iNEWSLETTER

INTERVIEW
WITH THEPRESIDENTii“NLMS_489” — 2020/6/29 — 11:43 — page 1 — #1

Issue: 489 - July 2020

COMPLEXECOLOGICAL
META-NETWORKSBOB RILEY
AND HIS
MATHEMATICSi

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OBITUARIES
is indeed ironic that the three authors of this very
special book have all died within a few months ofone another. The analysis of these games involves
a great deal of serious mathematics and it is noexaggeration to say that for Conway, ‘Mathematics
is a Game and Games are Mathematics’.
However, the discovery for which Conway would
most like to be remembered is that of what Donald
Knuth christened surreal numbers, which combined
the approaches of Dedekind and Cantor to produce
a rich system of �nite, in�nite and in�nitesimal
numbers with many remarkable properties. It isa striking fact that in 1968–69, the year Conway
referred to as his annus mirabilis, he had discovered
the three �nite simple groups named after him,
The Game of Life and the surreal numbers. Conway
continued to be immensely productive and original.
Again John McKay came on the scene, pointing outthat the smallest degree of an irreducible complex
representation of the Monster group is just one lessthan a coe�cient in the Fourier expansion of themodular function J. This innocent observation led tothe Conway–Norton theory of Monstrous Moonshine
and to the Monstrous Moonshine conjecture for the
proof of which Conway’s student Richard Borcherds
was awarded the Fields Medal.
By the late 1970s Conway’s personal life had becomechaotic and both his marriages to Eileen, with whom
he had four daughters (Susie, Rosie, Ellie and Annie)
and Larissa Queen, with whom he had two sons(Alexander and Oliver) ended in di�cult divorces.
It does seem that he was so utterly committed tomathematics that he could not a�ord to let humanrelationships interfere with his research. Some ofthose closest to him undoubtedly paid a price forhis brilliant work. He had moved to Princeton withLarissa in 1986 to take up the von Neumann chair
and, following this break-up, he married his third
wife Diana, with whom he has a son Gareth. But theinventive brilliance continued, not least in the Free
Will Theorem, which he proved together with Simon
Kochen in 2004.
Working closely with Conway was a joy and aninspiration. When dealing with some new structure
or concept he would hone and hone the notation
until he felt it conveyed all the information requiredof it as concisely as possible. I often came into workin the morning to �nd that the language with which
I had become familiar had been ditched overnight
to be replaced by a more elegant version. Despite
his being rather sni�y about combinatorics for its
own sake, feeling that every mathematician shouldii“NLMS_489” — 2020/6/29 — 11:43 — page 42 — #42

possess the required skills, he was a consummate
master of the art as is evident in so much of hiswork. His lectures, both to undergraduates and toresearch seminar audiences, were refreshing andspontaneous. In the early days he invariably lectured
without notes, o� the top of his head, spending
just a few moments in contemplation before going‘on stage’, although I understand that in later years
he prepared his lectures meticulously. Indeed, at
one time he had a cult following among Cambridge
mathematics undergraduates who founded theConway Appreciation Society.
Such is his international fame that he already has a
prize-winning biography written about him: Genius
at Play, the curious mind of John Horton Conway bySiobhan Roberts.
Conway received many honours during his
distinguished career. Apart from his LMS prizes, he
was awarded the Nemmers Prize in Mathematics in1998 and the Leroy P. Steele Prize for Mathematical
Exposition in 2000. He was elected a Fellow of theRoyal Society in 1981.
John Conway was my mentor, inspiration,co-researcher and friend. I shall miss him
enormously.

Freeman J. Dyson: 1923 – 2020
Professor Freeman J.
Dyson, who was electeda member of the London
Mathematical Society on
17 March 1943, died on
28 February 2020, aged
96. He was elected LMS
Honorary Membershipin 2000.
Michael Th. Rassias writes: Freeman J. Dyson was oneof the world’s most famous and vocal scientists. We
were all saddened by his passing, as – even at his
96 years – he seemed unstoppable, with his mostrecent book having been published in 2018. Honoredand humbled to be surrounded by such pillars ofscience as a visiting researcher at the Program inInterdisciplinary Studies of the Institute for Advanced
Study, Princeton, over the last years, I had the great
privilege of meeting Dyson around 2015. Since then,I had the opportunity to spend some time with him,
hoping to absorb some of his wisdom. Inspired by hisaccomplishments, I was always being carried away byi

