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{{short description|American mathematician}}
{{Short description|American mathematician (1940–2019)}}
{{Infobox scientist
{{Infobox scientist
| name = Elwyn Berlekamp
| name = Elwyn Berlekamp
| image = Elwyn R Berlekamp 2005.jpg
| image = Elwyn R Berlekamp 2005.jpg
| caption = Berlekamp in 2005
| caption = Berlekamp in 2005
| birth_name = Elwyn Ralph Berlekamp
| birth_name = Elwyn Ralph Berlekamp
| birth_date = {{Birth date|1940|9|6}}
| birth_date = {{Birth date|1940|9|6}}
| birth_place = [[Dover, Ohio]], U.S.
| birth_place = [[Dover, Ohio]], U.S.
| death_date = {{Death date and age|2019|04|09|1940|9|6}}
| death_date = {{Death date and age|2019|04|09|1940|9|6}}
| death_place=[[Piedmont, California]], U.S.
| death_place = [[Piedmont, California]], U.S.
⚫
| alma_mater = [[Massachusetts Institute of Technology]]
| nationality = American
⚫
| workplaces = [[University of California, Berkeley]]
⚫
| alma_mater = [[Massachusetts Institute of Technology]]
⚫
| doctoral_advisor = [[Robert G. Gallager]]
⚫
| workplaces = [[University of California, Berkeley]]
⚫
| thesis_title = Block coding with noiseless feedback
⚫
| doctoral_advisor = [[Robert G. Gallager]]
⚫
| thesis_year = 1964
⚫
| thesis_title = Block coding with noiseless feedback
⚫
| thesis_url = https://dspace.mit.edu/handle/1721.1/14783
⚫
| thesis_year = 1964
⚫
| thesis_url = https://dspace.mit.edu/handle/1721.1/14783
| doctoral_students = [[Julia Kempe]]
| doctoral_students = [[Julia Kempe]]
| notable_students = [[Ken Thompson]]
| notable_students = [[Ken Thompson]]
| fields = [[Information theory]], [[Coding theory]], [[Combinatorial game theory]]
| fields = [[Information theory]], [[Coding theory]], [[Combinatorial game theory]]
| known_for = [[Berlekamp's algorithm]], [[Berlekamp–Welch algorithm]], [[Berlekamp–Massey algorithm]], [[Coupon Go]]
| known_for = [[Berlekamp's algorithm]]<br>[[Berlekamp switching game]]<br>[[Berlekamp–Welch algorithm]]<br>[[Berlekamp–Massey algorithm]]<br>[[Berlekamp–Rabin algorithm]]<br>[[Berlekamp–Zassenhaus algorithm]]<br>[[Berlekamp–Van Lint–Seidel graph]]<br>[[Blockbusting (game)|Blockbusting]]<br>[[Combinatorial game theory]]<br>[[Cooling and heating (combinatorial game theory)|Cooling and heating]]<br>[[Coupon Go]]<br>[[Error-correcting codes with feedback]]<br>[[Partisan game]]<br>[[Phutball]]
| awards = [[IEEE Richard W. Hamming Medal]] <small>(1991)</small><br>[[Claude E. Shannon Award]] {{small|(1993)}}
| awards = [[IEEE Richard W. Hamming Medal]] (1991)<br />[[Claude E. Shannon Award]] (1993)
}}
}}
'''Elwyn Ralph Berlekamp''' (September 6, 1940 – April 9, 2019) was an American mathematician known for his work in computer science, [[coding theory]] and [[combinatorial game theory]]. He was a [[Professor#Retired faculty|professor emeritus]] of [[mathematics]] and [[Electrical Engineering and Computer Science|EECS]] at the [[University of California, Berkeley]].<ref name=44a>Contributors, ''IEEE Transactions on Information Theory'' '''42''', #3 (May 1996), p. 1048. DOI [https://dx.doi.org/10.1109/TIT.1996.490574 10.1109/TIT.1996.490574].</ref><ref name=ucb>[http://math.berkeley.edu/index.php?module=mathfacultyman&MATHFACULTY_MAN_op=sView&MATHFACULTY_id=111 Elwyn Berlekamp], listing at the Department of Mathematics, [[University of California, Berkeley]].</ref>
'''Elwyn Ralph Berlekamp''' (September 6, 1940 – April 9, 2019) was a professor of [[mathematics]] and [[computer science]] at the [[University of California, Berkeley]].<ref name="44a">{{Cite journal |date=May 1996 |title=Contributors |url=https://ieeexplore.ieee.org/document/490574/ |journal=IEEE Transactions on Information Theory |volume=42 |issue=3 |pages=1048 |doi=10.1109/TIT.1996.490574 |issn=0018-9448}}</ref><ref name=ucb>[http://math.berkeley.edu/index.php?module=mathfacultyman&MATHFACULTY_MAN_op=sView&MATHFACULTY_id=111 Elwyn Berlekamp], listing at the Department of Mathematics, [[University of California, Berkeley]].</ref> Berlekamp was widely known for his work in computer science, [[coding theory]] and [[combinatorial game theory]].


