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{{short description|American mathematician}}
{{Short description|American mathematician (b. 1966)}}
{{ Infobox scientist
{{Infobox scientist
| name = Noam Elkies
| name = Noam Elkies
| image = Noam Elkies.jpg
| image = Noam Elkies.jpg
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| caption = Noam Elkies in 2007
| caption = Noam Elkies in 2007
| birth_date = {{birth date and age|1966|08|25}}
| birth_date = {{birth date and age|1966|08|25}}
| birth_place = [[New York City]]
| birth_place = New York City, US
| death_date =
| death_date =
| death_place =
| death_place =
| nationality = American
| fields = [[Mathematics]]
| fields = [[Mathematics]]
| workplaces = [[Harvard University]]
| workplaces = [[Harvard University]]
| alma_mater = [[Columbia University]],<br/>[[Harvard University]]
| alma_mater = [[Columbia University]] ([[B. S.|BS]])<br/>[[Harvard University]] ([[PhD]])
| doctoral_advisor = [[Benedict Gross]]<br>[[Barry Mazur]]
| doctoral_advisor = [[Benedict Gross]]<br>[[Barry Mazur]]
| thesis_title = Supersingular primes of a given elliptic curve over a number field
| thesis_title = Supersingular primes of a given elliptic curve over a number field
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}}
}}


'''Noam David Elkies''' (born August 25, 1966) is an American [[mathematician]] and professor of [[mathematics]] at [[Harvard University]]. At the age of 26, he became the youngest professor to receive [[tenure]] at Harvard. He is also a [[Chess title|chess national master]] and a [[chess composer]].
'''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 title|chess national master]], and [[chess composer]].


==Early life==
==Early life and education==
Elkies was born to an engineer father and a piano teacher mother.<ref>{{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, he 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 [[List of International Mathematical Olympiad participants|youngest to ever do so]]. He went on to [[Columbia University]], where he won the [[Putnam competition]] at the age of sixteen years and four months, making him one of the youngest [[William Lowell Putnam Mathematical Competition#Putnam Fellows|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> He was a Putnam Fellow two more times 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}}</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>
Elkies was born to an engineer father and a piano teacher mother.<ref>{{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 [[List of International Mathematical Olympiad participants|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 [[William Lowell Putnam Mathematical Competition#Putnam Fellows|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}}</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 he 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 }} }}
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==
==Work in mathematics==
In 1987, he proved that an [[elliptic curve]] over the rational numbers is [[supersingular prime (for an elliptic curve)|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, he was made a full, [[tenure]]d professor at the age of 26. This made him the youngest full professor in the history of Harvard.<ref name="nyt">{{citation|url=https://www.nytimes.com/2010/08/29/crosswords/chess/29chess.html|newspaper=[[The New York Times]]|title=Skilled at the Chessboard, Keyboard and Blackboard|date=August 28, 2010|first=Dylan Loeb|last=McClain}}</ref> Along with [[A. O. L. Atkin]] he extended [[Schoof's algorithm]] to create the [[Schoof–Elkies–Atkin algorithm]].
In 1987, Elkies proved that an [[elliptic curve]] over the rational numbers is [[supersingular prime (for an elliptic curve)|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="nyt">{{citation|url=https://www.nytimes.com/2010/08/29/crosswords/chess/29chess.html|newspaper=[[The New York Times]]|title=Skilled at the Chessboard, Keyboard and Blackboard|date=August 28, 2010|first=Dylan Loeb|last=McClain}}</ref> 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 (cellular automaton)|still life]] patterns in that cellular automaton rule.<ref>{{cite journal
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 (cellular automaton)|still life]] patterns in that cellular automaton rule.<ref>{{cite journal
Line 38: Line 37:
| title = Voronoi's Impact on Modern Science, Book I
| title = Voronoi's Impact on Modern Science, Book I
| year = 1998
| year = 1998
}}</ref> Elkies is an associate of Harvard's [[Lowell House]].<ref>{{cite web|url=http://www.lowell.harvard.edu/scr/show.php?name_search_type=starts+with&name_search_value=noam&submitBtnName=Search|title=Lowell House: SCR|access-date=2009-07-27}} {{Dead link|date=September 2010|bot=H3llBot}}</ref>
}}</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 University|Brown]], [[Dartmouth College|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 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 University|Brown]], [[Dartmouth College|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 of an elliptic curve|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>
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 of an elliptic curve|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==
==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]] or a [[Mozart]]," citing "[h]is 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>
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==
==Chess==
Elkies is a [[chess composer|composer]] and [[Chess problem|solver]] of [[chess problem]]s (winning the 1996 [[World Chess Solving Championship]]).<ref name="nyt"/> One of his problems is used by the famed chess trainer [[Mark Dvoretsky]] in his 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> He holds the title of [[National Master]] from the [[United States Chess Federation]], but he no longer plays competitively.<ref>[http://www.uschess.org/msa/MbrDtlMain.php?11307183 Noam D Elkies rating card], USCF</ref>
Elkies is a [[chess composer|composer]] and [[Chess problem|solver]] of [[chess problem]]s (winning the 1996 [[World Chess Solving Championship]]).<ref name="nyt"/> 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==
==Awards and honors==
In 1994 he was an [[invited speaker at the International Congress of Mathematicians]] in [[Zurich]].<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}}</ref>
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}}</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>
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 he 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==
==References==
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[[Category:Columbia College (New York) alumni]]
[[Category:Columbia College (New York) alumni]]
[[Category:Harvard University alumni]]
[[Category:Harvard University alumni]]
[[Category:Harvard University faculty]]
[[Category:Harvard University Department of Mathematics faculty]]
[[Category:Cellular automatists]]
[[Category:Cellular automatists]]
[[Category:Chess composers]]
[[Category:Chess composers]]
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[[Category:Members of the United States National Academy of Sciences]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:Mathematicians from New York (state)]]
[[Category:Mathematicians from New York (state)]]
[[Category:Number theorists]]
[[Category:American number theorists]]

