Celebratio Mathematica

Elwyn Berlekamp

Elwyn Berlekamp

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.