Berlekamp was the inventor of an algorithm to factor polynomials, and was one of the inventors of the [[Berlekamp–Welch algorithm]] and the [[Berlekamp–Massey algorithm]]s, which are used to implement [[Reed–Solomon error correction]].
Berlekamp invented an [[Berlekamp%27s_algorithm|algorithm to factor polynomials]] and the [[Berlekamp switching game]], and was one of the inventors of the [[Berlekamp–Welch algorithm]] and the [[Berlekamp–Massey algorithm]]s, which are used to implement [[Reed–Solomon error correction]]. He also co-invented the [[Berlekamp–Rabin algorithm]], [[Berlekamp–Zassenhaus algorithm]], and the [[Berlekamp–Van Lint–Seidel graph]].


Berlekamp had also been active in [[money management]]. In 1986, he began information-theoretic studies of commodity and financial futures.
Berlekamp had also been active in [[investing]], and ran Axcom, which became the [[Renaissance Technologies]]' Medallion Fund.


==Life and education==
==Life and education==
Berlekamp was born in [[Dover, Ohio]]. His family moved to Northern Kentucky, where Berlekamp graduated from Ft. Thomas Highlands high school in Ft. Thomas, Campbell county, Kentucky. While an undergraduate at the [[Massachusetts Institute of Technology]] (MIT), he was a [[Putnam Fellow]] in 1961. He completed his bachelor's and master's degrees in [[electrical engineering]] in 1962. Continuing his studies at MIT, he finished his Ph.D. in electrical engineering in 1964; his advisors were [[Robert G. Gallager]], [[Peter Elias]], [[Claude Shannon]], and [[John Wozencraft]].
Berlekamp was born in [[Dover, Ohio]]. His family moved to Northern Kentucky, where Berlekamp graduated from Ft. Thomas Highlands high school in Ft. Thomas, Campbell county, Kentucky. While an undergraduate at the [[Massachusetts Institute of Technology]] (MIT), he was a [[Putnam Fellow]] in 1961.<ref name="MMA">{{cite web|title=Putnam Competition Individual and Team Winners |url=http://www.maa.org/programs/maa-awards/putnam-competition-individual-and-team-winners |publisher=[[Mathematical Association of America]]|access-date=December 12, 2021}}</ref> He completed his bachelor's and master's degrees in [[electrical engineering]] in 1962. Continuing his studies at MIT, he finished his Ph.D. in electrical engineering in 1964; his advisors were [[Robert G. Gallager]], [[Peter Elias]], [[Claude Shannon]], and [[John Wozencraft]].


Berlekamp had two daughters and a son with his wife Jennifer. He lived in [[Piedmont, California]] and died in April 2019 at the age of 78 from complications of [[pulmonary fibrosis]].<ref>''[https://news.berkeley.edu/2019/04/18/elwyn-berlekamp-game-theorist-and-coding-pioneer-dies-at-78/ Elwyn Berlekamp, game theorist and coding pioneer, dies at 78]'' Berkeley News, By Robert Sanders, April 18, 2019</ref>
Berlekamp had two daughters and a son with his wife Jennifer. He lived in [[Piedmont, California]] and died in April 2019 at the age of 78 from complications of [[pulmonary fibrosis]].<ref>{{Cite web |date=2022 |title=Elwyn Berlekamp, game theorist and coding pioneer, dies at 78 |url=https://news.berkeley.edu/2019/04/18/elwyn-berlekamp-game-theorist-and-coding-pioneer-dies-at-78 |access-date=2024-02-12 |website=Berkeley |language=en-us}}</ref>


