{{Short description|American mathematician (born 1966)}} {{Use mdy dates|date = April 2026}} {{Use American English|date = April 2026}} {{Infobox scientist | name = Noam Elkies | image = Noam Elkies.jpg | image_size = 220px | caption = Noam Elkies in 2007 | birth_date = {{birth date and age|1966|08|25}} | birth_place = New York City, US | death_date = | death_place = | fields = Mathematics | workplaces = Harvard University | alma_mater = Columbia University (BS 1985)<br/>Harvard University (PhD 1987) | doctoral_advisor = Benedict Gross<br>Barry Mazur | thesis_title = Supersingular primes of a given elliptic curve over a number field | thesis_year = 1987 | doctoral_students = Henry Cohn<ref>{{cite web|url=http://math.mit.edu/directory/profile.php?pid=1224|title=Henry Cohn: Adjunct Professor, Discrete Mathematics|website=Massachusetts Institute of Technology, Department of Mathematics|access-date=10 August 2018|archive-date=19 February 2022|archive-url=https://web.archive.org/web/20220219165822/https://math.mit.edu/directory/profile.php?pid=1224|url-status=dead}}</ref> | known_for = Elliptic curves | awards = Putnam Fellow <br> Lester R. Ford Award (2004) <br> Levi L. Conant Prize (2004) }}
'''Noam David Elkies''' (born August 25, 1966) is a professor of mathematics at Harvard University. At age 26, he became the youngest professor to receive tenure at Harvard. He is also a pianist,<ref>{{cite web|url=https://research.msu.edu/event/piano-recital-young-hyun-cho-and-noam-elkies|year=2018|title=Piano Recital with Young Hyun Cho and Noam Elkies}}</ref> chess national master, and chess composer.
==Early life and education== Elkies was born to an engineer father and a piano teacher mother.<ref name=":0">{{Cite news|last=McClain|first=Dylan Loeb|date=2010-08-28|title=Skilled at the Chessboard, Keyboard and Blackboard|language=en-US|work=The New York Times|url=https://www.nytimes.com/2010/08/29/crosswords/chess/29chess.html|access-date=2020-09-11|issn=0362-4331}}</ref> He attended Stuyvesant High School in New York City for three years<ref>{{cite news|title=Math and Music: For the Moment|first=Daniel|last=Altman|date=9 February 1995|work=The Harvard Crimson|url=https://www.thecrimson.com/article/1995/2/9/math-and-music-pbabt-the-tender/|quote=Elkies spent eight years of his youth in Israel, and he came to New York City having read a Hebrew translation of Euclid but without any significant knowledge of English.}}</ref> before graduating in 1982 at age 15.<ref name="cv">{{cite web|url=http://www.math.harvard.edu/~elkies/math_cv.html|first=Noam D.|last=Elkies|title=CV|website=Noam Elkies|publisher=Department of Mathematics, Harvard University|access-date=10 August 2018}}</ref><ref name=Crimson>{{cite news|last1=Castillo|first1=Tom|title=Fifteen Minutes: Gnoshin' with Noam|url=http://www.thecrimson.com/article/2000/4/20/fifteen-minutes-gnoshin-with-noam-phe/?page=single|newspaper=The Harvard Crimson|date=April 20, 2000}}</ref> 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,<ref>{{IMO results|id=10464}}</ref> 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.<ref>{{cite web |url=http://www.d.umn.edu/~jgallian/putnam05.pdf |title=The Putnam Competition from 1938–2006 |first=Joseph A. |last=Gallian |access-date=2007-10-31 |url-status=dead |archive-url=https://web.archive.org/web/20061113221122/http://www.d.umn.edu/~jgallian/putnam05.pdf |archive-date=2006-11-13 }}</ref> Elkies was a Putnam Fellow twice more during his undergraduate years.<ref>{{cite web|url=https://www.maa.org/programs-and-communities/member-communities/maa-awards/putnam-competition-individual-and-team-winners|title=Putnam Competition Individual and Team Winners|publisher=Mathematical Association of America|access-date=5 March 2019|archive-date=26 June 2013|archive-url=https://web.archive.org/web/20130626001918/http://www.maa.org/awards/putnam.html|url-status=dead}}</ref> He graduated valedictorian of his class in 1985.