American Philosophical Society
Member History

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104. Mathematics[X]
1Name:  Professor Vladimir I. Arnold
 Institution:  Steklov Institute of Mathematics & Academy of Sciences, Russia & CEREMADE, University of Paris, Dauphine, France
 Year Elected:  1990
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  International
 Living? :   Deceased
 Birth Date:  1937
 Death Date:  June 3, 2010
   
 
Vladimir Arnold was born in 1937 in Odessa (then U.S.S.R, presently Ukraine). One of the most distinguished mathematicians in the world, he was educated at Moscow State University and became famous at age 19 for his brilliant solution to Hilbert's 13th problem. In this solution, Dr. Arnold was able to prove that each continuous function of three variables is representable as a super position of continuous functions of two variables -- the exact opposite of what people expected. Dr. Arnold is also one of the founders of KAM theory. In this theory, if one perturbs a completely integratable Hamiltonian system the resulting system still possesses infinitely many invariant tori. The theory has many applications in celestial mechanics and plasma physics, among other fields. In his examination of infinite dimensional Hamiltonian systems, Dr. Arnold studied the Euler equations of ideal gas flow as equations of geodesics on an infinite dimensional lie group of smooth volume preserving transformation. He has conducted path-breaking work on singularity theory and its use in caustics and wave fronts, discovering connections with regular polyhedra and crystallographic symmetry groups - fundamental work connecting real algebraic topology and modern topology and in symplectic and variational problems. The author of a number of outstanding textbooks, Dr. Arnold held professorial positions at Moscow State University for twenty-five years. At present he teaches at Steklove Mathematical Institute in Moscow and the Universite Paris 9. He is a member of the American Academy of Arts & Sciences, the French Academy of Science and the Royal Society of London, among others. He is the recipient of many awards, including the 1982 Crafoord Prize of the Swedish Academy, the 2001 Dannie Heineman Prize for Mathematical Physics, the 2001 Wolf Prize in Mathematics, the 2007 State Prize of the Russian Federation and the 2008 Shaw Prize in Mathematical Sciences.
 
2Name:  Sir Michael Atiyah
 Institution:  University of Edinburgh
 Year Elected:  1991
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  International
 Living? :   Deceased
 Birth Date:  1929
 Death Date:  January 11, 2019
   
 
One of the greatest mathematicians of his times, Sir Michael Atiyah made fundamental contributions to many areas of mathematics, but especially to topology, geometry and analysis. From his first major contribution - topological K-theory - to his later work on quantum field theory, Sir Michael has been influential in the development of new theoretical tools and has supplied far-reaching insights. He was a notable collaborator, with his name linked with other oustanding mathematicians through their joint research. He was awarded a Fields Medal in 1966 and was President of the Royal Society and Master of Trinity College, Cambridge. A superb lecturer, he possesses the ability to explain sophisticated mathematics in a simple geometric way. Formerly a professor at both Oxford and Cambridge Universities and the Institute for Advanced Study, he was an inspiring teacher who instructed an outstanding group of former students. Sir Michael Atiyah was the recipient of many honors and awards, including election as a Fellow of the Royal Society in 1962, a knighthood in 1983 and the Order of Merit in 1992. He served as Chancellor of the University of Leicester from 1995-2005, as President of the Royal Society London from 1990-1995, as President of the Royal Society of Edinburgh from 2005-2008, and was later an Honorary Professor at Edinburgh University in Scotland. In 1993 he was awarded the American Philosophical Society's Benjamin Franklin Medal for Distinguished Achievement in the Sciences. The citation read "in recognition of significant contributions to a remarkable range of mathematical topics, which established links between differential geometry, topology, and analysis; and creating useful mathematical tools for physicists." Sir Michael Atiyah died on January 11, 2019 at the age of 89.
 
3Name:  Dr. Lipman Bers
 Institution:  Columbia University
 Year Elected:  1980
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Deceased
 Birth Date:  1914
 Death Date:  10/29/93
   
4Name:  Dr. Garrett Birkhoff
 Institution:  Harvard University
 Year Elected:  1960
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Deceased
 Birth Date:  1911
 Death Date:  11/22/96
   
5Name:  Dr. David Blackwell
 Institution:  University of California, Berkeley
 Year Elected:  1990
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Deceased
 Birth Date:  1919
 Death Date:  July 8, 2010
   
 
David Blackwell was professor of statistics and mathematics at the University of California, Berkeley from 1954 until his retirement in 1989, when he was named Professor Emeritus of Statistics. He also held positions at Southern University, Clark College and Howard University and worked for the RAND Corporation between 1948 and 1950, where he developed an interest in game theory. His research contributions combine great breadth with deep creativity, and in several areas his work set the course for subsequent research. He was one of the first major contributors in the field of sequential analysis, a subject that is of wide practical interest, and his analysis of Bayesian sequential procedures had a major impact on further developments in this field. His work on the theory of dynamic programming was central to the development of this immensely practical and widely applicable field. Dr. Blackwell has served as president of the Institute of Mathematical Statistics and has also been vice president of the American Statistical Association, the International Statistical Institute and the American Mathematical Society. In 1965 he became the first African American named to the National Academy of Sciences. Dr. Blackwell is the recipient of numerous honors, including the von Neumann Theory Prize, and is a member of the American Academy of Arts & Sciences. He died on July 8, 2010, in Berkeley, at age 91.
 
