing-Shen Chern was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geometry" and is widely regarded as a leader in geometry and one of the greatest mathematicians of the twentieth century, winning numerous awards and recognition including the Wolf Prize and the inaugural Shaw Prize. In memory of Shiing-Shen Chern, the International Mathematical Union established the Chern Medal in 2010 to recognize "an individual whose accomplishments warrant the highest level of recogn...

Go to ProfileRichard Streit Hamilton is an American mathematician who serves as the Davies Professor of Mathematics at Columbia University. He is known for contributions to geometric analysis and partial differential equations. Hamilton is best known for foundational contributions to the theory of the Ricci flow and the development of a corresponding program of techniques and ideas for resolving the Poincaré conjecture and geometrization conjecture in the field of geometric topology. Grigori Perelman built upon Hamilton's results to prove the conjectures, and was awarded a Millennium Prize for his work. H...

Go to ProfileIsrael Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand was a prominent Soviet-American mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the first Wolf Prize, he was a Foreign Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University. Gelfand is also a 1994 MacArthur Fellow.

Go to ProfileFriedrich Ernst Peter Hirzebruch ForMemRS was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. He has been described as "the most important mathematician in Germany of the postwar period."

Go to ProfileWilliam Paul Thurston was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds.

Go to ProfileEugenio Calabi is an Italian-born American mathematician and the Thomas A. Scott Professor of Mathematics, Emeritus, at the University of Pennsylvania, specializing in differential geometry, partial differential equations and their applications.

Go to ProfileGian-Carlo Rota was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, probability theory, and phenomenology.

Go to ProfileConnes is currently Professor at the Collège de France, IHÉS, in France, as well as at Ohio State University and Vanderbilt University. Connes’ work focuses on algebra, or what is known as “operator algebra,” an important area in functional analysis. Born in France, Connes received his undergraduate degree in Mathematics from the prestigious École normale supérieure in Paris and his Ph.D. from the University Pierre et Marie Curie. Among other notables, Connes was a member of Bourbaki, a group of predominantly French mathematicians who formed after the First World War in response to the loss of so many mathematicians in the wake of the war.

Go to ProfileRaoul Bott was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.

Go to ProfileWiles is Royal Society Research Professor at the University of Oxford. He became an overnight sensation when he proved one of the most famous conjectures in all of mathematics, known as Fermat’s Last Theorem, after the 17th century mathematician Pierre Fermat. Wiles received his bachelor’s degree in Mathematics from Oxford and his Ph.D. in Mathematics from the University of Cambridge. He spent a year at Princeton University’s Institute for Advanced Study and then became Professor of Mathematics at Princeton University. He has taught back and forth between Princeton and Oxford for much of his stellar career.

Go to ProfileBartel Leendert van der Waerden was a Dutch mathematician and historian of mathematics. Biography Education and early career Van der Waerden learned advanced mathematics at the University of Amsterdam and the University of Göttingen, from 1919 until 1926. He was much influenced by Emmy Noether at Göttingen, Germany. Amsterdam awarded him a Ph.D. for a thesis on algebraic geometry, supervised by Hendrick de Vries. Göttingen awarded him the habilitation in 1928. In that year, at the age of 25, he accepted a professorship at the University of Groningen.

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Overall Influence

1930 - 2019 (89 years)

Gorō Shimura was a Japanese mathematician and Michael Henry Strater Professor Emeritus of Mathematics at Princeton University who worked in number theory, automorphic forms, and arithmetic geometry. He was known for developing the theory of complex multiplication of abelian varieties and Shimura varieties, as well as posing the Taniyama–Shimura conjecture which ultimately led to the proof of Fermat's Last Theorem.

Go to ProfileLaurent-Moïse Schwartz was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields Medal in 1950 for his work on the theory of distributions. For several years he taught at the École polytechnique.

Go to ProfileJohn Willard Milnor is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook University and one of the five mathematicians to have won the Fields Medal, the Wolf Prize, and the Abel Prize .

Go to ProfileLouis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century. Nearly all of his work was in the field of partial differential equations. Many of his contributions are now regarded as fundamental to the field, such as his strong maximum principle for second-order parabolic partial differential equations and the Newlander-Nirenberg theorem in complex geometry. He is regarded as a foundational figure in the field of geometric analysis, with many of his works being closely related to the study of complex analysis and differential...

