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

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

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

tenure Tenure is a type of academic appointment that protects its holder from being fired or laid off except for cause, or under extraordinary circumstances such as financial exigency or program discontinuation. Academic tenure originated in the United ...

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

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 retro ...

Early life and education

Elkies was born to an engineer father and a piano teacher mother. He attended

Stuyvesant High School Stuyvesant High School ( ) is a co-ed, State school, public, college-preparatory, Specialized high schools in New York City, specialized high school in Manhattan, New York City. The school, commonly called "Stuy" ( ) by its students, faculty, a ...

New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...

for three years before graduating in 1982 at age 15. A

child prodigy A child prodigy is, technically, a child under the age of 10 who produces meaningful work in some domain at the level of an adult expert. The term is also applied more broadly to describe young people who are extraordinarily talented in some f ...

, in 1981, at age 14, Elkies was awarded a gold medal at the 22nd

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the wor ...

, receiving a perfect score of 42, one of the youngest to ever do so. He went on to

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

, where he won the Putnam competition at age 16 and four months, making him one of the youngest

Putnam Fellows Putnam may refer to: People * Putnam (surname) Places Canada * Putnam, Ontario, community in Thames Centre United States * Putnam, Alabama * Putnam, Connecticut, a New England town ** Putnam (CDP), Connecticut, the main village in the town * ...

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 Barry Charles Mazur (; born December 19, 1937) is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem in ...

. From 1987 to 1990, Elkies 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 intellect ...

Work in mathematics

In 1987, Elkies 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 the ...

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

Euler's sum of powers conjecture In number theory, Euler's conjecture is a disproved conjecture 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 ...

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 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 ...

to create the

Schoof–Elkies–Atkin algorithm The Schoof–Elkies–Atkin algorithm (SEA) is an algorithm used for finding the order of or calculating the number of points on an elliptic curve over a finite field. Its primary application is in elliptic curve cryptography. The algorithm is an ex ...

. Elkies also studies the connections between

music and mathematics Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo, chord progression, form, and meter. The attempt to structure and communicate new ways of composing and hearing music ...

; 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 as Conway's Game of Life or simply 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 ...

and has studied the mathematics of

still life A still life (: still lifes) is a work of art depicting mostly wikt:inanimate, inanimate subject matter, typically commonplace objects which are either natural (food, flowers, dead animals, plants, rocks, shells, etc.) or artificiality, human-m ...

patterns in that cellular automaton rule. Elkies is an associate of Harvard's

Lowell House Lowell House is one of twelve undergraduate Harvard House system, residential Houses at Harvard University, located at 10 Holyoke Place facing Mount Auburn Street between Harvard Yard and the Charles River. Officially, it is named for the Lowel ...

. 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, United States. BU was founded in 1839 by a group of Boston Methodism, Methodists with its original campus in Newbury (town), Vermont, Newbur ...

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 and painting, brown is usually made by combining the colors Orange (colour), orange and black. In the ...

, Dartmouth, Harvard, and

MIT The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

. Elkies is the discoverer (or joint-discoverer) of many current and past record-holding

elliptic curves In mathematics, an elliptic curve is a Smoothness, smooth, Projective variety, projective, algebraic curve of Genus of an algebraic curve, genus one, on which there is a specified point . An elliptic curve is defined over a field (mathematics), ...

, 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.

Music

Elkies is a

bass-baritone A bass-baritone is a high-lying bass or low-lying "classical" baritone voice type which shares certain qualities with the true baritone voice. The term arose in the late 19th century to describe the particular type of voice required to sing three ...

and formerly played the piano for the Harvard Glee Club. Jameson N. Marvin, former director of the Glee Club, compared him to "a

Bach Johann Sebastian Bach (German: �joːhan zeˈbasti̯an baχ ( – 28 July 1750) was a German composer and musician of the late Baroque period. He is known for his prolific output across a variety of instruments and forms, including the or ...

or a

Mozart Wolfgang Amadeus Mozart (27 January 1756 – 5 December 1791) was a prolific and influential composer of the Classical period (music), Classical period. Despite his short life, his rapid pace of composition and proficiency from an early age ...

", citing his "gifted musicality, superior musicianship and sight-reading ability". He rings the bells of

Chess

Elkies is a

composer A composer is a person who writes music. The term is especially used to indicate composers of Western classical music, or those who are composers by occupation. Many composers are, or were, also skilled performers of music. Etymology and def ...

and

solver A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a Library (computing), software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic ...

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

s (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 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 (FIDE). USCF administers the official national Chess ...

, but no longer plays competitively.

Awards and honors

In 1994, Elkies was an

invited speaker at the International Congress of Mathematicians An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...

Zürich Zurich (; ) is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zurich. It is in north-central Switzerland, at the northwestern tip of Lake Zurich. , the municipality had 448,664 inhabitants. The ...

. In 2004, he received a Lester R. Ford Award and the Levi L. Conant Prize. In 2017, Elkies was elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

.National Academy of Sciences Members and Foreign Associates Elected

, 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 Department of Mathematics 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) American number theorists