Latest revision as of 21:36, 20 December 2024

Noam Elkies
Noam Elkies in 2007
Born (1966-08-25) August 25, 1966 (age 58)
New York City, US
Alma materColumbia University (BS)
Harvard University (PhD)
AwardsPutnam Fellow
Lester R. Ford Award (2004)
Levi L. Conant Prize (2004)
Scientific career
FieldsMathematics
InstitutionsHarvard University
Thesis Supersingular primes of a given elliptic curve over a number field  (1987)
Doctoral advisorBenedict Gross
Barry Mazur
Doctoral studentsHenry Cohn[1]

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,[2] chess national master, and chess composer.

Early life and education

[edit]

Elkies was born to an engineer father and a piano teacher mother.[3] He attended Stuyvesant High School in New York City for three years[4] before graduating in 1982 at age 15.[5][6] 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,[7] 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.[8] Elkies was a Putnam Fellow twice more during his undergraduate years.[9] He graduated valedictorian of his class in 1985.[10] He then earned his PhD in 1987 under the supervision of Benedict Gross and Barry Mazur at Harvard University.[11]

From 1987 to 1990, Elkies was a junior fellow of the Harvard Society of Fellows.[12]

Work in mathematics

[edit]

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.[13] His work on these and other problems won him recognition and a position as an associate professor at Harvard in 1990.[5] In 1993, Elkies was made a full, tenured professor at age 26. This made him the youngest full professor in Harvard's history.[14] 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.[15] He has discovered many new patterns in Conway's Game of Life[16] and has studied the mathematics of still life patterns in that cellular automaton rule.[17] Elkies is an associate of Harvard's Lowell House.[18]

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.[19]

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).[20][21] 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.[22]

Music

[edit]

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".[23] He rings the bells of Lowell House.[24]

Chess

[edit]

Elkies is a composer and solver of chess problems (winning the 1996 World Chess Solving Championship).[14] One of his problems appears in the chess trainer Mark Dvoretsky's book Dvoretsky's Endgame Manual.[25] Elkies holds the title of National Master from the United States Chess Federation, but no longer plays competitively.[26]

Awards and honors

[edit]

In 1994, Elkies was an invited speaker at the International Congress of Mathematicians in Zürich.[27] In 2004, he received a Lester R. Ford Award[28] and the Levi L. Conant Prize.[29] In 2017, Elkies was elected to the National Academy of Sciences.[30]

