| **21** | **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 | | | |
**22** | **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. | |
**23** | **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. | |
**24** | **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. | |
**25** | **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. | |
**26** | **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 | | | |
**27** | **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 | | | |
**28** | **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. | |
**29** | **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. | |
**30** | **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 | | | |
**31** | **Name: ** | Dr. Cathleen S. Morawetz | | **Institution: ** | New York University & New York Mayor's Commission on Science & Technology | | **Year Elected: ** | 1996 | | **Class: ** | 1. Mathematical and Physical Sciences | | **Subdivision: ** | 104. Mathematics | | **Residency: ** | Resident | | **Living? : ** |
Deceased
| | **Birth Date: ** | 1923 | | **Death Date: ** | August 8, 2017 | | | | | Mathematician Cathleen Synge Morawetz was born in Toronto, Canada in 1923. She graduated from the University of Toronto in 1945 and received her master's degree from the Massachusetts Institute of Technology. She then earned her Ph.D. at New York University with a thesis on the stability of a spherical implosion. She became an assistant professor at the Courant Institute of Mathematical Sciences at NYU in 1957 and remained at NYU throughout her career, serving as the Institute's director from 1984-88. Dr. Morawetz is a member of the National Academy of Sciences, a former president of the American Mathematical Society and the recipient of the 1998 National Medal of Science. She was elected a member of the American Philosophical Society in 1996. Her research focused mainly on the study of the partial differential equations governing fluid flow, particularly those of mixed type occurring in transonic flow. She died August 8, 2017 at the age of 94 at home in Manhattan. | |
**32** | **Name: ** | Dr. Frederick Mosteller | | **Institution: ** | Harvard University & American Academy of Arts & Sciences | | **Year Elected: ** | 1961 | | **Class: ** | 1. Mathematical and Physical Sciences | | **Subdivision: ** | 104. Mathematics | | **Residency: ** | Resident | | **Living? : ** |
Deceased
| | **Birth Date: ** | 1916 | | **Death Date: ** | July 23, 2006 | | | |
**33** | **Name: ** | Dr. David Mumford | | **Institution: ** | Brown University | | **Year Elected: ** | 1997 | | **Class: ** | 1. Mathematical and Physical Sciences | | **Subdivision: ** | 104. Mathematics | | **Residency: ** | Resident | | **Living? : ** |
Living
| | **Birth Date: ** | 1937 | | | | | David Mumford is a mathematician known both for his distinguished work in algebraic geometry and for his research into vision and pattern theory. Currently a professor emeritus in the Division of Applied Mathematics at Brown University, he previously had a long academic career at Harvard University, where he became a full professor of mathematics at Harvard University at the age of 30. He received his Ph.D. from Harvard in 1961. Dr. Mumford's work in geometry always combined the traditional geometric insights with the latest algebraic techniques. He published on moduli spaces, with a theory summed up in his book Geometric Invariant Theory, on the equations defining an abelian variety, and on algebraic surfaces. He essentially founded the subject of the global moduli of algebraic curves, and in 1974, he was awarded the highest distinction in mathematics, the Fields Medal. During the 1980s Dr. Mumford left algebraic geometry in order to study brain structure. He was a MacArthur Fellow from 1987-92, won the Shaw Prize in 2006, and was awarded the 2010 National Medal of Science. His current area of work is pattern theory. | |
**34** | **Name: ** | Dr. John F. Nash | | **Institution: ** | Princeton University | | **Year Elected: ** | 2006 | | **Class: ** | 1. Mathematical and Physical Sciences | | **Subdivision: ** | 104. Mathematics | | **Residency: ** | Resident | | **Living? : ** |
Deceased
