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 higher le ...
. 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 ...
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
Stuyvesant High School (pronounced ), commonly referred to among its students as Stuy (pronounced ), is a State school, public university-preparatory school, college-preparatory, Specialized high schools in New York City, specialized high school ...
in
New York City
New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...
for three years before graduating in 1982 at age 15. A
child prodigy
A child prodigy is defined in psychology research literature as a person under the age of ten who produces meaningful output in some domain at the level of an adult expert. The term is also applied more broadly to young people who are extraor ...
in 1981, at age 14, he 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. The first IMO was held in Romania in 1959. It has since been held annually, except i ...
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 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 tow ...
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
Benedict Hyman Gross is an American mathematician who is a professor at the University of California San Diego, the George Vasmer Leverett Professor of Mathematics Emeritus at Harvard University, and former Dean of Harvard College.Barry Mazur 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 higher le ...
.
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
In mathematics, a supersingular variety is (usually) a smooth projective variety in nonzero characteristic such that for all ''n'' the slopes of the Newton polygon of the ''n''th crystalline cohomology are all ''n''/2 . For special classes o ...
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 is ...
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 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 ...
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
Arthur Oliver Lonsdale Atkin (31 July 1925 – 28 December 2008), who published under the name A. O. L. Atkin, was a British mathematician.
As an undergraduate during World War II, Atkin worked at Bletchley Park cracking German codes. He receiv ...
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 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 e ...
.
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 mus ...
; 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 further ...
and has studied the mathematics of
still life
A still life (plural: 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, m ...
patterns in that cellular automaton rule. Elkies is an associate of Harvard's
Lowell House
Lowell House is one of twelve undergraduate 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 Lowell family, but an orna ...
.
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 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 its original campu ...
,
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 used ...
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
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 ...
, 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
* H ...
, and the curve with the highest-known exact rank (=20).
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 thr ...
and plays the piano for the
Harvard Glee Club
The Harvard Glee Club is a 60-voice, Tenor-Bass choral ensemble at Harvard University. Founded in 1858 in the tradition of English and American glee clubs, it is the oldest collegiate chorus in the United States. The Glee Club is part of the H ...
. 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 w ...
or a
Mozart
Wolfgang Amadeus Mozart (27 January 17565 December 1791), baptised as Joannes Chrysostomus Wolfgangus Theophilus Mozart, was a prolific and influential composer of the Classical period (music), Classical period. Despite his short life, his ra ...
," citing " s gifted musicality, superior musicianship and sight-reading ability."
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 Defi ...
and
solver
A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates t ...
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
The World Chess Solving Championship (WCSC) is an annual competition in the solving of chess problems (also known as chess puzzles) organized by the World Federation for Chess Composition (WFCC), previously by FIDE via the Permanent Commission of ...
). One of his problems is used by the famed chess trainer
Mark Dvoretsky
Mark Izrailevich Dvoretsky (russian: Марк Изра́илевич Дворе́цкий; December 9, 1947 – September 26, 2016) was a Russian chess trainer, writer, and International Master.
Biography
Dvoretsky was born in Moscow in 1947. ...
in his book "Dvoretsky's Endgame Manual". He holds the title of
National Master
A chess title is a title regulated by a chess governing body and bestowed upon players based on their performance and rank. Such titles are usually granted for life. The international chess governing body FIDE grants several titles, the most pre ...
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 s ...
, but he no longer plays competitively.
Awards and honors
In 1994 he was an
invited speaker at the International Congress of Mathematicians
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...
Lester R. Ford Award
Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include:
People
Given name
* Lester Bangs (1948–1982), American music critic
* Lester W. Bentley (1908–1972), American artist from Wisc ...
and the
Levi L. Conant Prize The Levi L. Conant Prize is a mathematics prize of the American Mathematical Society, which has been awarded since 2000 for outstanding expository papers published in the ''Bulletin of the American Mathematical Society'' or the ''Notices of the Amer ...
.
In 2017 he was elected to the
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, 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 Nati ...
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, 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 Nati ...