| | 21 | Name: | Dr. Benedict H. Gross | | | Institution: | Harvard University | | | Year Elected: | 2017 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Living
| | | Birth Date: | 1950 | | | | | | |
Benedict Gross has contributed decisively to number theory, algebraic geometry, modular forms and group representations. Gross and Don Zagier solved the class number problem which had been formulated by APS member Karl Friedrich Gauss in 1798. This problem was to give an algorithm to list all discrete rings embedded in the complex numbers with a given class number. The class number is a measure of the failure of unique factorization in the ring. (The analogous problem for the real numbers was already solved by the ancient Greeks. There is only one discrete ring embedded in the real numbers, namely the integers. Euclid in 300 BC proved that unique factorization holds in the integers, hence its class number is 1, the minimum possible value.) The theorem of Gross and Zagier was one of the major achievements in number theory of the 20th century. Gross is an expert on analytic number theory, which exploits the striking relationships between analysis, in the sense of calculus, and arithmetic in the sense of counting. He has made many many diverse discoveries. Most recently, he has explored the role of exceptional Lie groups in number theory. His development of arithmetic invariant theory with Manjul Bhargava promises to generate a whole new field of future research. Together with Joe Harris, he developed a mathematics course for non-mathematicians at Harvard. This led to his popular book, The Magic of Numbers, co-authored with J. Harris, which provides a readable introduction to the patterns that emerge in number behavior and the often surprising applications of these patterns. | |
| 22 | Name: | Dr. Stephen William Hawking | | | Institution: | University of Cambridge | | | Year Elected: | 1984 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | International | | | Living? : |
Deceased
| | | Birth Date: | 1942 | | | Death Date: | March 13, 2018 | | | | | | |
Stephen William Hawking was born in 1942 in Oxford, England. He attended St. Albans School at age eleven and went on to University College, Oxford, where he studied physics, and Cambridge, where he conducted research in cosmology. After gaining his Ph.D. he became first a Research Fellow, and later on a Professorial Fellow at Gonville and Caius College, Cambridge. After leaving the Institute of Astronomy in 1973 Dr. Hawking came to the Department of Applied Mathematics and Theoretical Physics, and from 1979 held the post of Lucasian Professor of Mathematics, a position previously held by, among others, Isaac Barrow and Isaac Newton. Stephen Hawking had long studied the basic laws which govern the universe. With Roger Penrose he showed that Einstein's General Theory of Relativity implied that space and time would have a beginning in the Big Bang and an end in black holes. These results indicated it was necessary to unify General Relativity with Quantum Theory, the other great scientific development of the first half of the 20th century. One consequence of such a unification that he discovered was that black holes should not be completely black but should emit radiation and eventually evaporate and disappear. Another conjecture is that the universe has no edge or boundary in imaginary time. This would imply that the way the universe began was completely determined by the laws of science. Dr. Hawking's many publications include The Large Scale Structure of Spacetime (with G. F. R. Ellis); General Relativity: An Einstein Centenary Survey ; and 300 Years of Gravity (both with W. Israel). Dr. Hawking also published several popular books: his best seller A Brief History of Time, Black Holes and Baby Universes and Other Essays, and The Grand Design (2010). Professor Hawking held twelve honorary degrees, was awarded the CBE in 1982, and was made a Companion of Honour in 1989. He was the recipient of many awards, medals and prizes, including the Presidential Medal of Freedom (2009) and the Fundamental Physics Prize (2012), and was a Fellow of The Royal Society and a Member of the National Academy of Sciences. He became the first distinguished research chair at the Perimeter Institute for Theoretical Physics, Canada's leading scientifc trust, in 2008. Stephen Hawking died March 13, 2018, at age 76, in Cambridge, England. | |
| 23 | Name: | Dr. Samuel Karlin | | | Institution: | Stanford University | | | Year Elected: | 1995 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Deceased
| | | Birth Date: | 1924 | | | Death Date: | December 18, 2007 | | | | |
| 24 | Name: | Dr. Richard M. Karp | | | Institution: | University of California, Berkeley | | | Year Elected: | 1994 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Living
| | | Birth Date: | 1935 | | | | | | |
