Asia Pacific Mathematics Newsletter

Sol Golomb — My Friendand Mentor
Alfred W HalesSolomon W. Golomb, a noted mathematician anda giant in the applications of mathematics tocoding and communication theory, passed away
on May 1, 2016, at the age of 83. His wife Bo died twoweeks later, leaving their two daughters Astrid andBeatrice. He was initially my supervisor and mentor,
then colleague and friend.
Sol was born in Baltimore, MD, on May 30, 1932.
His father and grandfather were both rabbis, and his
father was a linguistics professor at Johns Hopkins – Solhimself was a linguist, speaking seven languages. He
attended Baltimore schools for grades K-12 and thenwent on to Johns Hopkins where he graduated Phi Beta
Kappa in mathematics, with an “A” average, in twoyears, before he turned 19.
Already by this time he had a strong interest in
number theory, and in fact his first “publication” was anumber theory problem he submitted, while still inhigh school, to the American Mathematical Monthly.
In 1952 he started graduate work in mathematics
at Harvard, eventually receiving his PhD for a thesis inanalytic number theory under the direction of David
Widder. During this time at Harvard he also worked
summers at the Glenn Martin company near Baltimore,on controls and on communications. This combinationof “pure” (at Harvard) and “applied” (at Glenn Martin)
training turned out to be critical for his future career.
As a result of his summer work, his initial results on
shift registers appeared in 1955 as a Glenn Martin
report. During this period his interest in (mathematical)
puzzles and games also began to flourish.
After completing his Harvard work, for the 1955–56
academic year, he went to Norway on a Fulbright
Fellowship where he continued his Harvard work on
the distribution of prime numbers and also his shift
register work. During this year, on a side trip toDenmark, he met Bodil (“Bo”) and returned to the US
with her as his wife. Upon returning he chose, among
several alternatives, to accept a position at Caltech’s Jet
Propulsion Laboratory (JPL) in California, in theirCommunications Research Group.

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Sol spent seven years (1956–1963) at JPL. During
this time he greatly extended his work on shift register
sequences, leading to his 1967 magnum opus “ShiftRegister Sequences” (to be revised and reprinted in1982 and in 2017). He also made very significant
contributions to the JPL mission, such as to orbit
determination for the Explorer 1 satellite and also tomeasuring accurately the distance to Venus. This latterwork led to a much improved value for the “astronomical unit” and to a new experimental test of generalrelativity. He also wrote a number of influential papers
in number theory, combinatorics, algebraic coding
theory and other areas.
In 1963, Sol decided it was time to move on, to an
academic position. He chose USC (over Caltech andUCLA) because it seemed to offer greater opportunities,and took a position in Electrical Engineering with ajoint appointment in Mathematics. At USC his careerflourished in many respects, enhancing not only hisreputation but that of USC as a whole (because of hisaccomplishments). In fact, he played a major role inbringing to USC other luminaries in his field (EE), quite
a few of whom had spent some time with him at JPL.
He authored over 200 research papers and seven books,
taught and mentored an untold number of students andpostdocs, and played an important part as well in USC
administration — as Faculty Senate President, Vice
Provost for Research, and Annenberg Center Technology Director. He held both the title of Distinguished
Professor and of University Professor, and occupied
the Viterbi Chair in Communications; and also received
the USC Presidential Medallion. At the time of hisdeath, at age (almost) 84, he was still teaching a
freshman seminar!
Sol is almost certainly best known for his pioneering
work on the mathematical theory and applications ofshift register sequences. These are ubiquitous in radar,cryptography, space communications, cell phones,
spread-spectrum, wireless communications, etc.
Among his other contributions to coding and communication theory are Golomb (entropy) coding, Golomb

Asia Pacific Mathematics Newsletter

rulers, and the Golomb construction for Costas arrays.
In this connection he wrote not only the “Shift RegisterSequences” book but also (with Guang Gong) the book“Signal Design for Good Correlation”. For his exceptional contributions to information sciences andsystems the IEEE awarded him both the ShannonAward (1985) and Hamming Medal (2000).
Sol also made many contributions to other fields,with extensive (and seminal) publications in number
theory, combinatorics, algebra, and even moleculargenetics. In number theory his early work on primes
and their distribution played a role in the recent
breakthroughs (Zhang, Maynard, etc.) on the twin
prime conjecture. He was a noted expert on mathematical puzzles and games — polyominoes were his
invention, and he wrote a book about them. And hehad a very great influence on future generations due tohis generous and insightful mentoring of young people.
In addition to those mentioned above, Sol received
many other prestigious awards for his work. He was anelected member of both the US National Academy ofEngineering (1976) and of the US National Academyof Sciences (2000), and an elected Fellow of five major
scientific/technical organisations. He received theLomonosov Medal from the Russian Academy ofScience and the Kapitsa Medal from the Russian
Academy of Natural Sciences. In 2012 he received theWilliam Proctor Award, the highest technical award

