Noam David Elkies (born August 25, 1966) is a professor of mathematics at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

. At the age of 26, he became the youngest professor to receive

tenure Tenure is a category of academic appointment existing in some countries. A tenured post is an indefinite academic appointment that can be terminated only for cause or under extraordinary circumstances, such as financial exigency or program disco ...

at Harvard. He is also a pianist, chess national master and a

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

Early life

Elkies was born to an engineer father and a piano teacher mother. He attended Stuyvesant High School in

New York City New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the Un ...

for three years before graduating in 1982 at age 15. 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, one of the youngest to ever do so. He went on to

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

, where he won the

Putnam competition The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regar ...

at the age of sixteen years and four months, making him one of the youngest Putnam Fellows in history. He was a Putnam Fellow two more times 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

. From 1987 to 1990 he was a junior fellow of the

Harvard Society of Fellows The Society of Fellows is a group of scholars selected at the beginnings of their careers by Harvard University for their potential to advance academic wisdom, upon whom are bestowed distinctive opportunities to foster their individual and intell ...

Work in mathematics

In 1987, he proved that an

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...

over the rational numbers is supersingular at infinitely many primes. In 1988, he found a counterexample to

Euler's sum of powers conjecture Euler's conjecture is a disproved conjecture in mathematics related to Fermat's Last Theorem. It was proposed by Leonhard Euler in 1769. It states that for all integers and greater than 1, if the sum of many th powers of positive integers i ...

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,

d professor at the age of 26. This made him the youngest full professor in the history of Harvard. Along with A. O. L. Atkin he extended

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 t ...

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 The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no furthe ...

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 Boston University (BU) is a Private university, private research university in Boston, Massachusetts. The university is nonsectarian, but has a historical affiliation with the United Methodist Church. It was founded in 1839 by Methodists with ...

Brown Brown is a color. It can be considered a composite color, but it is mainly a darker shade of orange. In the CMYK color model used in printing or painting, brown is usually made by combining the colors orange and black. In the RGB color model us ...

, Dartmouth, Harvard, and

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...

. 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 Rank is the relative position, value, worth, complexity, power, importance, authority, level, etc. of a person or object within a ranking, such as: Level or position in a hierarchical organization * Academic rank * Diplomatic rank * Hierarchy * ...

, and the curve with the highest-known exact rank (=20).

Music

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 Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late Baroque period. He is known for his orchestral music such as the ''Brandenburg Concertos''; instrumental compositions such as the Cello Suites; keyboard wor ...

or a Mozart," citing " s gifted musicality, superior musicianship and sight-reading ability."

Chess

Elkies is a composer and solver of

chess problem A chess problem, also called a chess composition, is a puzzle set by the composer using chess pieces on a chess board, which presents the solver with a particular task. For instance, a position may be given with the instruction that White is to ...

s (winning the 1996 World Chess Solving Championship). One of his problems is used by the famed chess trainer Mark Dvoretsky in his book "Dvoretsky's Endgame Manual". He holds the title of National Master from the

United States Chess Federation The United States Chess Federation (also known as US Chess or USCF) is the governing body for chess competition in the United States and represents the U.S. in FIDE, the World Chess Federation. US Chess administers the official national rating ...

, but he no longer plays competitively.

Awards and honors

In 1994 he was an invited speaker at the International Congress of Mathematicians in Zurich. In 2004 he received a Lester R. Ford Award and the Levi L. Conant Prize. In 2017 he was elected to the National Academy of Sciences.National Academy of Sciences Members and Foreign Associates Elected
National Academy of Sciences, May 2, 2017.

References

External links

Personal site
of Noam Elkies at Harvard University
Endgame Explorations
– an 11-part series of articles by Noam Elkies in ''Chess Horizons'' {{DEFAULTSORT:Elkies, Noam 1966 births Living people 20th-century American mathematicians 21st-century American mathematicians Stuyvesant High School alumni Putnam Fellows Harvard Fellows Columbia College (New York) alumni Harvard University alumni Harvard University faculty Cellular automatists Chess composers International Mathematical Olympiad participants International solving grandmasters Members of the United States National Academy of Sciences Mathematicians from New York (state) Number theorists