==Career==
==Career==
Berlekamp taught electrical engineering at the [[University of California, Berkeley]] from 1964 until 1966, when he became a mathematics researcher at [[Bell Labs]]. In 1971, Berlekamp returned to Berkeley as professor of mathematics and EECS, where he served as the advisor for over twenty doctoral students.<ref name=44a /><ref name=ucb /><ref name=43a>[http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=22678 Contributors], ''IEEE Transactions on Information Theory'' '''20''', #3 (May 1974), p. 408.</ref>
Berlekamp was a professor of electrical engineering at the [[University of California, Berkeley]] from 1964 until 1966, when he became a mathematics researcher at [[Bell Labs]]. In 1971, Berlekamp returned to Berkeley as professor of mathematics and computer science, where he served as the advisor for over twenty doctoral students.<ref name=44a /><ref name=ucb /><ref name=43a>[https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=22678 Contributors], ''IEEE Transactions on Information Theory'' '''20''', #3 (May 1974), p. 408.</ref>


He was a member of the [[National Academy of Engineering]] (1977)<ref name="NAE">{{cite web|url=http://www.nae.edu/MembersSection/Directory20412/29695.aspx |title=NAE Members Directory – Dr. Elwyn R. Berlekamp |publisher=[[National Academy of Engineering|NAE]] |access-date=June 16, 2011}}</ref> and the [[United States National Academy of Sciences|National Academy of Sciences]] (1999).<ref>{{cite web|url=http://www.nasonline.org/site/Dir?sid=1011&view=basic&pg=srch |title=NAS Membership Directory |publisher=[[United States National Academy of Sciences|NAS]] |access-date=June 16, 2011}} Search with "Last Name" is Berlekamp.</ref> He was elected a Fellow of the [[American Academy of Arts and Sciences]] in 1996,<ref name=AAAS>{{cite web|title=Book of Members, 1780–2010: Chapter B|url=http://www.amacad.org/publications/BookofMembers/ChapterB.pdf|publisher=American Academy of Arts and Sciences|access-date=June 16, 2011}}</ref> and became a fellow of the [[American Mathematical Society]] in 2012.<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10.</ref> In 1991, he received the [[IEEE Richard W. Hamming Medal]],<ref>{{cite web|url=http://www.ieee.org/documents/hamming_rl.pdf |title=IEEE Richard W. Hamming Medal Recipients |publisher=[[IEEE]] |access-date=May 29, 2011}}</ref> and in 1993, the [[Claude E. Shannon Award]]. In 1998, he received a Golden Jubilee Award for Technological Innovation from the [[IEEE Information Theory Society]].<ref>{{cite web|url=http://www.itsoc.org/honors/golden-jubilee-awards-for-technological-innovation |title=Golden Jubilee Awards for Technological Innovation |publisher=[[IEEE Information Theory Society]] |access-date=July 14, 2011}}</ref> He was one of the founders of [[Gathering 4 Gardner]] and was on its board for many years.<ref>[http://gathering4gardner.org/ABOUT.html About Gathering 4 Gardner Foundation] {{webarchive|url=https://web.archive.org/web/20160507111434/http://gathering4gardner.org/ABOUT.html |date=2016-05-07 }}</ref> In the mid-1980s, he was president of [[Cyclotomics, Inc.]], a corporation that developed error-correcting code technology.<ref name="44a" />
