by Robion C. Kirby
Elwyn Ralph Berlekamp, the son of Reverend Waldo Berlekamp and Loretta Kimmel Berlekamp, was born on 6 September, 1940, in Dover, Ohio, at the local hospital closest to his family home in nearby Strasbourg.
Elwyn’s father was the youngest of ten children whose family had roots in the rural Midwest. His grandfather, a farmer, had hoped to leave his farm in western Missouri to one of his sons, but none were interested, so the land eventually passed to his daughter who married a farmer and whose family still lives there. Elwyn’s father and another uncle left the farm to became ministers, about the only occupation that the grandfather thought was as good as farming. Waldo was a reverend in the United Church of Christ, the same church as Barack Obama, and in fact he was raising money for inner city missions at about the same time that Obama was on the church’s payroll.
One branch of Waldo’s family was German and they first arrived in the US in 1843. Another branch of the nineteenth-century family came from an area on the border between Holland and Germany, and when Elwyn’s wife first presented her future husband to her British family, whose relatives had keen memories of World War II, she explained that he was of Dutch rather than German extraction.
Elwyn was four years old at the end of the War and remembers thinking “Now I can get an electric train and we can go to California”! He did receive a train that Christmas, though a trip to California was still a decade off.
In 1948 Elwyn was able to tune into Cleveland radio stations and became a Cleveland Indians fan, the year they won the World Series against the Boston Braves. It was as a baseball fan that his mathematical prowess first became apparent: he had learned long division, and computed extensive tables of batting averages, so when a player got a hit, Elwyn would have his new batting average faster than the radio announcers.
In 1949, when Elwyn was in fourth grade, the family moved to Fort Thomas, Kentucky, across the Ohio River from Cincinnati. He did the usual things kids do to fit into a new environment, including trying out for the school Christmas play. Apparently the tryouts consisted of which child could best say “Bah Humbug!”. Elwyn won.
One day, a ten-year-old Elwyn came upon a group of much-older students who were pondering the famous problem of finding the odd coin of different weight among twelve otherwise identical coins. The problem is to use a balance scale and no more than three weighings to find the odd coin. After kibitzing for some time, Elwyn returned home and discovered the solution later that same night — alone. He was surprised to learn a few days later that the other, older students had not succeeded. This problem would recur in Elwyn’s thoughts as an example of a negacode of length \( 13 = (3^3 - 1)/2 \), which appears in his book on algebraic coding theory.
In high school, Elwyn joined the swim team, and swam the butterfly stroke on the medley relay team that won the state championship in 1957. He claimed to be the slowest of the four, having started the third leg with a several length lead and finishing a length behind, which was more than made up by the fourth leg free style swimmer. Weakest link or not, the win stands out in the math world as an athletic feat.
A summer at the High School Institute at Northwestern University convinced Elwyn to devote himself to science, engineering and mathematics, and in 1958 he enrolled at MIT. Even here, he was a stand-out: As a sophomore, Elwyn signed up for eight courses when the normal load was four. One could get away with five, or conceivably six, but not more. His advisor Peter Elias would periodically ask him, “Which two or three of your courses are you going to drop?” Elwyn would evade the question, one way or another, yet when the term ended, Elwyn had earned an “A” in all eight courses. Thereafter (when Elias had become chair), whenever Elwyn wanted something unusual, Elias would say to his colleagues, “Let Elwyn do what he wants”.
In college, Elwyn turned his formidable powers of concentration to other interests besides academics: he became a competitive bridge player. When the Putnam Exam conflicted with a bridge tournament, the latter took precedence. In fact, Elwyn only took the Exam once, in 1961, and finished in the top five.
Elwyn spent summers and one semester as a “coop student” at Bell Labs. His mentor there (and bridge partner) was initially John Kelly, Jr., author of a pioneering paper on financial mathematics. Later he worked with Edward David, Jr., who became Presidential Science advisor to Richard Nixon. David was chair of the National Research Council panel that produced the famous “David report”: it recommended a doubling of federal funds for mathematics and did, in fact, lead to striking increases.
Elwyn served energetically for 16 years on the MIT math department’s Visiting Committee, and argued for an increase in enrollment of underrepresented groups during his tenure as a Committee member. During his own student years, the overall percentage of women at MIT had been very low. His graduating class of 1962 (one year after the university’s centennial) consisted of 950 men and 50 women, no improvement over the very first graduating class, which had 19 men and only one woman. But by the the time Elwyn stepped down from the Committee, he could point to a significant positive change: women were then 48% of MIT students, and were a majority in all but two departments, mathematics and computer science.
Elwyn received his Ph.D. in 1964 with a thesis titled “Block coding with noiseless feedback”. His advisor was Robert G. Gallager. Other influential committee members were Peter Elias, Claude Shannon, and John Wozencraft.