<ref>{{Cite book|last=Columbia College (Columbia University). Office of Alumni Affairs and Development|url=http://archive.org/details/ldpd_12981092_029|title=Columbia College today|last2=Columbia College (Columbia University)|date=1987|publisher=New York, N.Y. : Columbia College, Office of Alumni Affairs and Development|others=Columbia University Libraries}}</ref> He then earned his PhD in 1987 under the supervision of Benedict Gross and Barry Mazur at Harvard University.<ref>{{MathGenealogy|id=22514}}</ref>
From 1987 to 1990, Elkies was a junior fellow of the Harvard Society of Fellows.{{refn|{{cite web |url=http://www.socfell.fas.harvard.edu/current%20and%20former%20jf%20term.html |title=Harvard University. Society of Fellows. Current and Former Junior Fellows |access-date=2013-01-16 |archive-url=https://web.archive.org/web/20130116051400/http://www.socfell.fas.harvard.edu/current%20and%20former%20jf%20term.html |archive-date=2013-01-16 |url-status=dead }} }}
==Work in mathematics== 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.<ref>{{cite web|url=https://www.sciencedaily.com/releases/2008/03/080314145039.htm|year=2008|title=Mathematicians Find New Solutions To An Ancient Puzzle}}</ref> His work on these and other problems won him recognition and a position as an associate professor at Harvard in 1990.<ref name="cv"/> In 1993, Elkies was made a full, tenured professor at age 26. This made him the youngest full professor in Harvard's history.<ref name=":0" /> 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''.<ref>{{cite web|url=https://www.tandfonline.com/action/aboutThisJournal?show=editorialBoard&journalCode=tmam20|title=Editorial Board of Mathematics and Music}}</ref> He has discovered many new patterns in Conway's Game of Life<ref>[http://entropymine.com/jason/life/status.html Game of Life Status page], Jason Summers.</ref> and has studied the mathematics of still life patterns in that cellular automaton rule.<ref>{{cite journal | last = Elkies | first = Noam D. | arxiv = math.CO/9905194 | pages = 228–253 | journal = Proc. Inst. Math. Nat. Acad. Sci. Ukraine |volume=21 | title = Voronoi's Impact on Modern Science, Book I | year = 1998 }}</ref> Elkies is an associate of Harvard's Lowell House.<ref>{{cite web|url=https://lowell.harvard.edu/people/noam-elkies|title=Noam Elkies|work=People: Senior Common Room Faculty|publisher=Lowell House, Harvard|access-date=2024-04-11}}</ref>
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.<ref>{{cite web|url=https://simonscollab.icerm.brown.edu/team/|title=Principal Investigators|work=Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation|publisher=Brown University|access-date=2018-09-17}}</ref>
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).<ref>{{cite web |last1=Dujella |first1=Andrej|title=History of elliptic curves rank records |url=https://web.math.pmf.unizg.hr/~duje/tors/rkeq20.html |access-date=30 March 2020}}</ref><ref>{{cite web |last1=Elkies |first1=Noam |title=New records for ranks of elliptic curves with torsion |url=https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;b636e6e5.2003&S= |website=NMBRTHRY Archives |access-date=30 March 2020}}</ref> 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.<ref name="Klagsbrun2024">{{cite web | last=Howlett | first=Joseph | title=New Elliptic Curve Breaks 18-Year-Old Record | website=Quanta Magazine | date=11 November 2024 | url=https://www.quantamagazine.org/new-elliptic-curve-breaks-18-year-old-record-20241111/ | access-date=11 November 2024}}</ref>