He was a member of the [[National Academy of Engineering]] (1977)<ref name="NAE">{{cite web|url=http://www.nae.edu/MembersSection/Directory20412/29695.aspx |title=NAE Members Directory – Dr. Elwyn R. Berlekamp |publisher=[[National Academy of Engineering|NAE]] |access-date=June 16, 2011}}</ref> and the [[United States National Academy of Sciences|National Academy of Sciences]] (1999).<ref>{{cite web|url=http://www.nasonline.org/site/Dir?sid=1011&view=basic&pg=srch |title=NAS Membership Directory |publisher=[[United States National Academy of Sciences|NAS]] |access-date=June 16, 2011}} Search with "Last Name" is Berlekamp.</ref> He was elected a Fellow of the [[American Academy of Arts and Sciences]] in 1996,<ref name=AAAS>{{cite web|title=Book of Members, 1780–2010: Chapter B|url=http://www.amacad.org/publications/BookofMembers/ChapterB.pdf|publisher=American Academy of Arts and Sciences|access-date=June 16, 2011}}</ref> and became a fellow of the [[American Mathematical Society]] in 2012.<ref>{{Cite web |title=Fellows of the American Mathematical Society |url=https://www.ams.org/cgi-bin/fellows/fellows.cgi |access-date=2024-02-12 |website=American Mathematical Society |language=en}}</ref> In 1991, he received the [[IEEE Richard W. Hamming Medal]],<ref>{{cite web|url=http://www.ieee.org/documents/hamming_rl.pdf |archive-url=https://web.archive.org/web/20100620000223/http://ieee.org/documents/hamming_rl.pdf |url-status=dead |archive-date=June 20, 2010 |title=IEEE Richard W. Hamming Medal Recipients |publisher=[[IEEE]] |access-date=May 29, 2011}}</ref> and in 1993, the [[Claude E. Shannon Award]]. In 1998, he received a Golden Jubilee Award for Technological Innovation from the [[IEEE Information Theory Society]].<ref>{{cite web|url=http://www.itsoc.org/honors/golden-jubilee-awards-for-technological-innovation |title=Golden Jubilee Awards for Technological Innovation |publisher=[[IEEE Information Theory Society]] |access-date=July 14, 2011}}</ref> Along with [[Tom Malin Rodgers|Tom M. Rodgers]]<ref name="rothstein">{{Cite news |last=Rothstein |first=Edward |date=2004-04-03 |title=Puzzles + Math = Magic |url=https://www.nytimes.com/2004/04/03/arts/puzzles-math-magic.html |access-date=2024-02-12 |work=The New York Times |language=en-US |issn=0362-4331}}</ref> he was one of the founders of [[Gathering 4 Gardner]] and was on its board for many years.<ref>[http://gathering4gardner.org/ABOUT.html About Gathering 4 Gardner Foundation] {{webarchive|url=https://web.archive.org/web/20160507111434/http://gathering4gardner.org/ABOUT.html |date=2016-05-07 }}</ref> In the mid-1980s, he was president of [[Cyclotomics, Inc.]], a corporation that developed error-correcting code technology.<ref name="44a" />