Richard M. Karp was born in Boston, Massachusetts on January 3, 1935. He attended Boston Latin School and Harvard University, receiving his Ph.D. in 1959. From 1959-68 he was a member of the Mathematical Sciences Department at IBM Research. From 1968-94 and from 1999 to the present he has been a Professor at the University of California, Berkeley, where he held the Class of 1939 Chair and is currently a University Professor. From 1988-95 and 1999 to the present he has been a Research Scientist at the International Computer Science Institute in Berkeley. From 1995-99 he was a Professor at the University of Washington. During the 1985-86 academic year he was the co-organizer of a Computational Complexity Year at the Mathematical Sciences Research Institute in Berkeley. During the 1999-2000 academic year he was the Hewlett-Packard Visiting Professor at the Mathematical Sciences Research Institute. The unifying theme in Karp's work has been the study of combinatorial algorithms. His 1972 paper, "Reducibility Among Combinatorial Problems," showed that many of the most commonly studied combinatorial problems are NP-complete, and hence likely to be intractable. Much of his work has concerned parallel algorithms, the probabilistic analysis of combinatorial optimization algorithms and the construction of randomized algorithms for combinatorial problems. His current activities center around algorithmic methods in genomics and computer networking. He has supervised thirty-six Ph.D. dissertations. His honors and awards include the U.S. National Medal of Science, the Turing Award, the Kyoto Prize, the Fulkerson Prize, the Harvey Prize (Technion), Harvard University's Centennial Medal, the Lanchester Prize, the Von Neumann Theory Prize and Lectureship, the University of California, Berkeley's Distinguished Teaching Award and Miller Research Professorship, the Babbage Prize, and ten honorary degrees. He is a member of the U.S. National Academies of Sciences and Engineering, the American Philosophical Society and the French Academy of Sciences, and a Fellow of the American Academy of Arts and Sciences, the American Association for the Advancement of Science, the Association for Computing Machinery and the Institute for Operations Research and Management Science. | |
| 25 | Name: | Dr. Saunders Mac Lane | | | Institution: | University of Chicago | | | Year Elected: | 1949 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Deceased
| | | Birth Date: | 1909 | | | Death Date: | April 14, 2005 | | | | |
| 26 | Name: | Dr. Robert P. Langlands | | | Institution: | Institute for Advanced Study | | | Year Elected: | 2004 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Living
| | | Birth Date: | 1936 | | | | | | |
The "Langlands Philosophy" is widely recognized as the most far-reaching dream that mathematicians currently have for the future development of mathematics. For the past three centuries, the subject of modular forms has been a major strand of mathematics, treated by such great mathematicians as Euler and Gauss. But it had the character of a bag of tricks and special results. Then, in 1967, Dr. Langlands announced the "Langlands conjectures," which displayed for the first time the underlying patterns at work. In the 35 years since then, these conjectures have become increasingly important. Guided by them, an underlying unity has been found, with deep consequences for many branches of mathematics. These include number theory (where Langlands' work played a role in Wiles' proof of Fermat's conjecture), algebraic geometry (where 30 of the best young geometers work in what they call "geometric Langlands theory"), and representation theory (where the Langlands conjectures lead to a classification of the representations that come up in the study of quantum mechanics). Today, the Langlands conjectures provide the basic motivation and guidance for the work of many mathematicians working in diverse fields. Dr. Langlands has also written extensively on mathematical physics, and he has a strong interest in history. A graduate of Yale University (Ph.D., 1960), he has been a professor at the Institute for Advanced Study since 1972. He is currently Professor of Mathematics Emeritus. He is a member of the American Academy of Arts & Sciences, a foreign member of the Russian Academy of Sciences, and has been awarded the Lester R. Ford Prize from the Mathematical Association of America. In 2018 he was awarded the Abel Prize. | |
| 27 | Name: | Dr. Peter D. Lax | | | Institution: | New York University | | | Year Elected: | 1996 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Living
| | | Birth Date: | 1926 | | | | | | |