Go to ProfileMartin Gardner was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton. He was also a leading authority on Lewis Carroll. The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century".

Go to ProfileAreas of Specialization: Computer Programming, Analysis of Algorithms Knuth is professor emeritus of computer science at Stanford University. He received his Ph.D. in Mathematics at the California Institute of Technology (Cal Tech). As an undergraduate at the Case Western Reserve University (then Case Institute of Technology), Knuth received the extraordinary honor of receiving his bachelor of science degree together with a master of science in mathematics based on the strength of his work at Case. He also helped redesign an early IBM computer while at Case, and made fundamental contributions ...

Go to ProfileSerge Lang was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He received the Frank Nelson Cole Prize in 1960 and was a member of the Bourbaki group.

Go to ProfileStephen Smale is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty of the University of California, Berkeley , where he currently is Professor Emeritus, with research interests in algorithms, numerical analysis and global analysis.

Go to ProfileRené Frédéric Thom was a French mathematician, who received the Fields Medal in 1958. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as founder of catastrophe theory .

Go to ProfileBenoit B. Mandelbrot was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.

Go to ProfileLászló Lovász is a Hungarian mathematician and professor emeritus at Eötvös Loránd University, best known for his work in combinatorics, for which he was awarded the 2021 Abel Prize jointly with Avi Wigderson. He was the president of the International Mathematical Union from 2007 to 2010 and the president of the Hungarian Academy of Sciences from 2014 to 2020.

Go to ProfileHungarian-born Peter Lax currently holds the title of Professor Emeritus at the Courant Institute of Mathematical Sciences at New York University. Lax began working at NYU in 1951; prior to that, he worked on the Manhattan Project. Lax’s family emigrated from Hungary in 1941 while he was a teenager, and at 17 he was able to study for three semesters at NYU (where he wound up acting as an instructor). He was drafted into the U.S. army and allowed to take classes at Texas A&M University, though his studies were again interrupted when he was sent to work at the Oak Ridge National Laboratory, as well as the Manhattan Project (all before earning an undergraduate degree).

Go to ProfileJean, Baron Bourgain was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.

Go to ProfileIgor Rostislavovich Shafarevich was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry. Outside mathematics, he wrote books and articles that criticised socialism and other books which were described as anti-semitic.

Go to ProfileMichael Artin is a German-American mathematician and a professor emeritus in the Massachusetts Institute of Technology Mathematics Department, known for his contributions to algebraic geometry. Life and career Michael Artin or Artinian of Armenian origin was born in Hamburg, Germany, and brought up in Indiana. His parents were Natalia Naumovna Jasny and Emil Artin, preeminent algebraist of the 20th century of Armenian descent. Artin's parents left Germany in 1937, because his mother's father was Jewish. His elder sister is , who was married to mathematician John Tate until the late 1980s.

Go to ProfileFreeman John Dyson was an British-American theoretical physicist and mathematician known for his works in quantum field theory, astrophysics, random matrices, mathematical formulation of quantum mechanics, condensed matter physics, nuclear physics, and engineering. He was Professor Emeritus in the Institute for Advanced Study in Princeton and a member of the Board of Sponsors of the Bulletin of the Atomic Scientists.

Go to ProfileHerman Heine Goldstine was a mathematician and computer scientist, who worked as the director of the IAS machine at Princeton University's Institute for Advanced Study and helped to develop ENIAC, the first of the modern electronic digital computers. He subsequently worked for many years at IBM as an IBM Fellow, the company's most prestigious technical position.

Go to ProfileBarry Mazur currently holds the title of Gerhard Gade University Professor at Harvard University, where he has worked as a professor since 1962. Prior to his long tenure at Harvard, Mazur held post-doctoral fellowships at Harvard and the Institute for Advanced Study. Mazur earned his PhD in Mathematics at Princeton University; though he attended MIT as an undergraduate, he did not complete a bachelor’s degree. Mazur boasts a long career of discoveries and advancements in geometry, arithmetic, and number theory. In fact, he has several discoveries and proofs named after him, including the Mazur swindle, the Mazur manifold, and Mazur’s torsion theorem.

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