Noam Elkies

Encyclopedia

**Noam David Elkies**is an American mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

and chess master.

At age 14, Elkies received a gold medal with a perfect score at the International Mathematical Olympiad

International Mathematical Olympiad

The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980...

, the youngest ever to do so. Elkies graduated from Stuyvesant High School

Stuyvesant High School

Stuyvesant High School , commonly referred to as Stuy , is a New York City public high school that specializes in mathematics and science. The school opened in 1904 on Manhattan's East Side and moved to a new building in Battery Park City in 1992. Stuyvesant is noted for its strong academic...

in 1982 and went on to Columbia University

Columbia University

Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...

, 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. He was a Putnam Fellow

William Lowell Putnam Mathematical Competition

The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students of the United States and Canada, awarding scholarships and cash prizes ranging from $250 to $2,500 for the top students and $5,000...

two more times during his undergraduate years. After graduating as valedictorian

Valedictorian

Valedictorian is an academic title conferred upon the student who delivers the closing or farewell statement at a graduation ceremony. Usually, the valedictorian is the highest ranked student among those graduating from an educational institution...

at age 18, summa in Mathematics and Music, he earned his Ph.D., at age 20, under supervision of Benedict Gross

Benedict Gross

Benedict Hyman Gross is an American mathematician, the George Vasmer Leverett Professor of Mathematics at Harvard University and former Dean of Harvard College....

and Barry Mazur

Barry Mazur

-Life:Born in New York City, Mazur attended the Bronx High School of Science and MIT, although he did not graduate from the latter on account of failing a then-present ROTC requirement. Regardless, he was accepted for graduate school and received his Ph.D. from Princeton University in 1959,...

at Harvard University

Harvard University

Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...

.

In 1987, he proved that an elliptic curve

Elliptic curve

In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety — that is, it has a multiplication defined algebraically with respect to which it is a group — and O serves as the identity...

over the rational numbers is supersingular

Supersingular prime (for an elliptic curve)

In algebraic number theory, a supersingular prime is a certain type of prime number. If E is an elliptic curve defined over the rational numbers, then a prime p is supersingular for E if the reduction of E modulo p is a supersingular elliptic curve over the residue field Fp.Noam Elkies showed that...

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, he was made a full, tenure

Tenure

Tenure commonly refers to life tenure in a job and specifically to a senior academic's contractual right not to have his or her position terminated without just cause.-19th century:...

d professor at the age of 26. This made him the youngest full professor in the history of Harvard, surpassing previous then-youngest professors Alan Dershowitz

Alan Dershowitz

Alan Morton Dershowitz is an American lawyer, jurist, and political commentator. He has spent most of his career at Harvard Law School where in 1967, at the age of 28, he became the youngest full professor of law in its history...

, William H. Press

William H. Press

William H. Press is an astrophysicist, theoretical physicist, and computational biologist. He is a member of the United States National Academy of Sciences, the American Academy of Arts and Sciences, and the Council on Foreign Relations. Other honors include the 1981 Helen B...

, and Lawrence Summers

Lawrence Summers

Lawrence Henry Summers is an American economist. He served as the 71st United States Secretary of the Treasury from 1999 to 2001 under President Bill Clinton. He was Director of the White House United States National Economic Council for President Barack Obama until November 2010.Summers is the...

(who were each made full professors at age 28).

Elkies, along with A. O. L. Atkin

A. O. L. Atkin

Arthur Oliver Lonsdale Atkin , who published under the name A. O. L. Atkin, was a Professor Emeritus of mathematics at the University of Illinois at Chicago. As an undergraduate during World War II, he worked at Bletchley Park cracking German codes. He received his Ph.D...

, extended Schoof's algorithm

Schoof's algorithm

Schoof's algorithm is an efficient algorithm to count points on elliptic curves over finite fields. The algorithm has applications in elliptic curve cryptography where it is important to know the number of points to judge the difficulty of solving the discrete logarithm problem in the group of...

to create the Schoof–Elkies–Atkin algorithm.

He is an accomplished composer

Chess composer

A chess composer is a person who creates endgame studies or chess problems. He usually specializes in a particular genre, e.g. endgame studies, twomovers, threemovers, moremovers, helpmates, selfmates, fairy problems...

and solver

Chess problem

A chess problem, also called a chess composition, is a puzzle set by somebody using chess pieces on a chess board, that presents the solver with a particular task to be achieved. For instance, a position might be given with the instruction that White is to move first, and checkmate Black in two...

of chess problem

Chess problem

A chess problem, also called a chess composition, is a puzzle set by somebody using chess pieces on a chess board, that presents the solver with a particular task to be achieved. For instance, a position might be given with the instruction that White is to move first, and checkmate Black in two...

s (winning the 1996 World Chess Solving Championship

World Chess Solving Championship

The World Chess Solving Championship is an annual competition in the solving of chess problems organised by FIDE via the Permanent Commission of the FIDE for Chess Compositions ....

) and musical composition

Musical composition

Musical composition can refer to an original piece of music, the structure of a musical piece, or the process of creating a new piece of music. People who practice composition are called composers.- Musical compositions :...

s. He has discovered many new patterns in Conway's Game of Life

Conway's Game of Life

The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970....

and has studied the mathematics of still life patterns in that cellular automaton rule.

Elkies is also renowned for his knowledge of the connections between mathematics and music. He sits on the Advisory Board of the Journal of Mathematics and Music.

Elkies is also a fellow at Harvard's Lowell House

Lowell House

Lowell House is one of the twelve undergraduate residential houses within Harvard College, located on Holyoke Place facing Mount Auburn Street between the Harvard Yard and the Charles River...

. He is a faculty adviser to the Harvard Israel Review.

## External links

- Personal site of Noam Elkies at Harvard University
- Endgame Explorations – an 11-part series of articles by Noam Elkies in
*Chess Horizons* - Noam Elkies on LifeWiki