He has studied various games, including [[Dots and Boxes|dots and boxes]], [[Fox and Geese]], and, especially, [[go (game)|Go]]. Berlekamp and co-author David Wolfe describe methods for analyzing certain classes of Go endgames in the book ''Mathematical Go.''
He studied various games, including [[dots and boxes]], [[fox and geese]], and, especially, [[go (game)|Go]]. Berlekamp and co-author David Wolfe describe methods for analyzing certain classes of Go endgames in the book ''Mathematical Go.''

In 1989, Berlekamp purchased the largest interest in a trading company named Axcom Trading Advisors. After the firm's futures trading algorithms were rewritten, Axcom's Medallion Fund had a return (in 1990) of 55%, net of all management fees and transaction costs. The fund has subsequently continued to realize annualized returns exceeding 30% under management by [[James Harris Simons]] and his [[Renaissance Technologies]] LLC.<ref>[http://math.berkeley.edu/~berlek/fineng.html Financial Engineering], Elwyn Berlekamp's Home Page. Accessed on line October 30, 2007.</ref>


==Berlekamp and Martin Gardner==
==Berlekamp and Martin Gardner==
Berlekamp was a close friend of [[Scientific American]] columnist [[Martin Gardner]] and was an important member of the gifted and diverse group of people that Gardner nurtured and acted as a conduit for; people who inspired Gardner and who were in turn inspired by him.<ref name=tribute>[https://www.gathering4gardner.org/?p=2840&preview=1&_ppp=519afa9f84 Elwyn Berlekamp Tribute] by Gathering 4 Gardner on April 17, 2019</ref> Berlekamp teamed up with [[John Horton Conway]] and [[Richard K. Guy]], two other close associates of Gardner, to co-author the book ''[[Winning Ways for your Mathematical Plays]]'', leading to his recognition as one of the founders of [[combinatorial game theory]].<ref name= Berlekamp2014>''[https://sinews.siam.org/DesktopModules/PackFlashPublish/ArticleDetail/ArticleDetailPrint.aspx?ArticleID=200&Template=Standard_Print.ascx&siteID=13 The Mathematical Legacy of Martin Gardner]'' by Elwyn Berlekamp, [[Society for Industrial and Applied Mathematics]] (SIAM), September 2, 2014: Partly because of what I had read about them in Martin Gardner’s columns, I was appropriately awestruck in the 1960s when I first met Sol Golomb and then Richard Guy, each of whom had a large influence on my subsequent work. In 1969 Richard introduced me to John Horton Conway, and the three of us immediately began collaborating on a book that eventually became ''Winning Ways for Your Mathematical Plays''. In the 1970s, I joined Conway in some of his many visits to Gardner’s home on Euclid Avenue, in Hastings-on-Hudson, New York. Gardner soon became an enthusiastic advocate of our book project, and he previewed various snippets of it in his Scientific American columns.</ref> The dedication of their book says, "To Martin Gardner, who has brought more mathematics to more millions than anyone else."<ref>Berlekamp, Elwyn R., John H. Conway, and Richard K. Guy (1982). ''Winning Ways for your Mathematical Plays'' Academic Press, {{ISBN|0120911507}}.</ref>
Berlekamp was a close friend of ''[[Scientific American]]'' columnist [[Martin Gardner]] and was an important member of the gifted and diverse group of people that Gardner nurtured and acted as a conduit for; people who inspired Gardner and who were in turn inspired by him.<ref name="tribute">{{Cite web |last=Hirth |first=Tiago |date=2020-01-24 |title=Remembering Elwyn Berlekamp |url=https://www.gathering4gardner.org/elwyn-berlekamp-tribute/ |access-date=2024-02-12 |website=Gathering 4 Gardner |language=en-US}}</ref> Berlekamp teamed up with [[John Horton Conway]] and [[Richard K. Guy]], two other close associates of Gardner, to co-author the book ''[[Winning Ways for your Mathematical Plays]]'', leading to his recognition as one of the founders of [[combinatorial game theory]].<ref name= Berlekamp2014>''[https://sinews.siam.org/DesktopModules/PackFlashPublish/ArticleDetail/ArticleDetailPrint.aspx?ArticleID=200&Template=Standard_Print.ascx&siteID=13 The Mathematical Legacy of Martin Gardner]'' by Elwyn Berlekamp, [[Society for Industrial and Applied Mathematics]] (SIAM), September 2, 2014: Partly because of what I had read about them in Martin Gardner’s columns, I was appropriately awestruck in the 1960s when I first met Sol Golomb and then Richard Guy, each of whom had a large influence on my subsequent work. In 1969 Richard introduced me to John Horton Conway, and the three of us immediately began collaborating on a book that eventually became ''Winning Ways for Your Mathematical Plays''. In the 1970s, I joined Conway in some of his many visits to Gardner’s home on Euclid Avenue, in Hastings-on-Hudson, New York. Gardner soon became an enthusiastic advocate of our book project, and he previewed various snippets of it in his Scientific American columns.</ref> The dedication of their book says, "To Martin Gardner, who has brought more mathematics to more millions than anyone else."<ref>Berlekamp, Elwyn R., John H. Conway, and Richard K. Guy (1982). ''Winning Ways for your Mathematical Plays'' Academic Press, {{ISBN|0120911507}}.</ref>


Berlekamp and Gardner both had great love for and were strong advocates of recreational mathematics.<ref name= Berlekamp2014/> Conferences called [[Gathering 4 Gardner]] (G4G) are held every two years to celebrate the Gardner legacy.<ref name=tribute/> Berlekamp was one of the founders of G4G and was on its board of directors for many years.<ref>[https://www.gathering4gardner.org/the-gathering-history/ History of the Gathering] Gathering 4 Gardner</ref>
Berlekamp and Gardner both had great love for and were strong advocates of recreational mathematics.<ref name= Berlekamp2014/> Conferences called [[Gathering 4 Gardner]] (G4G) are held every two years to celebrate the Gardner legacy.<ref name=tribute/> Berlekamp was one of the founders of G4G and was on its board of directors for many years.<ref>[https://www.gathering4gardner.org/the-gathering-history/ History of the Gathering] {{Webarchive|url=https://web.archive.org/web/20190418213053/https://www.gathering4gardner.org/the-gathering-history/ |date=2019-04-18 }} Gathering 4 Gardner</ref>