| | **Birth Date: ** | 1928 | | **Death Date: ** | May 23, 2015 | | | | | John Nash introduced what is now called "Nash equilibrium" in non-cooperative games and proved that such an equilibrium always exists. This work is foundational for Game Theory and led to his Nobel Prize in Economics. No less impressive is his work in pure mathematics, where his very deep and difficult theorems on embedding of manifolds initiated a whole new field of research. Tragically disabled by schizophrenia for over 30 years, he provided inspiration for many fellow sufferers by completely recovering, as told in the book and motion picture A Beautiful Mind. He then resumed his research in mathematics, having served as a researcher at Princeton University from 1994 to his death in 2015. In addition to the Nobel Prize, among Dr. Nash's many honors are the John Von Neumann Theory Prize of the Institute for Operations Research and Management Science (1978), the American Mathematical Society's Steele Prize (1999), and Norway's Abel Prize (2015). A graduate of Princeton University (Ph.D., 1950), he is a member of the American Academy of Arts & Sciences (1995) and the National Academy of Sciences (1996). He died May 23, 2015, at the age of 86 in New Jersey. | |
**35** | **Name: ** | Dr. Louis Nirenberg | | **Institution: ** | New York University | | **Year Elected: ** | 1987 | | **Class: ** | 1. Mathematical and Physical Sciences | | **Subdivision: ** | 104. Mathematics | | **Residency: ** | Resident | | **Living? : ** |
Deceased
| | **Birth Date: ** | 1925 | | **Death Date: ** | January 26, 2020 | | | | | A leading mathematician with broad cultural interests, Canadian-born Louis Nirenberg has made seminal contributions to the study of linear and non-linear partial differential equations and their applications. He discovered interactions between mathematical analysis, differential geometry and "complex analysis" and made deep applications to the theory of fluid flow and other physical phenomena. Winner of the first Crafoord Prize of the Royal Swedish Academy (1982), Dr. Nirenberg is currently professor of mathematics emeritus at New York University's Courant Institute of Mathematical Sciences. He began his career at NYU in 1949 after receiving his M.S. and Ph.D. degrees from the university. From 1970-72 he served as director of the Courant Institute. Dr. Nirenberg's numerous honors include the 1995 National Medal of Science, the American Mathematical Society's Bocher Prize (1959), Guggenheim and Sloan Fellowships and membership in the National Academy of Sciences and American Academy of Arts & Sciences. In 2010, he was awarded the Chern Medal from the International Congress of Mathematicians and in 2014 he received the Leroy P. Steele Prize for Seminal Contribution to Research with Robert Kohn and Luis Caffarelli. He was awarded the 2015 Abel Prize. | |
**36** | **Name: ** | Prof. Andrew M. Gleason | | **Institution: ** | Harvard University | | **Year Elected: ** | 1977 | | **Class: ** | 1. Mathematical and Physical Sciences | | **Subdivision: ** | 104. Mathematics | | **Residency: ** | Resident | | **Living? : ** |
Deceased
| | **Birth Date: ** | 1921 | | **Death Date: ** | October 17, 2008 | | | | | Mathematician Andrew Gleason is well known for his major part in the solution of "Hilbert's Fifth Problem," which concerns the characterization of lie groups. Following his undergraduate career at Yale University, he was appointed a Junior Fellow at Harvard University in 1946. He received an honorary M.A. from Harvard in 1953 and, after serving as assistant professor to professor of mathematics from 1950-69, he was named Hollis Professor of Mathematics and Natural Philosophy at Harvard. A member of the National Academy of Sciences and the American Academy of Arts & Sciences, Andrew Gleason retired from the Harvard faculty in 1992. | |
**37** | **Name: ** | Dr. Peter Sarnak | | **Institution: ** | Princeton University; Institute for Advanced Study | | **Year Elected: ** | 2008 | | **Class: ** | 1. Mathematical and Physical Sciences | | **Subdivision: ** | 104. Mathematics | | **Residency: ** | Resident | | **Living? : ** |
Living
| | **Birth Date: ** | 1953 | | | | | Peter Sarnak is Eugene Higgins Professor of Mathematics at Princeton University and a Professor of Mathematics at the Institute for Advanced Study. He received his Ph.D from Stanford University in 1980 and worked at Stanford and at New York University's Courant Institute prior to his appointment at Princeton. He chaired Princeton's Department of Mathematics from 1996-99 and has received numerous honors for his work, including the Polya Prize (1998), the Ostrowski Prize (2001); the Cole Prize (2005); and the Wolf Prize (2014). Sarnak's work has had an impact on areas ranging from computer science (through his 1988 construction of expander graphs which continues to have an impact) to mathematical physics (where he showed that the chaotic properties of waves on a surface depend on the arithmetic properties of the surface). His use of techniques from one area to address problems in another area has led to the solution of problems that were previously viewed as out of reach. His areas of specialty are analysis and number theory. He is the main pioneer of the powerful idea that number theory (the study of whole numbers, which is apparently a deterministic subject) is governed by the ideas of randomness, such as random matrices and quantum chaos. A very social mathematician, he has served as an advisor for many mathematical departments and institutes, worked with many postdoctoral fellows, and supervised 36 Ph.D. theses. Peter Sarnak is a member of the American Academy of Arts & Sciences (1991); the National Academy of Sciences (2002); and the Royal Society (2002). He was elected a member of the American Philosophical Society in 2008. | |