Peter D. Lax is a most distinguished mathematician who has earned renown for his contributions in both pure and applied mathematics. One of many methods named after him is Lax pairs, which came from his analysis of fluid dynamics. His name is connected with many major mathematical results and numerical methods, including the Lax equivalence theorem, Lax-Friedrichs scheme, Lax-Wendroff scheme, Lax entropy condition, and Lax-Levermore theory. His work covers all aspects of partial differential equations. In linear theory it includes his fundamental oscillatory approximation for solving hyperbolic equations, which led to the theory of Fourier Integral Operators. His famous collaboration with R.S. Phillips involves extremely deep work in scattering theory and connects with problems on automorphic functions in hyperbolic geometry. Dr. Lax has also done basic work in numerical analysis for partial differential equations. In nonlinear theory he has done fundamental work on shock waves, and on KdV equations: completely integrable systems possessing solition solutions. A native of Hungary, Dr. Lax earned his Ph.D. from New York University in 1949 and has served at NYU's Courant Institute of Mathematical Sciences since 1958. He has also directed the Courant Mathematics and Computing Lab and is currently Professor of Mathematics Emeritus. Dr. Lax has won many honors such as the Chauvenet Prize (1974), the National Medal of Science (1986), the Wolf Prize (1987), the Abel Prize (2005) and membership in the American Academy of Arts & Sciences and the National Academy of Sciences. Dr. Lax is the author of numerous works, including textbooks on functional analysis, linear algebra, calculus and partial differential equations. | |
| 28 | Name: | Dr. Jean Leray | | | Institution: | Collège de France | | | Year Elected: | 1959 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | International | | | Living? : |
Deceased
| | | Birth Date: | 1906 | | | Death Date: | 11/10/98 | | | | |
| 29 | Name: | Sir James Lighthill | | | Institution: | University College of London | | | Year Elected: | 1970 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | International | | | Living? : |
Deceased
| | | Birth Date: | 1924 | | | Death Date: | 7/17/98 | | | | |
| 30 | Name: | Dr. Chia-Chiao Lin | | | Institution: | Massachusetts Institute of Technology | | | Year Elected: | 1978 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Deceased
| | | Birth Date: | 1916 | | | Death Date: | January 13, 2013 | | | | | | |
Chinese-born physicist Chia-Chiao Lin made major contributions to the theory of superfluid helium, hydrodynamic stability and turbulent diffusion as well as in mathematics and astrophysics. He is also credited with finding a mathematical explanation for the propagation of a spiral structure in disk nebulae. After moving to the United States to study at the California Institute of Technology, Dr. Lin earned his Ph. D. in 1944. Since that time he has taught at Cal Tech (1943-45), Brown University (1945-47) and the Massachusetts Institute of Technology (1947-87), where he became Institute Professor in 1966 and retired in 1987. | |
| 31 | Name: | Dr. George W. Mackey | | | Institution: | Harvard University | | | Year Elected: | 1971 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Deceased
| | | Birth Date: | 1916 | | | Death Date: | March 15, 2006 | | | | |
| 32 | Name: | Dr. Robert MacPherson | | | Institution: | Institute for Advanced Study | | | Year Elected: | 1999 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Living
| | | Birth Date: | 1944 | | | | | | |
Robert MacPherson has done decisive research on a variety of problems in geometry, especially for manifolds with singularities. Previously mathematicians had understood only smooth varieties. Dr. MacPherson found he needed wholly new methods for treating those with singular points or singular curves. This has included his understanding of Chern classes; his development with Goresky of the "intersection" homology theory; his work with Fulton on coverings; and his introduction of the important concept of Perverse Sheaves. He has been especially effective in collaboration with other mathematicians, and his extraordinary mobilization of the American math community to rescue the poverty-stricken Russian mathematical community is a most admirable humanitarian act that displays his human concerns as well as his great energy and initiative. Dr. MacPherson received his Ph.D. from Harvard University in 1970, after which time he joined the faculty of Brown University. He moved to the Massachusetts Institute of Technology in 1987 and to the Institute of Advanced Study in 1994. The recipient of the 1992 National Academy of Sciences Award in Mathematics and the 2009 Swiss Federal Institute of Rechnology Heinz Hopf Prize, Dr. Macpherson is a member of the American Academy of Arts & Sciences and the National Academy of Sciences. He was elected to the membership of the American Philosophical Society in 1999. | |
| 33 | Name: | Dr. Benoit B. Mandelbrot | | | Institution: | Yale University | | | Year Elected: | 2004 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Deceased
| | | Birth Date: | 1924 | | | Death Date: | October 14, 2010 | | | | | | |