In 1964–66, Elwyn was an assistant professor in the Department of Electrical Engineering at the University of California, Berkeley. He had some exceptionally good students — in particular, Ken Thompson, who went on to Bell Labs where he “co-invented” the Unix operating system and the \( C \) programming language. Thompson received the ACM Turing Award in 1983 and the National Medal of Technology from President Clinton in 1988.
In January 1965, Elwyn got a call from Sol Golomb at the Jet Propulsion Lab (JPL) in Pasadena and soon began consulting with the Lab on a regular basis. He visited JPL weekly for the next year and a half, joining an illustrious group of researchers that included Marshall Hall, Irwin Jacobs, Andrew Viterbi, Lloyd Welch, Len Kleinrock, and Cal Tech students like Bob McEliece and Richard Stanley. They worked on ranging and communications with deep space probes.
While at a NATO conference (1965) on coding in France, Elwyn received a card from Jennifer, the woman he’d been dating and to whom he’d lent his car while he was abroad. The card showed an owl saying “Whoooo misses you?”, and inside she had drawn the car and herself. Elwyn remembered this as the closest thing to a love letter he ever received. They were married a year later.
In the fall of 1966, Elwyn went to the University of North Carolina (UNC) intending to work with R. C. Bose, one of whose students was D. K. Chaudhuri. Bose was ill and unavailable much of the time, so Elwyn turned his attention to a different purpose, and wrote most of his book Algebraic Coding Theory.
The move to UNC was fortuitous for at a conference there in the spring of 1967 Elwyn met Richard Guy, with whom he soon became friend and collaborator. Guy had completed an MA at the University of Cambridge in 1941 but had been drafted and then sent off to Iceland and, later, Bermuda to do weather forecasting. He eventually reentered academia, teaching at the Indian Institute of Technology for a time and then joining the faculty at the University of Calgary. Elwyn and Richard decided to write a book on games, but Guy thought they needed a third author, and he knew just the right person: John Conway. Thus their Winning Ways for your Mathematical Plays (A.K. Peters, 1982) was conceived, though it took 13 years to complete. One might add that, in mathematics, this is not an inordinate gestation period for a book that turns into four volumes!
\[ \star\qquad\star\qquad\star \]
During these years of academic involvement, Elwyn resumed a youthful diversion: he started juggling again, having first learned in junior high school. Sometimes he teamed up with others — like Ron Graham. Once they went to an international jugging conference together, where, though Elwyn was not really good enough to compete, he served as judge. Mathematician and information theorist Claude Shannon once advised Elwyn, upon seeing him head toward the library to read one of his papers, “Don’t do that; try to figure it out yourself!” (Shannon loved gadgets and built a machine that could juggle three balls.) Years later, Joe Buehler and David Eisenbud joined in and became proficient jugglers during their time together at the helm of MSRI.
\[ \star\qquad\star\qquad\star \]
Elwyn and Jennifer’s first daughter, Persis Dorothy Berlekamp was born in 1968.1 Elwyn was at Bell Labs at this time, and in 1971, before the birth of his second daughter, Brownen Janie (in 1972),2 he returned to Berkeley as a professor of Mathematics and Electrical Engineering and Computer Science. Elwyn’s youngest, David Andrew Roger Berlekamp, was born in 1982.
\[ \star\qquad\star\qquad\star \]
Elwyn early on showed an interest in and flair for entrepreneurial activity. In 1974, with collaborators Sol Golomb, and his own wife, Jennifer, Elwyn started a company called Cyclotomics. Together they pioneered the technology of algebraic error-correcting codes for applications in both computer memories and various communication systems. Cyclotomics was acquired by Eastman Kodak in 1985.
Elwyn also became active in money management, and in 1986 began information-theoretic studies of commodity and financial futures. In 1989 he bought a controlling interest in Axcom Trading Advisors, a futures trading company, and, together with James Harris Simons, began retooling the firm’s algorithms. The result was dramatic: In 1990, Axcom’s Medallion Fund had a net return of 55%. Berlekamp sold his stake in Axcom to Simons in 1992, and the Medallion fund has subsequently continued to realize annualized returns exceeding 30% under the management of Simons’ Renaissance Technologies Corporation.
\[ \star\qquad\star\qquad\star \]
Elwyn is a member of the National Academy of Engineering (since 1977) and the National Academy of Sciences (1999). He is a Fellow of the American Academy of Arts and Sciences (elected in 1996) and of the American Mathematical Society (2012). Other awards include the 1971 “Outstanding Young Electrical Engineer Award” from Eta Kappa Nu and the following awards from the Institute of Electrical and Electronics Engineers (IEEE): the 1989 Koji Kobayashi Award, the 1991 Richard W. Hamming Medal, the 1993 Claude E. Shannon Award, and a 1998 Golden Jubilee Award for Technological Innovation.
Added in Proof: Elwyn died on April 9, 2019, of complications from pulmonary fibrosis.
