Noam D. Elkies (born 1966 in New York City) is a mathematician. While an undergraduate at Columbia University, he was a three-time Putnam Fellow. He won the 1982 competition at the age of sixteen years and four months, making him possibly the youngest Putnam Fellow in history. After graduating as valedictorian, he earned his Ph.D. under supervision of Benedict Gross and Barry Mazur at Harvard University.

Richard Phillips Feynman was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. For his work on quantum electrodynamics, Feynman was a joint recipient of the Nobel Prize in Physics in 1965, …

Ravi D. Vakil (born February 22, 1970, Toronto, Ontario, Canada) is a Canadian-American mathematician. Vakil attended high school at Martingrove Collegiate Institute in Etobicoke, Ontario, where he won several mathematical contests and olympiads. After earning a BSc and MSc from the University of Toronto in 1992, he completed a Ph.D. in mathematics at Harvard University in 1997. He has since been an instructor at both Princeton University and MIT.

Don Coppersmith is a cryptographer and mathematician. He was involved in the design of the Data Encryption Standard block cipher at IBM, particularly the design of the S-boxes, strengthening them against differential cryptanalysis. He has also worked on algorithms for computing discrete logarithms, the cryptanalysis of RSA, methods for rapid matrix multiplication (see Coppersmith-Winograd algorithm) and IBM's MARS cipher.

Arthur L. Rubin is an American mathematician who has earned a place among the five top-ranked undergraduate competitors (who are themselves not ranked against each other) in the William Lowell Putnam Competition four times (1970–73), a feat matched by only six other undergraduate students since the first competition in 1938. His mother was J. E. H. Rubin, Professor of Mathematics at Purdue University for over 35 years, and his father, H. Rubin, …

John Willard Milnor (b. February 20, 1931 in Orange, New Jersey) is an American mathematician known for his work in differential topology, K-theory, and dynamical systems, and for his influential books, which are widely considered to be examples of fine mathematical writing. He won the Fields Medal in 1962. As of 2005, John Milnor is a distinguished professor at the State University of New York at Stony Brook. His wife, Dusa McDuff, is also a professor at Stony Brook.

Kenneth Geddes Wilson (born June 8, 1936) is an American theoretical physicist. As an undergraduate at Harvard, he was a Putnam Fellow. He earned his PhD from Caltech in 1961, studying under Murray Gell-Mann. He joined Cornell University in 1963 in the Department of Physics as a junior faculty member, becoming a full professor in 1970. His brother David is also a Professor at Cornell in the department of Molecular Biology and Genetics.

Irving Kaplansky was a Canadian mathematician. He was born in Toronto, Ontario, Canada and attended the University of Toronto as an undergraduate. After receiving his PhD from Harvard as Saunders Mac Lane's first student, Kaplansky was professor of mathematics at the University of Chicago from 1945 to 1984. He was chair of the department from 1962 to 1967. "Kap," as his friends and colleagues called him, made major contributions to group theory, ring theory, …

David Bryant Mumford (born 11 June 1937) is an American mathematician known for distinguished work in algebraic geometry, and then for research into vision and pattern theory. He is currently a University Professor in the Division of Applied Mathematics at Brown University, having previously had a long academic career at Harvard University.

Melanie Matchett Wood, born 1981 in Indianapolis, Indiana, is a graduate student mathematician currently studying at Princeton University. She has set numerous "firsts" as a woman in the area of mathematics.

Reid W. Barton is currently a graduate student at Harvard University in mathematics, and one of the all-time greatest performers in the International Science Olympiads. Barton was the first student to ever win four gold medals at the International Mathematical Olympiad, culminating in full-marks at the 2001 Olympiad held in Washington, D.C., shared only with fellow American Gabriel Carroll and Chinese teammates Xiao Liang and Zhang Zhiqiang.

Eugenio Calabi (born 1923) is an Italian-American mathematician and professor emeritus at the University of Pennsylvania, specializing in differential geometry, partial differential equations and their applications. Professor Calabi was a Putnam Fellow as an undergraduate at MIT in 1946. In 1950 he received his Ph.D. from Princeton University, where his advisor was Salomon Bochner. He later obtained a professorship at the University of Minnesota.

Abhinav Kumar is a mathematician, who works in algebraic geometry and number theory. He received his S.B. (2002) in mathematics, physics, and computer science from MIT, and his Ph.D. (2006) from Harvard University, where he studied under Barry Mazur and Noam Elkies. He is a twice Putnam fellow and has an Erdős number of 3. He works on sphere packing in high dimensions.

Gabriel D. Carroll is a recent graduate of Harvard who received numerous awards in mathematics while a student. Carroll won two gold medals (1998, 2001) and a silver medal (1999) at the International Mathematical Olympiad, earning a perfect score at the 2001 International Mathematical Olympiad held in Washington, D.C., shared only with American teammate Reid Barton and Chinese teammates Liang Xiao and Zhiqiang Zhang.

Neal Koblitz is a Professor of Mathematics at the University of Washington in the Department of Mathematics. He is also an adjunct professor with the Centre for Applied Cryptographic Research. He is the creator of hyperelliptic curve cryptography and the independent co-creator of elliptic curve cryptography. Professor Koblitz received his undergraduate degree from Harvard University, where he was a Putnam Fellow, in 1968.