==Music== 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".<ref>{{cite news|last1=Morantz|first1=Alison D.|title=Music + Math: A Common Equation?|url=http://www.thecrimson.com/article/1988/11/30/music-math-a-common-equation/?page=single|newspaper=The Harvard Crimson|date=November 30, 1988}}</ref> He rings the bells of Lowell House.<ref>{{Cite web |title=Fifteen Professors to Meet {{!}} Magazine {{!}} The Harvard Crimson |url=https://www.thecrimson.com/article/2015/9/17/fifteen-to-meet-2015/ |access-date=2024-07-08 |website=www.thecrimson.com}}</ref>
==Chess== Elkies is a composer and solver of chess problems (winning the 1996 World Chess Solving Championship).<ref name=":0" /> One of his problems appears in the chess trainer Mark Dvoretsky's book ''Dvoretsky's Endgame Manual''.<ref>Mark Dvoretsky: Dvoretsky's Endgame Manual, 4th Edition 2014. Russell Enterprises, Milford, CT. {{ISBN|978-1-941270-04-2}}. Chapter 1: Pawn Endings.</ref> Elkies holds the title of National Master from the United States Chess Federation, but no longer plays competitively.<ref>[http://www.uschess.org/msa/MbrDtlMain.php?11307183 Noam D Elkies rating card], USCF</ref>
==Awards and honors== In 1994, Elkies was an invited speaker at the International Congress of Mathematicians in Zürich.<ref>{{cite web |url=http://www.mathunion.org/db/ICM/Speakers/SortedByLastname.php |url-status=dead |archive-url=https://web.archive.org/web/20110927014538/http://www.mathunion.org/db/ICM/Speakers/SortedByLastname.php |archive-date=2011-09-27 |title=International Mathematical Union (IMU)}}</ref> In 2004, he received a Lester R. Ford Award<ref>{{cite web|title=Paul R. Halmos – Lester R. Ford Awards|url=https://www.maa.org/programs-and-communities/member-communities/maa-awards/writing-awards/paul-halmos-lester-ford-awards|website=Mathematical Association of America|access-date=10 August 2018|archive-date=26 June 2017|archive-url=https://web.archive.org/web/20170626200452/http://www.maa.org/programs/maa-awards/writing-awards/paul-halmos-lester-ford-awards|url-status=dead}}</ref> and the Levi L. Conant Prize.<ref>{{citation|url=https://www.ams.org/notices/200404/comm-conant.pdf|title=2004 Conant Prize|journal=Notices of the American Mathematical Society|volume=51|issue=4|date=April 2004|pages=433–434}}</ref> In 2017, Elkies was elected to the National Academy of Sciences.<ref>[http://www.nasonline.org/news-and-multimedia/news/may-2-2017-NAS-Election.html National Academy of Sciences Members and Foreign Associates Elected], National Academy of Sciences, May 2, 2017.</ref>
==References== {{Reflist}}
==External links== {{Sister project links| wikt=no | commons=Category:Noam Elkies | b=no | n=no | q=Noam Elkies | s=no | v=no | voy=no | species=no | d=no}}
* [http://www.math.harvard.edu/~elkies/ Personal site] of Noam Elkies at Harvard University * [https://web.archive.org/web/20160102194527/http://www.permutationpuzzles.org/chess/Elkies/ Endgame Explorations] – an 11-part series of articles by Noam Elkies in ''Chess Horizons''
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{{DEFAULTSORT:Elkies, Noam}} Category:1966 births Category:Living people Category:20th-century American mathematicians Category:21st-century American mathematicians Category:Stuyvesant High School alumni Category:Putnam Fellows Category:Harvard Fellows Category:Columbia College, Columbia University alumni Category:Harvard University alumni Category:Harvard University Department of Mathematics faculty Category:Cellular automatists Category:Chess composers Category:International Mathematical Olympiad participants Category:International solving grandmasters Category:Members of the United States National Academy of Sciences Category:Mathematicians from New York (state) Category:American number theorists