6Name:  Dr. Armand Borel
 Institution:  Institute for Advanced Study
 Year Elected:  1985
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  International
 Living? :   Deceased
 Birth Date:  1923
 Death Date:  August 11, 2003
   
7Name:  Dr. Shiing-shen Chern
 Institution:  University of California, Berkeley
 Year Elected:  1989
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Deceased
 Birth Date:  1911
 Death Date:  December 3, 2004
   
8Name:  Dr. Paul J. Cohen
 Institution:  Stanford University
 Year Elected:  1972
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Deceased
 Birth Date:  1934
 Death Date:  March 23, 2007
   
9Name:  Sir David Cox
 Institution:  Nuffield College, Oxford
 Year Elected:  1990
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  International
 Living? :   Living
 Birth Date:  1924
   
 
A statistician of considerable distinction, Sir David Cox has been instrumental in the exploration and expansion of statistical methodology. The new methods and formations he has proposed include: discrimination between non-contagious families of distributions (1961); databased choice of transformations (1964); and introduction of the Cox model of survival analysis (1972). He received his Ph.D. from the University of Leeds in 1949 and has taught at the University of Cambridge (assistant lecturer, 1950-55) , Birkbeck College (reader in and professor of statistics, 1956-66) and the Imperial College of Science and Technology (professor of statistics, 1966-88, and head of the math department, 1970-74). Currently affiliated with the Department of Statistics, University of Oxford, where he is also an Honorary Fellow of Nuffield College, Sir David also served as Warden of the College from 1988-94. His academic awards include the Guy Medal in Silver and Guy Medal in Gold, both from the Royal Statistical Society; the Weldon Memorial Prize, University of Oxford; the Kettering Prize and Gold Medal for Cancer Research; the Max Planck Forschungspreise; the International Prize in Statistics (2016); and the BBVA Foundations Frontiers of Knowledge Award in the Basic Sciences (2017).
 
10Name:  Dr. Ingrid Daubechies
 Institution:  Duke University
 Year Elected:  2003
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Living
 Birth Date:  1954
   
 
Ingrid Daubechies is a mathematician who has worked primarily on mathematical foundations of quantum theory, but she is best known for her important work on wavelets. "Wavelets" are signal components used in the efficient transmission of compressed data. Wavelet theory provides the essential background for many practical applications including speech transmission, high-density TV, and recent animated movies such as "A Bug's Life." According to a recent National Academy of Sciences report, Dr. Daubechies' work "...turn(ed) the theory into a practical tool that can be easily programmed..." An excellent speaker, Dr. Daubechies has recently been active in mathematics education, serving on the Mathematics and Science Education Board and with the Center for Science, Mathematics, and Engineering Education. Born in Belgium, she earned her Ph.D. from Virge University in 1980 and was a professor of mathematics at Princeton University 1993-2011. She joined the faculty of Duke University as Professor of Mathematics in January 2011. She became a John Simon Guggenheim Memorial Foundation Fellow in 2010 and won the 2011 Benjamin Franklin Medal in Electrical Engineering from the Franklin Institute.
 
11Name:  Dr. Pierre Deligne
 Institution:  Institute for Advanced Study
 Year Elected:  2009
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Living
 Birth Date:  1944
   
 
Pierre Deligne has been a professor at the Institute for Advanced Study in Princeton since 1984. He is the world's leading algebraic geometer, having received his Doctorat en mathématiques from the University of Brussels in 1968 and his Doctorat d'Etat des Sciences Mathématiques from the University of Paris-Sud in 1972. The methods he introduced have so completely permeated the subject that a large portion of the current research in algebraic geometry can't even be formulated without them. Consequently, his research is constantly referred to by young workers in the field. So far as is known, Deligne is the only mathematician in history to be commemorated by a postage stamp during his lifetime (.70 Euro, Belgium). He was awarded the Fields Medal in 1978, the Crafoord Prize in 1998, the Balzan Prize in Mathematics in 2004, the Wolf Prize in 2008, and the Able prize in 2013. He belongs to the Académie des Sciences, Paris (1978), the American Academy of Arts & Sciences (1978), the National Academy of Sciences (2007), and the Royal Swedish Academy of Sciences (2009).
 