==Selected publications==
==Selected publications==
Line 53: Line 50:
**1st edition, New York: [[Academic Press]], 2 vols., 1982;<ref>{{cite journal|author=Golomb, Solomon|author-link=Solomon W. Golomb|title=Review: ''Winning ways for your mathematical plays'', by E. R. Berlekamp, J. H. Conway, and R. K. Guy|journal=Bull. Amer. Math. Soc. (N.S.)|year=1983|volume=8|issue=1|pages=108–111|doi=10.1090/s0273-0979-1983-15098-x|doi-access=free}}</ref> vol. 1, hardback: {{ISBN|0-12-091150-7}}, paperback: {{ISBN|0-12-091101-9}}; vol. 2, hardback: {{ISBN|0-12-091152-3}}, paperback: {{ISBN|0-12-091102-7}}.
**1st edition, New York: [[Academic Press]], 2 vols., 1982;<ref>{{cite journal|author=Golomb, Solomon|author-link=Solomon W. Golomb|title=Review: ''Winning ways for your mathematical plays'', by E. R. Berlekamp, J. H. Conway, and R. K. Guy|journal=Bull. Amer. Math. Soc. (N.S.)|year=1983|volume=8|issue=1|pages=108–111|doi=10.1090/s0273-0979-1983-15098-x|doi-access=free}}</ref> vol. 1, hardback: {{ISBN|0-12-091150-7}}, paperback: {{ISBN|0-12-091101-9}}; vol. 2, hardback: {{ISBN|0-12-091152-3}}, paperback: {{ISBN|0-12-091102-7}}.
**2nd edition, [[Wellesley, Massachusetts|Wellesley]], [[Massachusetts]]: [[A. K. Peters Ltd.]], 4 vols., 2001–2004; vol. 1: {{ISBN|1-56881-130-6}}; vol. 2: {{ISBN|1-56881-142-X}}; vol. 3: {{ISBN|1-56881-143-8}}; vol. 4: {{ISBN|1-56881-144-6}}.
**2nd edition, [[Wellesley, Massachusetts|Wellesley]], [[Massachusetts]]: [[A. K. Peters Ltd.]], 4 vols., 2001–2004; vol. 1: {{ISBN|1-56881-130-6}}; vol. 2: {{ISBN|1-56881-142-X}}; vol. 3: {{ISBN|1-56881-143-8}}; vol. 4: {{ISBN|1-56881-144-6}}.
* (with [[David Wolfe (mathematician)|David Wolfe]]) ''Mathematical Go''. Wellesley, Massachusetts: A. K. Peters Ltd., 1994. {{ISBN|1-56881-032-6}}.<ref>{{cite journal|author=Guy, Richard K.|author2=Nowakowski, Richard J.|title=Review: ''Mathematical Go: Chilling gets the last point'', by Elwyn Berlekamp and David Wolfe|journal=Bull. Amer. Math. Soc. (N.S.)|year=1995|volume=32|issue=4|pages=437–441|url=http://www.ams.org/journals/bull/1995-32-04/S0273-0979-1995-00601-4/S0273-0979-1995-00601-4.pdf|doi=10.1090/S0273-0979-1995-00601-4}}</ref>
* (with [[David Wolfe (mathematician)|David Wolfe]]) ''Mathematical Go''. Wellesley, Massachusetts: A. K. Peters Ltd., 1994. {{ISBN|1-56881-032-6}}.<ref>{{cite journal|author=Guy, Richard K.|author2=Nowakowski, Richard J.|title=Review: ''Mathematical Go: Chilling gets the last point'', by Elwyn Berlekamp and David Wolfe|journal=Bull. Amer. Math. Soc. (N.S.)|year=1995|volume=32|issue=4|pages=437–441|url=https://www.ams.org/journals/bull/1995-32-04/S0273-0979-1995-00601-4/S0273-0979-1995-00601-4.pdf|doi=10.1090/S0273-0979-1995-00601-4|doi-access=free}}</ref>
* ''The Dots-and-Boxes Game''. [[Natick, Massachusetts|Natick]], [[Massachusetts]]: [[A. K. Peters Ltd.]], 2000. {{ISBN|1-56881-129-2}}.
* ''The Dots-and-Boxes Game''. [[Natick, Massachusetts|Natick]], [[Massachusetts]]: [[A. K. Peters Ltd.]], 2000. {{ISBN|1-56881-129-2}}.


==See also==
==See also==

[[Berlekamp switching game]]
* [[Berlekamp switching game]]
* [[Berlekamp–Zassenhaus algorithm]]


==References==
==References==
{{Reflist|2}}
{{reflist}}


==External links==
==External links==
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[[Category:Fellows of the American Academy of Arts and Sciences]]
[[Category:Fellows of the American Academy of Arts and Sciences]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Go (game) researchers]]
[[Category:MIT School of Engineering alumni]]
[[Category:MIT School of Engineering alumni]]
[[Category:Mathematicians from Ohio]]
[[Category:Mathematicians from Ohio]]

