Noam Elkies

Noam Elkies studied at Harvard University, Columbia University and Stuyvesant High School. The field of work recorded is mathematics, Diophantine geometry and computational number theory. Employment is recorded with Harvard University and Radcliffe College. Distinctions recorded are Putnam Fellow, Cours Peccot, Paul R. Halmos - Lester R. Ford Awards and Packard Fellowship for Science and Engineering.

• Name — Noam Elkies • Born — 25 August 1966 • Birthplace — New York City, US • Fields — Mathematics • Workplaces — Harvard University • Alma Mater — Columbia University (BS 1985) Harvard University (PhD 1987) • Doctoral Advisor — Benedict Gross Barry Mazur • Thesis Title — Supersingular primes of a given elliptic curve over a number field • Thesis Year — 1987 • Doctoral Students — Henry Cohn • Known for — Elliptic curves • Awards — Putnam Fellow Lester R. Ford Award (2004) Levi L. Conant Prize (2004)

Elkies was born to an engineer father and a piano teacher mother. He attended Stuyvesant High School in New York City for three years before graduating in 1982 at age 15. A child prodigy, in 1981, at age 14, Elkies was awarded a gold medal at the 22nd International Mathematical Olympiad, receiving a perfect score of 42, one of the youngest to ever do so. He went on to Columbia University, where he won the Putnam competition at age 16 and four months, making him one of the youngest Putnam Fellows in history. Elkies was a Putnam Fellow twice more during his undergraduate years. He graduated valedictorian of his class in 1985. He then earned his PhD in 1987 under the supervision of Benedict Gross and Barry Mazur at Harvard University. From 1987 to 1990, Elkies was a junior fellow of the Harvard Society of Fellows.

In 1987, Elkies 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. His work on these and other problems won him recognition and a position as an associate professor at Harvard in 1990. In 1993, Elkies was made a full, tenured professor at age 26. This made him the youngest full professor in Harvard's history. He and A. O. L. Atkin 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. He has discovered many new patterns in Conway's Game of Life and has studied the mathematics of still life patterns in that cellular automaton rule. Elkies is an associate of Harvard's Lowell House. 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. 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). In August 2024, he posted to a number theory listserv that he and Zev Klagsbrun had found an elliptic curve of rank at least 29 by methods similar to those used to find the rank 28 example.

Elkies is a bass-baritone and formerly played 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 his "gifted musicality, superior musicianship and sight-reading ability". He rings the bells of Lowell House.

Elkies is a composer and solver of chess problems (winning the 1996 World Chess Solving Championship). One of his problems appears in the chess trainer Mark Dvoretsky's book Dvoretsky's Endgame Manual. Elkies holds the title of National Master from the United States Chess Federation, but no longer plays competitively.

Noam Elkies worked in mathematics, Diophantine geometry and computational number theory. He was employed by Harvard University and Radcliffe College. He belonged to National Academy of Sciences.