Celebratio Mathematica

El­wyn Ber­lekamp, a UC Berke­ley math­em­atician and game the­or­ist whose er­ror-cor­rect­ing codes al­lowed space­craft from Voy­ager to the Hubble Space Tele­scope to send ac­cur­ate, de­tailed and beau­ti­ful im­ages back to Earth, died April 9 at his home in Pied­mont, Cali­for­nia, from com­plic­a­tions of pul­mon­ary fibrosis.

A pro­fess­or emer­it­us of math­em­at­ics and of elec­tric­al en­gin­eer­ing and com­puter sci­ences, Ber­lekamp was 78.

Ber­lekamp was a “geni­us” in many areas, ac­cord­ing to col­league Richard Karp, a UC Berke­ley pro­fess­or emer­it­us of elec­tric­al en­gin­eer­ing and com­puter sci­ences and hold­er of com­puter sci­ence’s premi­er hon­or, the Tur­ing Award.

“He was a bril­liant per­son who was al­ways ef­fect­ive in everything he tried to do, wheth­er it was math­em­at­ics or game the­ory or con­sult­ing and in­vest­ment. He had a curi­ous and power­ful mind,” said Karp, who was the first chair of UC Berke­ley’s com­puter sci­ences di­vi­sion upon its cre­ation and mer­ger with elec­tric­al en­gin­eer­ing in 1973. Ber­lekamp suc­ceeded Karp as chair from 1975 to 1977.

Ber­lekamp came of age dur­ing the early years of the di­git­al re­volu­tion and fo­cused on a prob­lem en­countered whenev­er in­form­a­tion is sent from one device to an­oth­er: How do you ac­count for lost bits of data? He de­veloped al­geb­ra­ic al­gorithms for com­press­ing im­ages or oth­er in­form­a­tion in ways that al­lowed pre­cise re­con­struc­tion, even if parts of the data stream were miss­ing due to noise or faulty trans­mis­sion.

When he felt that his er­ror-cor­rect­ing codes were not be­ing im­ple­men­ted prop­erly, he foun­ded a com­pany, Cyc­lo­tom­ics, to en­sure that they were. The com­pany’s bit-seri­al en­coders and Ber­lekamp de­coders be­came the NASA stand­ard for space com­mu­nic­a­tions. They’re still op­er­at­ing on the Voy­ager I and II space­craft, which were launched in 1977 and are now at the out­er edges of our sol­ar sys­tem.

The com­pany em­ployed er­ror-cor­rect­ing codes to de­vel­op nu­mer­ous in­nov­at­ive elec­tron­ic sub­sys­tems and cus­tom in­teg­rated cir­cuits that were used in mil­it­ary com­mu­nic­a­tions, op­tic­al disk memor­ies, mag­net­ic disk memor­ies, floppy disk memor­ies and com­pact disks, while the tech­niques were ad­ap­ted for op­tic­ally en­cod­ing di­git­al sound tracks on movie film.

Cyc­lo­tom­ics’ sound en­cod­ing/de­cod­ing sys­tem was a pro­to­type for East­man Kodak’s Di­git­al Sound Sys­tem, which won an Academy Award for sci­entif­ic and tech­nic­al achieve­ment in 1995, but was later sup­planted by oth­er tech­niques, in­clud­ing Dolby Sound. Kodak ac­quired Cyc­lo­tom­ics in 1985 and re­named it Kodak Berke­ley Re­search.

Ber­lekamp later branched out in­to cryp­to­graphy and the fin­an­cial mar­ket, where com­pan­ies were be­gin­ning to use com­plex math­em­at­ics to pre­dict stock per­form­ance, most not­ably in de­riv­at­ives. In 1989, he bought con­trolling shares in a fail­ing firm, Ax­com, that had asked for his help with its al­gorithms. He re­wrote them and turned the com­pany around, mak­ing a 55% net re­turn dur­ing its first year.

In 1990, he sold his in­terest in the com­pany for six times the pur­chase price to math­em­atician and former Renais­sance Tech­no­lo­gies CEO James Si­mons, then re­turned to re­search at UC Berke­ley. The com­pany’s al­gorithms, with a con­tinu­al series of en­hance­ments and im­prove­ments, per­formed well for the re­mainder of the dec­ade, lay­ing the found­a­tion for Renais­sance’s Medal­lion Fund, which is the most suc­cess­ful hedge fund in the world.

Ber­lekamp foun­ded his own hedge fund, Berke­ley Quant­it­at­ive, in 2008, fo­cus­ing on trad­ing in the fu­tures mar­kets, but it closed after two and a half years.

For the last three dec­ades of his life, he fo­cused on the the­ory of com­bin­at­or­i­al games, the most simple ex­ample of which, Dots and Boxes, had fas­cin­ated him since first grade. He de­veloped the­or­ies of the game that al­lowed him, or any­one, to al­ways win.

His two-volume series, Win­ning Ways for Your Math­em­at­ic­al Plays (1982, Aca­dem­ic Press), writ­ten with John Con­way and Richard Guy, delved in­to the math of Dots and Boxes and oth­er pop­u­lar games, in­clud­ing Amazons, a game played on a chess board with queens only. It was re­pub­lished in 2001–2004 in four volumes.

“In these books, he man­ages to de­scribe deep math­em­at­ics in a way that is really en­joy­able to the read­er,” Karp said. “He presents it more as a nar­rat­ive and ex­plains it with real pre­ci­sion, but in a way that is ac­tu­ally charm­ing. He was a won­der­ful au­thor as well.”