Latest revision as of 16:48, 12 October 2024

Elwyn Berlekamp
Berlekamp in 2005
Born
Elwyn Ralph Berlekamp

(1940-09-06)September 6, 1940
Dover, Ohio, U.S.
DiedApril 9, 2019(2019-04-09) (aged 78)
Piedmont, California, U.S.
Alma materMassachusetts Institute of Technology
Known forBerlekamp's algorithm
Berlekamp switching game
Berlekamp–Welch algorithm
Berlekamp–Massey algorithm
Berlekamp–Rabin algorithm
Berlekamp–Zassenhaus algorithm
Berlekamp–Van Lint–Seidel graph
Blockbusting
Combinatorial game theory
Cooling and heating
Coupon Go
Error-correcting codes with feedback
Partisan game
Phutball
AwardsIEEE Richard W. Hamming Medal (1991)
Claude E. Shannon Award (1993)
Scientific career
FieldsInformation theory, Coding theory, Combinatorial game theory
InstitutionsUniversity of California, Berkeley
ThesisBlock coding with noiseless feedback (1964)
Doctoral advisorRobert G. Gallager
Doctoral studentsJulia Kempe
Other notable studentsKen Thompson

Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley.[1][2] Berlekamp was widely known for his work in computer science, coding theory and combinatorial game theory.

Berlekamp invented an algorithm to factor polynomials and the Berlekamp switching game, and was one of the inventors of the Berlekamp–Welch algorithm and the Berlekamp–Massey algorithms, which are used to implement Reed–Solomon error correction. He also co-invented the Berlekamp–Rabin algorithm, Berlekamp–Zassenhaus algorithm, and the Berlekamp–Van Lint–Seidel graph.

Berlekamp had also been active in investing, and ran Axcom, which became the Renaissance Technologies' Medallion Fund.

Life and education

[edit]

Berlekamp was born in Dover, Ohio. His family moved to Northern Kentucky, where Berlekamp graduated from Ft. Thomas Highlands high school in Ft. Thomas, Campbell county, Kentucky. While an undergraduate at the Massachusetts Institute of Technology (MIT), he was a Putnam Fellow in 1961.[3] He completed his bachelor's and master's degrees in electrical engineering in 1962. Continuing his studies at MIT, he finished his Ph.D. in electrical engineering in 1964; his advisors were Robert G. Gallager, Peter Elias, Claude Shannon, and John Wozencraft.

Berlekamp had two daughters and a son with his wife Jennifer. He lived in Piedmont, California and died in April 2019 at the age of 78 from complications of pulmonary fibrosis.[4]

Career

[edit]

Berlekamp was a professor of electrical engineering at the University of California, Berkeley from 1964 until 1966, when he became a mathematics researcher at Bell Labs. In 1971, Berlekamp returned to Berkeley as professor of mathematics and computer science, where he served as the advisor for over twenty doctoral students.[1][2][5]

He was a member of the National Academy of Engineering (1977)[6] and the National Academy of Sciences (1999).[7] He was elected a Fellow of the American Academy of Arts and Sciences in 1996,[8] and became a fellow of the American Mathematical Society in 2012.[9] In 1991, he received the IEEE Richard W. Hamming Medal,[10] and in 1993, the Claude E. Shannon Award. In 1998, he received a Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society.[11] Along with Tom M. Rodgers[12] he was one of the founders of Gathering 4 Gardner and was on its board for many years.[13] In the mid-1980s, he was president of Cyclotomics, Inc., a corporation that developed error-correcting code technology.[1]

He studied various games, including dots and boxes, fox and geese, and, especially, Go. Berlekamp and co-author David Wolfe describe methods for analyzing certain classes of Go endgames in the book Mathematical Go.

Berlekamp and Martin Gardner

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Berlekamp was a close friend of Scientific American columnist Martin Gardner and was an important member of the gifted and diverse group of people that Gardner nurtured and acted as a conduit for; people who inspired Gardner and who were in turn inspired by him.[14] Berlekamp teamed up with John Horton Conway and Richard K. Guy, two other close associates of Gardner, to co-author the book Winning Ways for your Mathematical Plays, leading to his recognition as one of the founders of combinatorial game theory.[15] The dedication of their book says, "To Martin Gardner, who has brought more mathematics to more millions than anyone else."[16]

Berlekamp and Gardner both had great love for and were strong advocates of recreational mathematics.[15] Conferences called Gathering 4 Gardner (G4G) are held every two years to celebrate the Gardner legacy.[14] Berlekamp was one of the founders of G4G and was on its board of directors for many years.[17]