References

[edit]
  1. ^ "Henry Cohn: Adjunct Professor, Discrete Mathematics". Massachusetts Institute of Technology, Department of Mathematics. Retrieved 10 August 2018.
  2. ^ "Piano Recital with Young Hyun Cho and Noam Elkies". 2018.
  3. ^ McClain, Dylan Loeb (2010-08-28). "Skilled at the Chessboard, Keyboard and Blackboard". The New York Times. ISSN 0362-4331. Retrieved 2020-09-11.
  4. ^ Altman, Daniel (9 February 1995). "Math and Music: For the Moment". The Harvard Crimson. 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.
  5. ^ a b Elkies, Noam D. "CV". Noam Elkies. Department of Mathematics, Harvard University. Retrieved 10 August 2018.
  6. ^ Castillo, Tom (April 20, 2000). "Fifteen Minutes: Gnoshin' with Noam". The Harvard Crimson.
  7. ^ Noam Elkies's results at International Mathematical Olympiad
  8. ^ Gallian, Joseph A. "The Putnam Competition from 1938–2006" (PDF). Archived from the original (PDF) on 2006-11-13. Retrieved 2007-10-31.
  9. ^ "Putnam Competition Individual and Team Winners". Mathematical Association of America. Retrieved 5 March 2019.
  10. ^ Columbia College (Columbia University). Office of Alumni Affairs and Development; Columbia College (Columbia University) (1987). Columbia College today. Columbia University Libraries. New York, N.Y. : Columbia College, Office of Alumni Affairs and Development.
  11. ^ Noam Elkies at the Mathematics Genealogy Project
  12. ^ "Harvard University. Society of Fellows. Current and Former Junior Fellows". Archived from the original on 2013-01-16. Retrieved 2013-01-16.
  13. ^ "Mathematicians Find New Solutions To An Ancient Puzzle". 2008.
  14. ^ a b McClain, Dylan Loeb (August 28, 2010), "Skilled at the Chessboard, Keyboard and Blackboard", The New York Times
  15. ^ "Editorial Board of Mathematics and Music".
  16. ^ Game of Life Status page, Jason Summers.
  17. ^ Elkies, Noam D. (1998). "Voronoi's Impact on Modern Science, Book I". Proc. Inst. Math. Nat. Acad. Sci. Ukraine. 21: 228–253. arXiv:math.CO/9905194.
  18. ^ "Noam Elkies". People: Senior Common Room Faculty. Lowell House, Harvard. Retrieved 2024-04-11.
  19. ^ "Principal Investigators". Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation. Brown University. Retrieved 2018-09-17.
  20. ^ Dujella, Andrej. "History of elliptic curves rank records". Retrieved 30 March 2020.
  21. ^ Elkies, Noam. "New records for ranks of elliptic curves with torsion". NMBRTHRY Archives. Retrieved 30 March 2020.
  22. ^ Howlett, Joseph (11 November 2024). "New Elliptic Curve Breaks 18-Year-Old Record". Quanta Magazine. Retrieved 11 November 2024.
  23. ^ Morantz, Alison D. (November 30, 1988). "Music + Math: A Common Equation?". The Harvard Crimson.
  24. ^ "Fifteen Professors to Meet | Magazine | The Harvard Crimson". www.thecrimson.com. Retrieved 2024-07-08.
  25. ^ Mark Dvoretsky: Dvoretsky's Endgame Manual, 4th Edition 2014. Russell Enterprises, Milford, CT. ISBN 978-1-941270-04-2. Chapter 1: Pawn Endings.
  26. ^ Noam D Elkies rating card, USCF
  27. ^ "International Mathematical Union (IMU)". Archived from the original on 2011-09-27.
  28. ^ "Paul R. Halmos – Lester R. Ford Awards". Mathematical Association of America. Retrieved 10 August 2018.
  29. ^ "2004 Conant Prize" (PDF), Notices of the American Mathematical Society, 51 (4): 433–434, April 2004
  30. ^ National Academy of Sciences Members and Foreign Associates Elected, National Academy of Sciences, May 2, 2017.
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