One of his pas­sions was the Asi­an game of Go, which he ana­lyzed with coau­thor Dav­id Wolfe in the book Math­em­at­ic­al Go (1994, A. K. Peters Ltd.) — one of the rare books on Go to be trans­lated from Eng­lish in­to Ja­pan­ese, rather than vice versa. He fo­cused on Go’s en­dgame, said math­em­atician and col­league Dav­id Eis­en­bud, and once chal­lenged a top Ja­pan­ese Go mas­ter to a series of en­dgames se­lec­ted by Ber­lekamp. He beat the Go mas­ter in sev­en straight games, play­ing both sides of the board — white and black.

“It was math­em­at­ics against in­tu­ition, and math­em­at­ics won,” said Eis­en­bud, dir­ect­or of the Math­em­at­ic­al Sci­ences Re­search In­sti­tute (MSRI). “It was an im­press­ive demon­stra­tion of which he was very proud.”

While the math­em­at­ic­al ana­lys­is of games is still very pop­u­lar, com­puters have taken the field in a dif­fer­ent dir­ec­tion: they em­ploy brute force or ma­chine learn­ing to beat Go and chess mas­ters.

From the 1970s on, Ber­lekamp was a strong sup­port­er of MSRI, a non-profit math­em­at­ics think tank launched in 1982 and housed in a build­ing on land leased from the uni­versity in the hills above the cam­pus. He served as chair­man of the board from 1994–1998, dur­ing which time Eis­en­bud was hired as dir­ect­or, in 1997, and spear­headed fun­drais­ing that proved crit­ic­al to the long-term suc­cess of the in­sti­tute.

His con­tri­bu­tions to MSRI are honored by a Ber­lekamp Postdoc­tor­al Fel­low­ship, which was en­dowed in 2014 with more than \$1 mil­lion in dona­tions from friends, and a Ber­lekamp Garden cre­ated in 2006.

Ber­lekamp was born in Dover, Ohio, the son of a min­is­ter, on Sept. 6, 1940, and later moved with his fam­ily to north­ern Ken­tucky, where he gradu­ated from Ft. Thomas High­lands High School in 1958. He at­ten­ded the Mas­sachu­setts In­sti­tute of Tech­no­logy, ob­tain­ing a B.S. and an M.S. in elec­tric­al en­gin­eer­ing in 1962 and a Ph.D. in elec­tric­al en­gin­eer­ing in 1964.

That same year, he was ap­poin­ted an as­sist­ant pro­fess­or of elec­tric­al en­gin­eer­ing at Berke­ley, but left in 1967 for Bell Tele­phone Labor­at­or­ies, where he had in­terned as an un­der­gradu­ate. While at Bell Labs, he wrote his sem­in­al book, Al­geb­ra­ic Cod­ing The­ory (1968), which is con­sidered the bible of the field. The well-known Ber­lekamp poly­no­mi­al factor­ing al­gorithm was the first, and for many years the most ef­fi­cient, tech­nique for find­ing solu­tions of large poly­no­mi­al equa­tions cre­ated in fields like cod­ing, and is still used in cryp­to­graphy.

He re­turned to Berke­ley in 1971 with a joint ap­point­ment in math­em­at­ics and elec­tric­al en­gin­eer­ing, re­duced his teach­ing ap­point­ment to part-time in 1982 to fo­cus on his com­pany, Cyc­lo­tom­ics, and re­tired in 2006.

“He was a bril­liant per­son, caring fath­er, ac­com­plished jug­gler and he had a great sense of hu­mor. He’ll not be for­got­ten,” said Dav­id Pat­ter­son, a pro­fess­or emer­it­us of elec­tric­al en­gin­eer­ing and com­puter sci­ences at Berke­ley who is now a dis­tin­guished en­gin­eer at Google and a Tur­ing Award win­ner.

Ber­lekamp and his wife, Jen­nifer, sup­por­ted vari­ous char­it­able causes and in 2013 foun­ded the El­wyn and Jen­nifer Ber­lekamp Found­a­tion, a small private op­er­at­ing found­a­tion based in Oak­land to sup­port math and sci­ence out­reach and edu­ca­tion, in gen­er­al, and com­bin­at­or­i­al game the­ory, in par­tic­u­lar.

Ber­lekamp was a mem­ber of the Na­tion­al Academy of Sci­ences and Na­tion­al Academy of En­gin­eer­ing and a fel­low of the In­sti­tute of Elec­tric­al and Elec­tron­ics En­gin­eers (IEEE), the Amer­ic­an Math­em­at­ic­al So­ci­ety, the Amer­ic­an As­so­ci­ation for the Ad­vance­ment of Sci­ence and the Amer­ic­an Academy of Arts and Sci­ences. He re­ceived vari­ous hon­ors, in­clud­ing the Centen­ni­al Medal, the Koji Kobay­ashi Com­puters and Com­mu­nic­a­tions Award and the R. W. Ham­ming Medal, all from IEEE, and was se­lec­ted as Eta Kappa Nu’s “Out­stand­ing Young Elec­tric­al En­gin­eer” in 1971 and as a Put­nam Fel­low in 1961. He held more than a dozen pat­ents, all of them now in the pub­lic do­main.

He is sur­vived by his wife, Jen­nifer; daugh­ters Per­sis Ber­lekamp, an art his­tor­i­an at the Uni­versity of Chica­go, and Bron­wen Ber­lekamp O’Wril of Port­land, Maine; and son Dav­id of Oak­land.