Peter W. Shor (born August 14, 1959) is an American theoretical computer scientist most famous for his work on quantum computation, in particular for devising a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical computer (see Shor's algorithm). He was working then at AT&T Bell Laboratories in 1994. Currently, he is a professor of applied mathematics at MIT, …

Daniel Grey ("Dan") Quillen (born June 21, 1940) is an American mathematician and a Fields Medalist. From 1984 to 2006 he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. He is renowned for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978.

Barry Simon is an eminent American mathematical physicist and the IBM Professor of Mathematics and Theoretical Physics at Caltech, known for his prolific contributions in spectral theory, functional analysis, and nonrelativistic quantum mechanics (particularly Schrödinger operators), including the connections to atomic and molecular physics. He has authored more than 300 publications on mathematics and physics.

Miller Puckette received his B.S. in mathematics from MIT in 1980. As an undergraduate he was the top scorer in the 1979-1980 William Lowell Putnam mathematics competition. He was awarded Putnam and NSF fellowships for graduate study at Harvard, where he finished his Ph.D. in 1986. From 1979 through 1986 Puckette also studied computer music at the MIT Media Lab, specializing in real-time techniques for live music performance.

Elwyn Ralph Berlekamp (born September 6, 1940 in Dover, Ohio, United States) is a professor of mathematics at the University of California, Berkeley. He is known for his work in information theory and combinatorial game theory. As an undergraduate at MIT, he was a Putnam Fellow in 1961. He completed his Bachelor's and Master's degrees in electrical engineering in 1962.

Melvin Hochster is an eminent American mathematician, regarded as one of the leading commutative algebraists active today. He is currently the Jack E. McLaughlin Distinguished University Professor of Mathematics at the University of Michigan. Hochster attended Stuyvesant High School, where he was captain of the Math Team, and received a B.A. from Harvard University. While at Harvard, he was a Putnam Fellow in 1960. He earned his Ph.D. in 1967 from Princeton University, …

Stephen L. Adler (b. 1939 in New York City) is an American physicist specializing in elementary particles and field theory. He received an A.B. degree at Harvard University in 1961 and a Ph.D. from Princeton University in 1964. He became a member of the Institute for Advanced Study in 1966, becoming a full Professor of Theoretical Physics in 1969, and was named "New Jersey Albert Einstein Professor" at the institute in 1979.

Jeffrey C. Lagarias is a professor at the University of Michigan. He was a Putnam Fellow in 1970. He received his Ph.D. in Mathematics from Massachusetts Institute of Technology in 1974. In 1975 he joined AT&T Bell Laboratories and eventually became Distinguished Member of Technical Staff. Since 1995, he has been a Technology Consultant at AT&T Research Laboratories. While his recent work has been in theoretical computer science, …

Arthur Pentland Dempster is a Professor Emeritus in the Harvard University Department of Statistics. He was one of four faculty when the department was founded in 1957. He was a Putnam Fellow in 1951. He obtained his Ph.D. from Princeton University in 1956. His thesis, titled "The two-sample multivariate problem in the degenerate case", was written under the supervision of John Tukey.

William Aaron Nierenberg (1919 - 2000) was an American physicist and the director of the Scripps Institution of Oceanography from 1965 through 1986. A building on that campus is named after him, as is the Nierenberg Prize.

Roger Evans Howe is the William R. Kenan Jr. Professor of Mathematics at Yale University. He is well-known for his contributions to Representation theory. He attended Harvard University as an undergraduate, winning the William Lowell Putnam Mathematical Competition in 1964. He obtained his Ph.D. from University of California, Berkeley in 1969. His thesis, titled "On representations of nilpotent groups", was written under the supervision of Calvin Moore.

George Whitelaw Mackey (born February 1, 1916 in St. Louis, Missouri, died March 15, 2006 in Belmont, Massachusetts) was an American mathematician. Mackey obtained his Ph.D. at Harvard University in 1942 under the direction of Marshall H. Stone. He joined the Harvard University Mathematics Department in 1943, was appointed Landon T. Clay Professor of Mathematics and Theoretical Science in 1969 and remained there until he retired in 1985.

Robert L. Mills (April 15, 1927 - October 27, 1999) was a physicist, specializing in quantum field theory, the theory of alloys, and many-body theory. While sharing an office at Brookhaven National Laboratory, in 1954, Chen Ning Yang and Mills proposed a tensor equation for what are now called Yang-Mills fields. This equation reduces to Maxwell's Equations as a special case, …

Don Bernhard Zagier is a German mathematician. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany, and a professor at the "Collège de France" in Paris, France. He was born in Heidelberg, Germany. He grew up in the United States, and studied for three years at M.I.T., completing his bachelor's and master's degree and being named a Putnam Fellow in 1967 at the age of 16.

Richard C. Schroeppel is an American mathematician born in Illinois. His research has included magic squares, elliptic curves, and cryptography. In 1973 he discovered the number of 5x5 normal magic squares, and in 1998–1999 he designed the Hasty Pudding Cipher which was a candidate for the Advanced Encryption Standard. His Erdős number is 2.