NE WS L E T T ER
OF THE EUROPEAN MATHEMATICAL SOCIETY

S EMM
E S

EuropeanMathematicalSocietyFeatures
Renormalisation ofStochastic PDEs
Approximate Groups
Interviews
Freeman Dyson
David Ruelle
Obituary
Hagen Neidhardt

Freeman Dyson (photo: Dan Komoda/IAS, Princeton, NJ USA)

March 2020
Issue 115ISSN 1027-488X

Interview

A Discussion with Freeman Dyson
Michael Th. Rassias (University of Zürich, Switzerland)Note: Just a few days before this article was printed, wewere all saddened by Freeman Dyson’s passing on February 28, 2020. The article below is published in its originalform.

Freeman Dyson presenting his new book Maker of Patterns. (Photo:Dan Komoda/Institute for Advanced Study, Princeton, NJ, USA)

Freeman J. Dyson, born in 1923 in Crowthorne in Berkshire, England, is a world-famous American theoreticalphysicist and mathematician, whose academic stature isthat of a historical figure of science. At the beginning ofhis career he worked as a civilian scientist for the Royal Air Force in World War II. In 1945 he obtained hisB.A. degree in mathematics from Cambridge University.
He had a job as an instructor at Imperial College from1945–1946, and in 1947 he went to Cornell University asa graduate student, where he worked with Hans Bethe
and Richard Feynman. Subsequently, he was a memberof the Institute for Advanced Study, Princeton, from1948–1949 and a research fellow at the University ofBirmingham from 1949–1951. 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 actually obtained a Ph.D. (a topic also discussed with him
below). In 1953 he became a permanent professor at theInstitute for Advanced Study, Princeton, where he hasremained throughout the rest of his career.
Freeman Dyson has made numerous profound contributions in a broad spectrum of subjects of mathematics and physics, among which is the unification of thethree versions of quantum electrodynamics invented
by Richard Feynman, Julian Schwinger and Shin’ichirō
Tomonaga. His work and lectures on Feynman’s theories played an integral role in making them understandable to physicists of the time, and this helped Feynman’s
work to be accepted by the academic community. His
work on this subject impressed J. Robert Oppenheimer

EMS Newsletter March 2020and had an impact on him being offered a permanent
position at the Institute for Advanced Study, Princeton.
Among his participation in many diverse and important projects, it is also worth mentioning that in 1958 he
was a member of the design team under Edward Teller
for a small and really safe nuclear reactor used throughout the world in hospitals and universities for the production of medical isotopes.
Dyson’s passion has always been to explore problems
through which mathematics can be usefully applied. His
span of scientific interests and his everlasting appetite
for exploration have lead him to investigate problems
not only in mathematics, physics and their interconnections, but also in other subjects such as biology.
During his career, he has been bestowed with a plethora of awards and distinctions, including becoming a Fellow of the Royal Society (1952), receiving the Lorentz
Medal (1966), the Wolf Prize (1981), the Enrico Fermi
Award (1993), the Templeton Prize (2000), the Henri
Poincaré Prize (2012), to name just a few.
Honoured and humbled to be surrounded by such
pillars of science during my time as a visiting researcher
at the Program in Interdisciplinary Studies of the Institute for Advanced Study, Princeton, I had the great privilege of first meeting Freeman Dyson in around 2015.
Since then, I have had the opportunity to spend sometime with him, hoping to absorb some of his wisdom.
Inspired by his accomplishments, and always spellboundby his beautiful tales of the numerous interesting eventsof his life, the idea arose for the following discussion to
be shared with the readers of the EMS Newsletter.
You started your academic career as a pure mathematician, worked with Davenport for a while and among
other things proved Minkowski’s conjecture in four dimensions using methods from various areas of mathematics. You later turned to physics. At which age did
you decide to become a mathematician?
I met Davenport during the year 1945–1946 when I hada job at Imperial College as an instructor. He was atUniversity College, so I was not officially his student. He
generously supplied me with problems to work on, hardenough to be challenging but not impossibly hard. Firstwas the Siegel conjecture that every algebraic number
can be approximable by rational (p/q) with accuracy notbetter than q to the power two-plus-epsilon. I failed toprove it and the conjecture was later proved by Klaus
Roth. Second was the Minkowski conjecture in fourdimensions, which I succeeded in proving, and used as athesis for a research fellowship at Trinity College Cambridge. I remained a life-long friend of Davenport.
I think my choice of pure mathematics for a career
was mostly the result of reading Men of Mathematics by17

Interview

Freeman Dyson giving a lecture at the Institute for Advanced Study.
(Photo: Dan Komoda/Institute for Advanced Study, Princeton, NJ,USA)