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OBITUARIES
his beautiful narrations of the numerous interesting
events of his life.
Dyson, born at Crowthorne in Berkshire, England, wasan American theoretical physicist and mathematician
whose academic stature had reached that of ahistorical �gure of science, long before his passing.
At the age of 17, in 1941, he arrived at Trinity College,Cambridge, as an undergraduate at a period when
Hardy, Littlewood, Besicovitch and other alreadyfamous professors were there, with whom he became
personal friends: “Especially with Besicovitch, who
was the owner of the billiard table”, he smilinglypointed out raising his �nger. In 1945 he obtained hisBA in Mathematics from Cambridge University, forthe period 1945–46 he was an Instructor at Imperial
College and in 1947 he went to Cornell University
as a graduate student, where he worked with Hans
Bethe and Richard Feynman. Subsequently, for theperiod 1948–49 he was a Member at the Institutefor Advanced Study, Princeton, and for the period
1949–51 he was a Research Fellow at the Universityof Birmingham. He then became Professor at Cornell
University where he remained until 1953. Surprisingly,
he was made Professor at Cornell notwithstanding
the fact that he did not have and never actuallyobtained a PhD. Throughout his career he was aharsh critic of the PhD system, which he strongly
believed should be abolished. In a discussion wehad, he said that he considered himself “lucky tohave been educated in England at a time when thePhD was not required as an entrance ticket to an
academic career”. He was very much bothered by thefact that the current rigid and lengthy PhD system is
one of the main reasons why talented women dropout of academic careers.
In 1953, Dyson became a permanent Professor atthe Institute for Advanced Study, Princeton, where
he remained throughout the rest of his career.
Dyson has made numerous, profound and versatile
contributions in a broad spectrum of subjects ofMathematics and Physics. Among his most important
contributions is the uni�cation of the three versionsof quantum electrodynamics invented by RichardFeynman, Julian Schwinger and Shin’ichirō Tomonaga,
all three of whom were awarded the Nobel Prize inPhysics in 1965. His work and lectures on Feynman’s
theories played a decisive role in making themunderstandable to physicists of the time and thisvery much helped Feynman’s work being acceptedby the academic community. Dyson’s work on thissubject impressed J. Robert Oppenheimer – whoi43

was at the time the Director of the Institute forAdvanced Study, Princeton – and had an impacton him being o�ered a permanent position there.
Curiously, despite his stellar accomplishments, Dyson
was never awarded the Nobel Prize. He somehow
missed his chance. On this subject, he humorously
said with his playful character that it is better for
people to ask you why you did not get a Nobel prize,
rather than why you actually did.
In 1958, at the age of 35, he was a member ofthe design team under Edward Teller for a small
and really safe nuclear reactor called TRIGA usedthroughout the world in hospitals and universities forthe production of medical isotopes. Some of thesereactors are still in use, sixty years later.
Teller, Feynman, Hardy, Littlewood, Besicovitch, Gödel,and many other legendary names were just a few
of the people entangled with Dyson’s spectacular
academic life. I must admit that I often caught myself
being mesmerized by the surreality of discussing
with a living piece of history when I immersed myself
in one of the two opposite armchairs in his o�ce at
the Institute for Advanced Study.
Throughout his career, Dyson had the characteristic
passion to delve into the exploration of problems
through which Mathematics can be usefully applied.
His span of scienti�c interests and his everlasting
appetite for research quests and the pursuit of thetruth, had lead him to investigate problems not onlyin Mathematics, Physics and their interconnections,but also to other fascinating subjects, such as
Astrobiology.
During his career, he had been bestowed with aplethora of awards and distinctions. However, noaward bestowment provided him with greater joy
than that of unraveling the mystery and beauty ofNature.

Jan Saxl: 1948 – 2020
Jan Saxl, who waselected a member of theLondon MathematicalSociety on 19 March 1976,
died on 2 May 2020,
aged 71.
Martin Liebeck writes:
Jan Saxl was bornand grew up in Brno,Czechoslovakia. He began his university studies
in 1966 at Masaryk University in Brno, but his lifei