Selected publications

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  • Block coding with noiseless feedback. Thesis, Massachusetts Institute of Technology, Dept. of Electrical Engineering, 1964.
  • Algebraic Coding Theory, New York: McGraw-Hill, 1968. Revised ed., Aegean Park Press, 1984, ISBN 0-89412-063-8.
  • (with John Horton Conway and Richard K. Guy) Winning Ways for your Mathematical Plays.
  • (with David Wolfe) Mathematical Go. Wellesley, Massachusetts: A. K. Peters Ltd., 1994. ISBN 1-56881-032-6.[19]
  • The Dots-and-Boxes Game. Natick, Massachusetts: A. K. Peters Ltd., 2000. ISBN 1-56881-129-2.

See also

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References

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  1. ^ a b c "Contributors". IEEE Transactions on Information Theory. 42 (3): 1048. May 1996. doi:10.1109/TIT.1996.490574. ISSN 0018-9448.
  2. ^ a b Elwyn Berlekamp, listing at the Department of Mathematics, University of California, Berkeley.
  3. ^ "Putnam Competition Individual and Team Winners". Mathematical Association of America. Retrieved December 12, 2021.
  4. ^ "Elwyn Berlekamp, game theorist and coding pioneer, dies at 78". Berkeley. 2022. Retrieved 2024-02-12.
  5. ^ Contributors, IEEE Transactions on Information Theory 20, #3 (May 1974), p. 408.
  6. ^ "NAE Members Directory – Dr. Elwyn R. Berlekamp". NAE. Retrieved June 16, 2011.
  7. ^ "NAS Membership Directory". NAS. Retrieved June 16, 2011. Search with "Last Name" is Berlekamp.
  8. ^ "Book of Members, 1780–2010: Chapter B" (PDF). American Academy of Arts and Sciences. Retrieved June 16, 2011.
  9. ^ "Fellows of the American Mathematical Society". American Mathematical Society. Retrieved 2024-02-12.
  10. ^ "IEEE Richard W. Hamming Medal Recipients" (PDF). IEEE. Archived from the original (PDF) on June 20, 2010. Retrieved May 29, 2011.
  11. ^ "Golden Jubilee Awards for Technological Innovation". IEEE Information Theory Society. Retrieved July 14, 2011.
  12. ^ Rothstein, Edward (2004-04-03). "Puzzles + Math = Magic". The New York Times. ISSN 0362-4331. Retrieved 2024-02-12.
  13. ^ About Gathering 4 Gardner Foundation Archived 2016-05-07 at the Wayback Machine
  14. ^ a b Hirth, Tiago (2020-01-24). "Remembering Elwyn Berlekamp". Gathering 4 Gardner. Retrieved 2024-02-12.
  15. ^ a b The Mathematical Legacy of Martin Gardner by Elwyn Berlekamp, Society for Industrial and Applied Mathematics (SIAM), September 2, 2014: Partly because of what I had read about them in Martin Gardner’s columns, I was appropriately awestruck in the 1960s when I first met Sol Golomb and then Richard Guy, each of whom had a large influence on my subsequent work. In 1969 Richard introduced me to John Horton Conway, and the three of us immediately began collaborating on a book that eventually became Winning Ways for Your Mathematical Plays. In the 1970s, I joined Conway in some of his many visits to Gardner’s home on Euclid Avenue, in Hastings-on-Hudson, New York. Gardner soon became an enthusiastic advocate of our book project, and he previewed various snippets of it in his Scientific American columns.
  16. ^ Berlekamp, Elwyn R., John H. Conway, and Richard K. Guy (1982). Winning Ways for your Mathematical Plays Academic Press, ISBN 0120911507.
  17. ^ History of the Gathering Archived 2019-04-18 at the Wayback Machine Gathering 4 Gardner
  18. ^ Golomb, Solomon (1983). "Review: Winning ways for your mathematical plays, by E. R. Berlekamp, J. H. Conway, and R. K. Guy". Bull. Amer. Math. Soc. (N.S.). 8 (1): 108–111. doi:10.1090/s0273-0979-1983-15098-x.
  19. ^ Guy, Richard K.; Nowakowski, Richard J. (1995). "Review: Mathematical Go: Chilling gets the last point, by Elwyn Berlekamp and David Wolfe" (PDF). Bull. Amer. Math. Soc. (N.S.). 32 (4): 437–441. doi:10.1090/S0273-0979-1995-00601-4.
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