His Wolf Prize citation hails Benoit Mandelbrot for having "changed our view of nature", and IBM had cited him earlier in words that have been repeatedly confirmed: "Few contemporary scholars have made such penetrating contributions to as many fields of physical and social science. . . His success, where others have faltered, has been due to a combination of command of mathematical tools, extraordinary breadth, and even rarer intellectual courage." Fractal geometry, which he pioneered and named, also changed the way students and the world at large view mathematics and science. In pure mathematics, examination of masterful computer graphics led him to conjectures of great taste and difficulty that brought several slowly moving fields to intense activity. His observations revived iteration theory after a half century of forced inactivity; but his MLC conjecture (that the "Mandelbrot set is locally connected") is still unsolved after more than a quarter century. In probability theory, his conjecture that the boundary of a segment of Brownian notion is of dimension 4/3 was only proved after 18 years. He broadened the scope of physics by quantifying for the first time a holdover basic sensation, showing that the roughness of typical surfaces can actually be measured by a fractal dimension or Hölder exponent that turned out to be a new "universal." He showed how the support of intermittent turbulence can be measured and how the physics of diverse clusters is determined by their fractal geometry. In economics he enunciated the scaling principle in the 1960s, and his models for price variation, including his later notion of variable (fractal) trading time, are central to current developments in finance. A native of Poland, Benoit Mandelbrot became Docteur d'Etat ès Sciences Mathématiques in Paris in 1952. He was IBM Fellow Emeritus in Physics and Sterling Professor Emeritus of Mathematical Sciences at Yale University at the time of his death on October 14,2010, at the age of 85. | |
| 34 | Name: | Dr. Barry Mazur | | | Institution: | Harvard University | | | Year Elected: | 2001 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Living
| | | Birth Date: | 1937 | | | | | | |
Barry Mazur is one of the most distinguished mathematicians in America. In 1959 he astonished the mathematical world by introducing the "method of infinite repetition" to prove an appropriate version of the Schoenflies embedding theorem for spheres and other theorems about manifolds. For this work in topology he was awarded (jointly with M. W. Brown) the Veblen Prize of the American Mathematical Society in 1966. Thereafter he switched his attention to algebraic number theory, and in that field he won the Cole Prize in 1982. His work in number theory played a prominent role in the developments leading up to the solution of the Fermat problem a few years ago. He is recognized as a leading expositor in the field of number theory and is also deeply interested in philosophy and the history of mathematics. Dr. Mazur has been affiliated with Harvard University since 1959 and has held the title of Gerhard Gade University Professor since 1999. He won the National Medal of Science in 2012. | |
| 35 | Name: | Dr. Dusa McDuff | | | Institution: | Barnard College | | | Year Elected: | 2013 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Living
| | | Birth Date: | 1945 | | | | | | |
Dusa McDuff launched her career while she was a graduate student at Cambridge University (where she earned her PhD in 1970 under George Reid) when she solved a well-known problem about von Neumann algebras, constructing infinitely many different factors of "type II-one." She traveled to Moscow in 1969-70 where she had the good fortune to study with Israel M. Gelfand. He shared her view of mathematics as a kind of poetry and was a great inspiration, encouraging her to study topology. McDuff returned to Cambridge for a two-year Science Research Council Fellowship, working with Frank Adams and later Graeme Segal. She was appointed Lecturer first at the University of York (1972-76) and then at the University of Warwick (1976-78), and spent 1974-75 at MIT.
McDuff was on the faculty of the State University of New York at Stony Brook from 1978-2008, starting as an Assistant Professor and ending as a Distinguished Professor, along the way serving as Department Chair, 1991-93, and Undergraduate Director, 1998-2000. She moved to Barnard College in 2007 to take up the Kimmel Chair of Mathematics. Throughout her career she has been concerned with educational issues at both undergraduate and graduate levels, as well as being active in encouraging more women to study mathematics.
McDuff has worked in symplectic topology since the early 1980s. She has written over 90 papers, as well as co-authoring three books with Dietmar Salamon, most recently J-holomorphic curves and Symplectic Topology (AMS Colloquium Publication 52, 2 edition (2012)).
McDuff has held visiting positions at the Institute for Advanced Studies, UC Berkeley, MIT, Harvard, and at MSRI, in addition to serving on MSRI’s Scientific Advisory Committee (1990-98, Chair 1993-96). She has served on the MSRI Board of Trustees, as Chair 1998-2001, and currently as an ordinary member (2006-2017).
