Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

and

computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

.Elwyn Berlekamp
listing at the Department of Mathematics,

. Berlekamp was widely known for his work in computer science,

coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data sto ...

and

combinatorial game theory Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a ''position'' ev ...

. Berlekamp invented an algorithm to factor polynomials and the Berlekamp switching game, and was one of the inventors of the

Berlekamp–Welch algorithm The Berlekamp–Welch algorithm, also known as the Welch–Berlekamp algorithm, is named for Elwyn R. Berlekamp and Lloyd R. Welch. This is a decoder algorithm that efficiently corrects errors in Reed–Solomon error correction, Reed–Solomon code ...

and the

Berlekamp–Massey algorithm The Berlekamp–Massey algorithm is an algorithm that will find the shortest linear-feedback shift register (LFSR) for a given binary output sequence. The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an ar ...

s, which are used to implement

Reed–Solomon error correction In information theory and coding theory, Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960. They have many applications, including consumer technologies such as MiniDiscs, ...

. He also co-invented the

Berlekamp–Rabin algorithm In number theory, Berlekamp's root finding algorithm, also called the Berlekamp–Rabin algorithm, is the probabilistic method of finding roots of polynomials over the field \mathbb F_p with p elements. The method was discovered by Elwyn Berlekam ...

, Berlekamp–Zassenhaus algorithm, and the Berlekamp–Van Lint–Seidel graph. Berlekamp had also been active in

investing Investment is traditionally defined as the "commitment of resources into something expected to gain value over time". If an investment involves money, then it can be defined as a "commitment of money to receive more money later". From a broade ...

, and ran Axcom, which became the

Renaissance Technologies Renaissance Technologies LLC (also known as RenTec or RenTech) is an American hedge fund based in East Setauket, New York, on Long Island, that specializes in systematic trading using quantitative models derived from mathematical and statist ...

' Medallion Fund.

Life and education

Berlekamp was born in Dover, Ohio. His family moved to Northern Kentucky, where from 1954 Berlekamp attended Fort Thomas Highlands High School in Fort Thomas, Kentucky. He was elected class president and joined the swim team which practiced naked at the local YMCA pool; Berlekamp was the slowest swimmer but chose swimming because of the low level of competition compared to other sports. He decided to attend the

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

(MIT) after learning it did not have an

American football American football, referred to simply as football in the United States and Canada and also known as gridiron football, is a team sport played by two teams of eleven players on a rectangular American football field, field with goalposts at e ...

team. At MIT, his freshman professors included

John Forbes Nash Jr. John Forbes Nash Jr. (June 13, 1928 – May 23, 2015), known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differentia ...

and he was a

Putnam Fellow 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 ...

during his senior year in 1961. He completed his bachelor's and master's degrees in

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

in 1962. Berlekamp did

internships An internship is a period of work experience offered by an organization for a limited period of time. Once confined to medical graduates, internship is used to practice for a wide range of placements in businesses, non-profit organizations and g ...

at Bell Labs in 1960 and 1962, where his boss was John Larry Kelly Jr. 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 Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and the man who laid the foundations of th ...

, and John Wozencraft. Berlekamp met his wife, Jennifer Wilson, in 1964 after juggling in his apartment and having to apologize for causing a noise disturbance. They had two daughters and a son. He lived in Piedmont, California and died in April 2019 at the age of 78 from complications of

pulmonary fibrosis Pulmonary fibrosis is a condition in which the lungs become scarred over time. Symptoms include shortness of breath, a dry cough, feeling tired, weight loss, and nail clubbing. Complications may include pulmonary hypertension, respiratory ...

Career

Berlekamp was a professor of electrical engineering at the

from 1964 until 1966, when he became a mathematics researcher at

Bell Labs Nokia Bell Labs, commonly referred to as ''Bell Labs'', is an American industrial research and development company owned by Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, Murray Hill, New Jersey, the compa ...

. In 1971, Berlekamp returned to Berkeley as professor of mathematics and computer science, where he served as the advisor for over twenty doctoral students.Contributors
''IEEE Transactions on Information Theory'' 20, #3 (May 1974), p. 408. He was a member of the

National Academy of Engineering The National Academy of Engineering (NAE) is an American Nonprofit organization, nonprofit, NGO, non-governmental organization. It is part of the National Academies of Sciences, Engineering, and Medicine (NASEM), along with the National Academ ...

(1977) and 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 ...

(1999). He was elected a Fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

in 1996, and became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

in 2012. In 1991, he received the IEEE Richard W. Hamming Medal, 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 The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) organization, 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE ...

. Along with Tom M. Rodgers he was one of the founders of Gathering 4 Gardner and was on its board for many years. In the mid-1980s, he was president of Cyclotomics, Inc., a corporation that developed error-correcting code technology. He studied various games, including dots and boxes, fox and geese, and, especially, Go. Berlekamp and co-author David Wolfe described methods for analyzing certain classes of Go endgames in the book ''Mathematical Go.''

Berlekamp and Martin Gardner

Berlekamp was a member of the group of people around the ''

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it, with more than 150 Nobel Pri ...

'' columnist

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writin ...

, a close friend. Berlekamp teamed up with

John Horton Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician. He was active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many b ...

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

.
The Mathematical Legacy of Martin Gardner
' by Elwyn Berlekamp,

Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific soci ...

(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. The dedication of their book says, "To Martin Gardner, who has brought more mathematics to more millions than anyone else." Berlekamp and Gardner both supported

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research-and-application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

. Conferences called Gathering 4 Gardner (G4G) are held every two years to celebrate the Gardner legacy. Berlekamp was one of the founders of G4G and was on its board of directors for many years.

Selected publications

* ''Block coding with noiseless feedback''. Thesis,

, Dept. of Electrical Engineering, 1964. * ''Algebraic Coding Theory'',

New York New York most commonly refers to: * New York (state), a state in the northeastern United States * New York City, the most populous city in the United States, located in the state of New York New York may also refer to: Places United Kingdom * ...

McGraw-Hill McGraw Hill is an American education science company that provides educational content, software, and services for students and educators across various levels—from K-12 to higher education and professional settings. They produce textbooks, ...

, 1968. Revised ed., Aegean Park Press, 1984, . * (with

and Richard K. Guy) '' Winning Ways for your Mathematical Plays''. **1st edition, New York:

Academic Press Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal complete ...

, 2 vols., 1982; vol. 1, hardback: , paperback: ; vol. 2, hardback: , paperback: . **2nd edition, Wellesley,

Massachusetts Massachusetts ( ; ), officially the Commonwealth of Massachusetts, is a U.S. state, state in the New England region of the Northeastern United States. It borders the Atlantic Ocean and the Gulf of Maine to its east, Connecticut and Rhode ...

: A. K. Peters Ltd., 4 vols., 2001–2004; vol. 1: ; vol. 2: ; vol. 3: ; vol. 4: . * (with David Wolfe) ''Mathematical Go''. Wellesley, Massachusetts: A. K. Peters Ltd., 1994. . * ''The Dots-and-Boxes Game''. Natick,

: A. K. Peters Ltd., 2000. .

References

External links