bestowed by the Sigma Xi honorary society. In 2013
he received the National Medal of Science from President Barack Obama in a White House ceremony. And,
only a week before his death, he was awarded the 2016
Benjamin Franklin Medal of the Franklin Institute, forElectrical Engineering.
In conclusion here are three “aphorisms” which canbe (and have been) said about Sol’s accomplishments:
1) he brought modern combinatorial mathematics toSouthern California;
2) he disproved the opinion of G. H. Hardy, and ofmany of his Harvard teachers, that number theory
had no useful applications; and3) he changed the course of communications fromanalog to digital.
I first met Sol in 1958 when, as a Caltech student, Istarted working summers under his supervision at JPL.
We wrote three papers together, and I was a (junior)coauthor of his book “Shift Register Sequences”. He hada very major positive effect on my career and I owe him
a great deal. I last saw him at the Franklin Institute
ceremony mentioned above, a week before he died, andwe exchanged several e-mails during that last week. (Iwas helping with the final revisions for the third editionof his book.) The world has lost a uniquely talented
individual, and I personally miss him every day.

Alfred W Hales
Alfred W Hales was born in Pasadena, California in 1938. He received his BS degree
in mathematics from the California Institute of Technology (Caltech) in Pasadenain 1960, and his PhD in mathematics from Caltech in 1962.
During 1962–1963 he was an NSF Postdoctoral Fellow in Cambridge, England. From
1963–1966 he was a Benjamin Peirce Instructor at Harvard University. In 1966 hejoined the Mathematics Department at UCLA, where he was Department Chair(1988–1991) and is now Professor Emeritus. From 1992 to 2003 he was Directorof the Institute for Defense Analyses’ Center for Communications Research in La Jolla, CA, where he is now aResearch Staff Member. He is the author of over 75 research articles and was a (junior) co-author of Golomb’s
book on Shift Register Sequences (1967, 1982, 2017). His research interests include algebra, number theory
and combinatorics.
Prof. Hales is a Fellow of the American Association for the Advancement of Science and an Inaugural Fellowof the American Mathematical Society. From 2010–2017 he was Chair of the Board of Trustees of the NSF
Institute for Pure and Applied Mathematics at UCLA. In 1972 he was a co-recipient of the first Polya Prize inCombinatorics, from the Society for Industrial and Applied Mathematics, for his work in Ramsey Theory (theso-called Hales–Jewett Theorem).

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Being the granddaughter of a rabbi myself, I appreciatethat Dr. Golomb was both the son and grandson of rabbis.
A portion of the afternoon’s memorial service was givenby the campus Hillel rabbi, Hebrew songs were sung bychildren and Bailey London, Executive Director of USC
Hillel also paid tribute to Dr Golomb. The office of thePresident of USC co-sponsored the afternoon tribute andheld a private reception in Dr. Golomb’s honour.
UC San Diego’s Information Theory and Applications(ITA) Center, at its 2017 Workshop in February, devoted
an afternoon memorial session to “Remembering SolGolomb”. It was organised by Tuvi Etzion (Israel), withthe following speakers:1) Guang Gong (Canada), “Golomb’s Invariants andModern Cryptology”;
2) Tor Helleseth (Norway), “Shift Register Sequences
and Golomb’s Norwegian Connections”;

3) Hong-Yeop Song (Korea), “Existence of cyclic
Hadamard difference sets and some memories ofProf. SW. Golomb”; and
4) Andrew Viterbi (USA), “Celebrating the Life ofSolomon Wolf Golomb”.
That evening an interactive puzzle session (with prizes)
in Sol’s honour was also held, organised by Joe Buhler,Paul Cuff, Al Hales and Richard Stong.
Dr. Golomb will be missed but his legacy lives throughhis 50 years of teaching at USC, how he revolutionised
digital communications with his book on shift register
sequences and his kindness that touched me deeply after
being with him just a handful of times. I was honoured
to have been his editor.

Rochelle Kronzek
Rochelle Kronzek is Executive Editor for World Scientific based in
the United States.

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