Elwyn Berlekamp: The Mathematics of Winning
A Berkeley mathematician once challenged a top Japanese Go master to a series of endgames — not full games, just the closing positions, where a lifetime of trained intuition is supposed to be decisive. He won seven in a row. David Eisenbud's summary is the cleanest description of Elwyn Berlekamp's whole career: "It was mathematics against intuition, and mathematics won." The same instinct put error-correcting code on the Voyager spacecraft, into compact discs, and eventually into one of the most profitable hedge funds ever built.
Dover, Ohio
Elwyn Ralph Berlekamp was born on 6 September 1940 in Dover, Ohio, to Waldo Berlekamp, a United Church of Christ minister of German descent, and Loretta Kimmel Berlekamp. The family moved to northern Kentucky, where he attended Fort Thomas Highlands High School from 1954, was class president and swam competitively. He chose MIT, by his own account, partly because it did not have an American football team.
At MIT his freshman professors included John Forbes Nash Jr. He made Putnam Fellow in his senior year of 1961, took bachelor's and master's degrees in electrical engineering by 1962, and completed a doctorate in 1964 with a dissertation on block coding with noiseless feedback. His advisors were Robert Gallager, Peter Elias, Claude Shannon and John Wozencraft — a supervisory committee containing the founder of information theory and three of the people who built the field around him. He interned at Bell Labs in 1960 and 1962 under John Larry Kelly Jr.
Making Noise Survivable
Berlekamp taught electrical engineering at Berkeley from 1964 to 1966, went to Bell Labs as a mathematics researcher, and returned to Berkeley in 1971 as a professor of mathematics and computer science, where he would supervise more than twenty doctoral students. In 1968 he published *Algebraic Coding Theory*, still regarded as the field's foundational text.
The algorithms carry his name in unusual density. Berlekamp's algorithm factors polynomials over finite fields and remains in use in cryptography. The Berlekamp–Massey and Berlekamp–Welch algorithms made Reed–Solomon error correction practical — which is why a scratched compact disc still plays and why a signal from the outer solar system arrives intelligible. There are also the Berlekamp–Rabin and Berlekamp–Zassenhaus algorithms and the Berlekamp–Van Lint–Seidel graph. Few mathematicians have their surname attached to that many distinct working tools.
Games as Mathematics
The second career would have been enough on its own. With John Horton Conway and Richard K. Guy, Berlekamp wrote *Winning Ways for Your Mathematical Plays* — two volumes from Academic Press in 1982, expanded to four in 2001–04 — which founded combinatorial game theory as a discipline. The dedication reads: "To Martin Gardner, who has brought more mathematics to more millions than anyone else." He followed it with *Mathematical Go* (1994) with David Wolfe, the work behind those seven straight endgame wins, and *The Dots-and-Boxes Game* (2000), which took a schoolchild's pastime and demonstrated it was a serious mathematical object.
With Tom Rodgers he founded Gathering 4 Gardner, the biennial recreational-mathematics conference honouring Martin Gardner, and sat on its board for years.
The Money
In the mid-1980s Berlekamp founded and ran Cyclotomics, Inc., built to implement his error-correcting codes properly rather than watch others implement them badly. It produced the NASA-standard encoders and decoders that are still working aboard Voyager I and II. Kodak bought the company in 1985 and renamed it Kodak Berkeley Research.
Then the strangest chapter. In 1989 Berlekamp bought a controlling stake in Axcom, a failing trading firm, rewrote its algorithms, and produced a 55 per cent return in the first year. In 1990 he sold his stake to James Simons for six times what he had paid. The rebuilt system became the groundwork for Renaissance Technologies' Medallion Fund, the most successful quantitative fund in history. He also chaired the board of the Mathematical Sciences Research Institute from 1994 to 1998, leading the fundraising that stabilised it around David Eisenbud's appointment as director.
Why Elwyn Is Called a Genius
The specific faculty is unusually easy to name: Berlekamp could convert games into algebra. Every major thing he did is the same operation performed on a different object. An error-correcting code is a game against noise, and he found the winning strategy. A Go endgame is a game against a human, and he decomposed it into independent sub-positions with computable values and beat a professional seven times running. A financial market is a game against other traders, and he rewrote the equations and returned 55 per cent. Richard Karp, who worked alongside him at Berkeley, described "a curious and powerful mind" and "a brilliant person who was always effective in everything he tried" — and singled out something rarer than raw ability: a talent for presenting hard mathematics with "real precision, but in a way that is actually charming." *Winning Ways* is the proof; it is a rigorous foundational text that people read for pleasure.
The honest qualification is about kind rather than degree. Berlekamp was not a builder of grand theoretical edifices in the mould of his advisor Claude Shannon, who created a field from nothing. He was a problem-solver and an algorithmist of the first rank, and his deepest work — combinatorial game theory — was co-authored with Conway and Guy, with Conway supplying the surreal-number machinery that gave the theory its foundations. His name attaches to methods rather than to theorems that reorganise mathematics. But the methods are load-bearing infrastructure: the argument that Reed–Solomon decoding matters more to daily life than most celebrated pure results is not a difficult one to make. David Patterson's memory of him — "a brilliant person, caring father, accomplished juggler" with "a great sense of humor" — catches the unusual thing, which is that none of it seemed to cost him his lightness.
Legacy
Berlekamp was elected to the National Academy of Engineering in 1977, made a fellow of the American Academy of Arts and Sciences in 1996, elected to the National Academy of Sciences in 1999, and became a fellow of the American Mathematical Society in 2012. He received the IEEE Richard W. Hamming Medal in 1991, the Claude E. Shannon Award in 1993 — named for his own doctoral advisor — and the IEEE Information Theory Society's Golden Jubilee Award in 1998. He died on 9 April 2019 at his home in Piedmont, California, aged seventy-eight, of complications from pulmonary fibrosis, survived by his wife Jennifer, whom he met in 1964, and their three children. His codes are still running on a spacecraft twenty-four billion kilometres away.
Achievements
- IEEE Richard W. Hamming Medal — 1991
- Held posts at University of California, Berkeley and Bell Labs
- Fields: information theory, coding theory and computer science