12Name:  Dr. Persi Diaconis
 Institution:  Stanford University
 Year Elected:  2005
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Living
 Birth Date:  1945
   
 
Persi Diaconis works at the interface between mathematics and statistics. He studies problems such as "how many times should a deck of cards be shuffled to mix it up?" (The answer is about seven.) Related problems are determining relaxation times for natural mixing processes in Monte Carlo sampling. His work uses probability theory, group theory and combinatorics. He also works hard at trying to make common (and mathematical) sense out of recent statistical procedures. He is well-known as a debunker of pseudo-science and through his former life as a professional magician.
 
13Name:  Dr. David L. Donoho
 Institution:  Stanford University
 Year Elected:  2019
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Living
 Birth Date:  1957
   
 
David L. Donoho is currently Professor of Statistics and Anne T. and Robert M. Bass Professor in the Humanities and Sciences at Stanford University. He earned his Ph.D. from Harvard University in 1984. Prior to moving to Stanford, he worked for a decade at the University of California, Berkeley. Dramatic developments in technology present fundamental new challenges in theoretical and applied mathematical statistics. David Donoho has played a major role in building powerful new mathematical and statistical tools to deal with these problems, ranging from how best to extract information from large data-sets in high dimensions to how to deal with contamination by noise. His work provides fast, efficient, and often optimal algorithms that are founded on rigorous mathematical analysis. He introduced many now standard techniques that overcome difficulties caused by noise with very little loss of efficiency or reliability. Along the way, he demonstrated the power of the mathematical theory of wavelets in dealing with such problems in statistics. He also developed efficient techniques for sparse representation and recovery in large data-sets. Among his awards are a MacArthur Fellowship in 1991, the John von Neumann Prize of the Society for Industrial and Applied Mathematics (SIAM) in 2001, the Weiner Prize of AMS-SIAM in 2011, and the Shaw Prize in 2013. He is a member of the National Academy of Sciences (1998), French Academy of Sciences (2009), and the American Academy of Arts & Sciences (2012). David Donoho was elected a member of the American Philosophical Society in 2019.
 
14Name:  Dr. Andrei N. Kolmogorov
 Year Elected:  1961
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  International
 Living? :   Deceased
 Birth Date:  1903
 Death Date:  10/20/87
   
15Name:  Dr. André Weil
 Institution:  Institute for Advanced Study
 Year Elected:  1995
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  International
 Living? :   Deceased
 Birth Date:  1906
 Death Date:  8/6/98
   
16Name:  Dr. Andrew J. Wiles
 Institution:  University of Oxford
 Year Elected:  1997
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Living
 Birth Date:  1953
   
 
Andrew Wiles is currently Royal Society Research Professor at Oxford University. He was a professor at Princeton from 1994 to 2011. Dr. Wiles has made major breakthroughs in the study of rational elliptic curves associated with modular forms and is most famous for proving Fermat's Last Theorem, which for 350 years stood as a "Mount Everest" of mathematics. He was introduced to the theorem at age ten and tried to prove it during his youth before stopping to study elliptic curves during his graduate studies. He eventually dedicated eight years to the proof, announcing a solution on June 23, 1993 at the conclusion of a lecture at the Isaac Newton Institute in Cambridge, England. When mathematicians raised questions about his proof, Dr. Wiles himself noticed a flaw, which sent him back to work for nearly a year. In October 1994, he unveiled his revised proof, which has been confirmed by experts in the field. For his efforts, Dr. Wiles has received, among other awards, the Schock Prize (1995), the Cole Prize (1996), the Royal Medal (1996), the Wolf Prize (1996), the Clay Research Award (1999) and a silver plaque from the International Mathematics Union recognizing his achievements. He earned his BA degree from Merton College, Oxford University in 1974 and his Ph.D. from Clare College, Cambridge University in 1980. In 2000 he was named a Knight of the British Empire.
 
17Name:  Dr. Charles L. Fefferman
 Institution:  Princeton University
 Year Elected:  1988
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Living
 Birth Date:  1949
   
 
Charles Fefferman has been professor of mathematics at Princeton University since 1974. After earning his Ph.D. from Princeton at the age of 20, he joined the faculty of the University of Chicago, becoming in 1971 the youngest full professor at an American university. In 1974 he returned to Princeton. Winner of the Fields Medal, Dr. Fefferman has obtained results of unusual depth in several fields of classical analysis: Fourier analysis; the general theory of linear partial differential equations; and the theory of holomorphic mappings and pseudoconvex domains in several complex variables. He is a member of the American Academy of Arts & Sciences and the National Academy of Sciences.
 