**38** | **Name: ** | Dr. I. M. Singer | | **Institution: ** | Massachusetts Institute of Technology | | **Year Elected: ** | 1985 | | **Class: ** | 1. Mathematical and Physical Sciences | | **Subdivision: ** | 104. Mathematics | | **Residency: ** | Resident | | **Living? : ** |
Deceased
| | **Birth Date: ** | 1924 | | **Death Date: ** | February 11, 2021 | | | | | Noted for his work with Sir Michael Atiyah on the Atiyah-Singer index theorem, I.M. Singer was Institute Professor of Mathematics Emeritus at the Massachusetts Institute of Technology. He began his teaching career at M.I.T. in 1950 after earning a Ph.D. from the University of Chicago. In addition to spending much of his career at M.I.T, he has also served on the faculties of the University of California, Los Angeles (1952-54), Columbia University (1955), the Institute for Advanced Study (1955-56) and Harvard University (1984-). In his research Dr. Singer has covered deeper analytic properties of partial differential equations on manifold turnout that depend on ideas from differential geometry. He made decisive advances in this direction and applied his understanding of geometry to the use of fiber bundles for Yang-Mills fields, sparking a convergence between theoretical physics and mathematics. Additionally, his spectacular development of the Atiyah-Singer index theorem described how the index of an elliptic differential operator on a compact manifold can be determined by topolotical variance. He has applied these ideas to Yang-Mills fields in stantors and non-abelian theories. Dr. Singer has been honored with the National Medal of Science (1983), the American Mathematical Society's Bocher Prize (1969) and the Steele Prize for Lifetime Achievement (2000) and with membership in the American Academy of Arts & Sciences and the National Academy of Sciences. He has also served as chairman of the NAS Committee on Science and Public Policy (1976-80). He died on February 11, 2021. | |
**39** | **Name: ** | Dr. Shlomo Sternberg | | **Institution: ** | Harvard University | | **Year Elected: ** | 2010 | | **Class: ** | 1. Mathematical and Physical Sciences | | **Subdivision: ** | 104. Mathematics | | **Residency: ** | Resident | | **Living? : ** |
Deceased
| | **Birth Date: ** | 1936 | | **Death Date: ** | 8/23/2024 | | | | | Shlomo Sternberg is one of the foremost differential geometers of his generation and a mathematician who has shaped the subject with his extensive breadth and many scholarly contributions. His papers extend across many subjects, including Lie groups (finite and infinite dimensional), symplectic geometry and mechanics, quantum groups, scattering theory, conformal field theory - the list is long and inclusive of many subjects. He has written several books with V. Guillemin which are foundational references for research mathematicians in several fields, including Geometric Asymptotics (1977), Variations on a Theme by Kepler, (1990), and Symplectic Techniques in Physics (1990), as well as several of the basic graduate texts for students of mathematics and physics. He currently serves as George Putnam Professor of Pure and Applied Mathematics at Harvard University, having joined the Harvard faculty in 1959. He received his Ph.D. in 1956 from Johns Hopkins University. In 1980 he was made a permanent Fellow of the Mortimer and Raymond Sackler Institute of Advanced Studies at Tel Aviv University. He is a member of the American Academy of Arts & Sciences and the National Academy of Sciences and was elected to membership in the American Philosophical Society in 2010. | |
**40** | **Name: ** | Dr. Marshall Stone | | **Institution: ** | University of Chicago & University of Massachusetts | | **Year Elected: ** | 1943 | | **Class: ** | 1. Mathematical and Physical Sciences | | **Subdivision: ** | 104. Mathematics | | **Residency: ** | Resident | | **Living? : ** |
Deceased
| | **Birth Date: ** | 1903 | | **Death Date: ** | 1/9/89 | | | |
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