Noam Elkies

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Noam Elkies
Noam Elkies.jpg
Noam Elkies in 2007
Born (1966-08-25) August 25, 1966 (age 56)
New York City, US
Alma materColumbia University, B.S. (1985)
Harvard University, Ph.D. (1987)
AwardsPutnam Fellow
Lester R. Ford Award (2004)
Levi L. Conant Prize (2004)
Scientific career
InstitutionsHarvard University
ThesisSupersingular primes of a given elliptic curve over a number field (1987)
Doctoral advisorBenedict Gross
Barry Mazur
Doctoral studentsHenry Cohn[1]

Noam David Elkies (born August 25, 1966) is a professor of mathematics at Harvard University. At the age of 26, he became the youngest professor to receive tenure at Harvard. He is also a pianist,[2] chess national master and a chess composer.

Early life[edit]

Elkies was born to an engineer father and a piano teacher mother.[3] He attended Stuyvesant High School in New York City for three years[4] before graduating in 1982 at age 15.[5][6] A child prodigy in 1981, at age 14, he was awarded a gold medal at the 22nd International Mathematical Olympiad, receiving a perfect score of 42,[7] one of the youngest to ever do so. He went on to Columbia University, where he won the Putnam competition at the age of sixteen years and four months, making him one of the youngest Putnam Fellows in history.[8] He was a Putnam Fellow two more times during his undergraduate years.[9] He graduated valedictorian of his class in 1985.[10] He then earned his PhD in 1987 under the supervision of Benedict Gross and Barry Mazur at Harvard University.[11]

From 1987 to 1990 he was a junior fellow of the Harvard Society of Fellows.[12]

Work in mathematics[edit]

In 1987, he proved that an elliptic curve over the rational numbers is supersingular at infinitely many primes. In 1988, he found a counterexample to Euler's sum of powers conjecture for fourth powers.[13] His work on these and other problems won him recognition and a position as an associate professor at Harvard in 1990.[5] In 1993, he was made a full, tenured professor at the age of 26. This made him the youngest full professor in the history of Harvard.[14] Along with A. O. L. Atkin he extended Schoof's algorithm to create the Schoof–Elkies–Atkin algorithm.

Elkies also studies the connections between music and mathematics; he is on the advisory board of the Journal of Mathematics and Music.[15] He has discovered many new patterns in Conway's Game of Life[16] and has studied the mathematics of still life patterns in that cellular automaton rule.[17] Elkies is an associate of Harvard's Lowell House.[18]

Elkies is one of the principal investigators of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation, a large multi-university collaboration involving Boston University, Brown, Dartmouth, Harvard, and MIT.[19]

Elkies is the discoverer (or joint-discoverer) of many current and past record-holding elliptic curves, including the curve with the highest-known lower bound (≥28) on its rank, and the curve with the highest-known exact rank (=20).[20][21]


Elkies is a bass-baritone and plays the piano for the Harvard Glee Club. Jameson N. Marvin, former director of the Glee Club, compared him to "a Bach or a Mozart," citing "[h]is gifted musicality, superior musicianship and sight-reading ability."[22]


Elkies is a composer and solver of chess problems (winning the 1996 World Chess Solving Championship).[14] One of his problems is used by the famed chess trainer Mark Dvoretsky in his book "Dvoretsky's Endgame Manual".[23] He holds the title of National Master from the United States Chess Federation, but he no longer plays competitively.[24]

Awards and honors[edit]

In 1994 he was an invited speaker at the International Congress of Mathematicians in Zurich.[25] In 2004 he received a Lester R. Ford Award[26] and the Levi L. Conant Prize.[27] In 2017 he was elected to the National Academy of Sciences.[28]


  1. ^ "Henry Cohn: Adjunct Professor, Discrete Mathematics". Massachusetts Institute of Technology, Department of Mathematics. Retrieved 10 August 2018.
  2. ^ "Piano Recital with Young Hyun Cho and Noam Elkies". 2018.
  3. ^ McClain, Dylan Loeb (2010-08-28). "Skilled at the Chessboard, Keyboard and Blackboard". The New York Times. ISSN 0362-4331. Retrieved 2020-09-11.
  4. ^ Altman, Daniel (9 February 1995). "Math and Music: For the Moment". The Harvard Crimson. Elkies spent eight years of his youth in Israel, and he came to New York City having read a Hebrew translation of Euclid but without any significant knowledge of English.
  5. ^ a b Elkies, Noam D. "CV". Noam Elkies. Department of Mathematics, Harvard University. Retrieved 10 August 2018.
  6. ^ Castillo, Tom (April 20, 2000). "Fifteen Minutes: Gnoshin' with Noam". The Harvard Crimson.
  7. ^ Noam Elkies's results at International Mathematical Olympiad
  8. ^ Gallian, Joseph A. "The Putnam Competition from 1938–2006" (PDF). Archived from the original (PDF) on 2006-11-13. Retrieved 2007-10-31.
  9. ^ "Putnam Competition Individual and Team Winners". Mathematical Association of America. Retrieved 5 March 2019.
  10. ^ Columbia College (Columbia University). Office of Alumni Affairs and Development; Columbia College (Columbia University) (1987). Columbia College today. Columbia University Libraries. New York, N.Y. : Columbia College, Office of Alumni Affairs and Development.
  11. ^ Noam Elkies at the Mathematics Genealogy Project
  12. ^ "Harvard University. Society of Fellows. Current and Former Junior Fellows". Archived from the original on 2013-01-16. Retrieved 2013-01-16.
  13. ^ "Mathematicians Find New Solutions To An Ancient Puzzle". 2008.
  14. ^ a b McClain, Dylan Loeb (August 28, 2010), "Skilled at the Chessboard, Keyboard and Blackboard", The New York Times
  15. ^ "Editorial Board of Mathematics and Music".
  16. ^ Game of Life Status page, Jason Summers.
  17. ^ Elkies, Noam D. (1998). "Voronoi's Impact on Modern Science, Book I". Proc. Inst. Math. Nat. Acad. Sci. Ukraine. 21: 228–253. arXiv:math.CO/9905194.
  18. ^ "Lowell House: SCR". Retrieved 2009-07-27.[dead link]
  19. ^ "Principal Investigators". Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation. Brown University. Retrieved 2018-09-17.
  20. ^ Dujella, Andrej. "History of elliptic curves rank records". Retrieved 30 March 2020.
  21. ^ Elkies, Noam. "New records for ranks of elliptic curves with torsion". NMBRTHRY Archives. Retrieved 30 March 2020.
  22. ^ Morantz, Alison D. (November 30, 1988). "Music + Math: A Common Equation?". The Harvard Crimson.
  23. ^ Mark Dvoretsky: Dvoretsky's Endgame Manual, 4th Edition 2014. Russell Enterprises, Milford, CT. ISBN 978-1-941270-04-2. Chapter 1: Pawn Endings.
  24. ^ Noam D Elkies rating card, USCF
  25. ^ "International Mathematical Union (IMU)". Archived from the original on 2011-09-27.
  26. ^ "Paul R. Halmos – Lester R. Ford Awards". Mathematical Association of America. Retrieved 10 August 2018.
  27. ^ "2004 Conant Prize" (PDF), Notices of the American Mathematical Society, 51 (4): 433–434, April 2004
  28. ^ National Academy of Sciences Members and Foreign Associates Elected, National Academy of Sciences, May 2, 2017.

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