18Name:  Dr. Ralph Edward Gomory
 Institution:  Alfred P. Sloan Foundation; NYU Stern
 Year Elected:  1985
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Living
 Birth Date:  1929
   
 
Ralph E. Gomory served as President of the Alfred P. Sloan Foundation from June 1989 to January 2008. He now serves as Director of Special Programs. Dr. Gomory received his B.A. from Williams College in 1950, studied at Cambridge University and received his Ph.D. in mathematics from Princeton University in 1954. He served in the U.S. Navy from 1954 to 1957. Dr. Gomory was Higgins Lecturer and Assistant Professor at Princeton University from 1957 to 59. He joined the Research Division of IBM in 1959, was named IBM Fellow in 1964, and became Director of the Mathematical Sciences Department in 1965. He was made IBM Director of Research in 1970 a position he held until 1986, becoming IBM Vice President in 1973 and Senior Vice President in 1985. In 1986 he became IBM Senior Vice President for Science and Technology, a position which he held until 1989 when he retired from IBM. Dr. Gomory is a member of both the National Academies of Science and of Engineering. He has been awarded a number of honorary degrees and prizes including the Lanchester Prize in 1963; the John von Neumann Theory Prize in 1984; the IEEE Engineering Leadership Recognition Award in 1988; the National Medal of Science in 1988; the Arthur M. Bueche Award of the National Academy of Engineering in 1993; the Heinz Award for Technology, the Economy and Employment in 1998; the Madison Medal Award of Princeton University in 1999; and the Sheffield Fellowship Award of the Yale University Faculty of Engineering in 2000. He was named to the President's Council of Advisors on Science and Technology in 1990 and served to March 1993. Dr. Gomory has been an American Philosophical Society member since 1985.
 
19Name:  Dr. William Timothy Gowers
 Institution:  University of Cambridge & Trinity College
 Year Elected:  2010
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  International
 Living? :   Living
 Birth Date:  1963
   
 
Early in his career, Timothy Gowers did outstanding work in abstract Banach space theory, a theory which involves sets which are operators or functions. In a series of brilliant papers, he solved several long-standing problems, introducing extensive use of methods from combinatorial number theory. One of his surprising results is the construction of a Banach space with almost no symmetry. He is now better known to the broad mathematical community by his later work in combinatorial number theory. His very original ideas (for example "Gowers norms"), led to a new proof of Szmeredi's theorem, which concerns the occurrence of arithmetic progressions in sets of integers. His ideas have led to many breakthroughs in the field, in particular concerning the occurrence of arithmetic progressions in the primes (a longstanding conjecture of Erdos and now a theorem of Gowers’ students Ben Green and Terry Tao.) He continues to lead the research in this combinatorial number theory, which is now having impact on and benefiting computer science. Gowers has also put much effort into bringing mathematics to the public in his writing which includes his book Mathematics: A Very Short Introduction (2002) and his many public lectures. He recently organized the writing of The Princeton Companion to Mathematics (2008). This is a book of over 1,000 pages, incorporating sections by over 100 of the world's best mathematicians. It is aimed at giving anyone with some undergraduate training in mathematics a taste of current knowledge in all of modern mathematics. This kind of contribution, by one of the world's leading researchers at the height of his productive years, is very unusual.
 
20Name:  Dr. Phillip A. Griffiths
 Institution:  Institute for Advanced Study; University of Miami
 Year Elected:  1992
 Class:  1. Mathematical and Physical Sciences
 Subdivision:  104. Mathematics
 Residency:  Resident
 Living? :   Living
 Birth Date:  1938
   
 
Phillip A. Griffiths is Professor Emeritus at the Institute for Advanced Study's School of Mathematics. He holds a Ph.D. from Princeton University and has served on the faculties of the University of California, Berkeley (1964-67), Harvard University (1967-83)and Duke University (1983-91). Dr. Griffiths's mathematical research is in geometry. He and his collaborators initiated the theory of variation of Hodge structure, which has come to play a central role in many aspects of algebraic geometry and the uses of that subject in modern theoretical physics. In addition to algebraic geometry, Dr. Griffiths has made contributions to differential and integral geometry, geometric function theory and the geometry of partial differential equations. Past Director of the Institute for Advanced Study (1991-2003), Dr. Griffiths leads the Millennium Science Initiative (MSI) whose primary goal is to create and nurture world-class science and scientific talent in the developing world. He is a member of the National Academy of Sciences and the recipient of numerous awards, including the American Mathematical Society's LeRoy P. Steele Prize (1972, 2013), the Gottingen Academy of Sciences's Dannie Heineman Prize (1979); the Wolf Prize (jointly with Pierre Deligne and David Mumford, 2008); the Royal Dutch Mathematical Society's Brouwer Prize (2008); and the Chern Medal (2014).
 
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