Dusa McDuff has been awarded numerous honors including the Ruth Lyttle Satter Prize of the American Mathematical Society in 1991 and honorary doctorates from the University of Edinburgh (where she was an undergraduate), the University of York and the University of Strasbourg. She was elected a Fellow of the Royal Society of London in 1994 and a Fellow of the American Academy of Arts and Sciences in 1995; she became a member of the United States National Academy of Sciences in 1999. She is an Honorary Fellow of Girton College, Cambridge, an Honorary Member of the London Mathematical Society and a corresponding member of the Royal Society of Edinburgh. She was elected a member of the American Philosophical Society in 2013.
McDuff has lectured widely in the US and abroad: for example Plenary Lecture at ICM Berlin (1998), AWM Noether Lecturer (1998), London Mathematical Society Hardy Lecturer (1999), Rademacher Lecturer, University of Pennsylvania (2001) and Andrejewski Lecturer, University of Gottingen (2001). She was awarded the AMS Steele Prize for Exposition in 2017. | |
| 36 | Name: | Dr. Curtis T. McMullen | | | Institution: | Harvard University | | | Year Elected: | 2023 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Living
| | | Birth Date: | 1958 | | | | |
| 37 | Name: | Dr. Edward J. McShane | | | Institution: | University of Virginia | | | Year Elected: | 1959 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Deceased
| | | Birth Date: | 1904 | | | Death Date: | 6/1/89 | | | | |
| 38 | Name: | Dr. John W. Milnor | | | Institution: | State University of New York, Stony Brook | | | Year Elected: | 1965 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Living
| | | Birth Date: | 1931 | | | | | | |
John W. Milnor is a professor at the State University of New York, Stony Brook, where he also co-directs the Institute for Mathematical Sciences. Known for his work in differential topology, K-theory and dynamical systems, Dr. Milnor was for many years associated with Princeton University, earning his Ph.D. there in 1954 and becoming Henry Putnam University Professor of Mathematics in 1962. His most celebrated single result is his proof of the existence of 7-dimensional spheres with nonstandard differential structure. Later, he showed that the 7-sphere has 15 differentiable structures (28 if you consider orientation). An n-sphere with nonstandard differential structure is called an exotic sphere, a term coined by Dr. Milnor. An accomplished mathematical writer with numerous books and papers, including many on topology and game theory, to his credit, he has also served as editor of the Annals of Mathematics since 1962. That same year, Dr. Milnor was awarded the Fields Medal for his work in differential topology, and since that time he has received many other awards, including the National Medal of Science (1967), the Leroy P. Steele Prize for Seminal Contribution to Research (1982), the Wolf Prize in Mathematics (1989), the Leroy P. Steele Prize for Mathematical Exposition (2004), and both the Leroy P. Steele Prize for Lifetime Acheivement and the Abel Prize in 2011. He is a member of the National Academy of Sciences. | |
| 39 | Name: | Dr. Maryam Mirzakhani | | | Year Elected: | 2015 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Deceased
| | | Birth Date: | 1977 | | | Death Date: | July 15, 2017 | | | | | | |
Maryam Mirzakhani was the first female recipient of the Fields Medal, the leading international prize for mathematical research that must be awarded by the age of 40. To earn this distinction she had made outstanding contributions to understanding the dynamics and geometry of two-dimensional surfaces (known as Riemann surfaces) and their deformation (or moduli) spaces. She extended and integrated insights developed by other mathematical pioneers such as Thurston, Ratner, Margulis, and Bers in a wide variety of fields including algebraic geometry, topology and probability theory. Her work probed the structure of these moduli spaces by studying the behavior of simple geodesics, which are curves on the surface with no self-intersections that minimize the distance between any two points lying sufficiently close to each other on the curve. Mirzakhani and her coworkers produced the long sought-after proof of the conjecture that while the closure of a real geodesic in moduli space can be fractal the closure of a complex geodesic is always well-behaved, indeed an algebraic subvariety.
Born in Iran, Mirzakhani completed a bachelor's degree at Sharif University of Technology in Tehran and completed her doctorate at Harvard University. She was a professor at Princeton University before moving to Stanford University in 2008. Dr. Mirzakhani died July 15, 2017, at the age of 40. | |
| 40 | Name: | Dr. Deane Montgomery | | | Institution: | Institute for Advanced Study | | | Year Elected: | 1958 | | | Class: | 1. Mathematical and Physical Sciences | | | Subdivision: | 104. Mathematics | | | Residency: | Resident | | | Living? : |
Deceased
| | | Birth Date: | 1909 | | | Death Date: | 3/15/92 | | | | |
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