Eric Bell at the age of 13. I was doubly lucky, as Bell’sbook was newly published in 1937, and it was given tome as a high-school prize by Winchester College. The
book is a collection of mathematical biographies, bringing mathematicians to life as real people, and explaining
their work with enough technical detail to bring theirideas to life.
What made you later move towards physics?
The move to physics happened when I moved to Trinity
College in 1946. There I met Nicholas Kemmer, a worldclass theoretical physicist who was also a dedicatedteacher. He taught me most of what I needed to know
to become a physicist. I saw that my nineteenth-century
mathematics would be useful for practical problems inphysics, while I remained ignorant of the more abstract
ideas that were then dominating pure mathematics. It
would be much more exciting to join the crowd exploring the mysteries of nuclear and particle physics than toremain in the small world of number theory. As a physicist I had no difficulty in finding funds to visit the UnitedStates where the particle physics revolution was alreadyin full swing.

students in the nineteenth century and was well suited totheir needs. It is totally unsuited to the needs of a large
and diverse population of students in the twenty-firstcentury. It is especially harmful to women, who have todeal with the biological clock of child bearing while therigid and lengthy Ph.D. system is eating up their bestyears. It is one of the main reasons why talented women
drop out of academic careers. It is also harmful to young
people of all genders who do not happen to belong towealthy or professional-class families. It has the effect ofincreasing and perpetuating the inequality between richand poor in modern societies.
Is there a mathematician who influenced you the most?
Either through your mutual collaboration or interaction or even by studying his/her work? I remember you
mentioning A. Besicovitch in the past as one such case,
who happened to also be a close friend of yours.
The mathematician who influenced me most was Besicovitch. I was lucky to arrive at Trinity College as an undergraduate at age 17 in 1941, when there were hardly any
advanced students. The old and famous mathematicians,Hardy, Littlewood, Besicovitch, lavished their time andattention on the few advanced students who were there.
I quickly became a personal friend of the famous mathematicians and especially with Besicovitch, who was theowner of the billiard table. I played billiards mostly with
Besicovitch, but also with Hardy. Besicovitch gave me
hard mathematical problems to work on and took mewith him for long walks around Cambridge, on which
only Russian was spoken.

Was there a specific paper, book, lecture, or even a theorem you came across that had a lasting impact on you
to the extent that it made you chose to become a scientist, rather than – say – a musician like your father?
The book that most influenced my choice of career was
Men of Mathematics. My father was a composer andconductor and administrator. He became director of theRoyal College of Music in 1938. He had the wisdom tosee that I had no musical talent and never tried to push
me into music. He always encouraged me to follow myown path in science.

Being an analyst and analytic number theorist, I was
fascinated when you first told me in the past that you
actually knew G. H. Hardy rather well and had evenspent time with him playing billiards at Cambridge.
Would you like to share some memories from your timewith him, as he is known for his particular personality.
Hardy gave wonderful lectures on function theory andanalysis to a group of four students sitting around asmall table. He prepared his lectures with great care, sothat the discussion came to a dramatic climax just as thehour ended. He included stories about the personal lives
and idiosyncrasies of the famous mathematicians that hehad known. He talked fast and with a wealth of detail,so that I had to listen to every word. He spoke for threehours a week without ever repeating a lecture. He was
fiercely opposed to the Tripos examination system that
dominated Cambridge in those days just as the Ph.D.
system does today. He tried and failed to abolish the Tripos just as I tried and failed to abolish the Ph.D.

You never followed a doctoral program in order to obtain a Ph.D. In this subject you also have some interesting views which are fairly divergent from the norm.
I was lucky to be educated in England at a time when
the Ph.D. was not required as an entrance ticket to an
academic career. I was always opposed to the Ph.D. system as it became more and more rigid in later years. It
was a system designed for a small population of German

You also think that Hardy is partly to be blamed for
Ramanujan’s death, if I remember well?
The story of Ramanujan’s illness only became clear
after his death. What is clear is that he died of amoebic
hepatitis contracted in India before he came to England.
Amoebic hepatitis was a well-known disease, which any
doctor specialised in tropical medicine would have recognised. It was already then a curable disease with an18

EMS Newsletter March 2020

Interview

From left to right: Enrico Bombieri, Freeman Dyson, Dan Rockmore, Robbert Dijkgraaf. (Photo: Andrea Kane/Institute for Advanced Study,Princeton, NJ, USA)effective chemical antidote. Hardy was responsible for
Ramanujan’s well-being when he became sick in England. Hardy never had him examined by a specialist intropical medicine. The local doctors in Cambridge misdiagnosed his disease as tuberculosis and treated it withstandard tuberculosis treatment, which was obviously
ineffective. Hardy saw Ramanujan chronically sick forseveral years but never seemed to take the problem seriously. He enjoyed Ramanujan as a brilliant mind and anactive collaborator, but did not care for him as a humanbeing. That is a harsh verdict, but I think it is justified by
the evidence.
On a humorous note, if – like in the case of Ramanujan – there were a supreme being that could hand you
solutions to important problems in your sleep, and saythat you could have only one such dream, the solution
to which problem would you like to see?
I find it unattractive to have a dream giving me the solution of a deep mathematical or physical problem such as
the Riemann hypothesis or the value of the fine structure constant. That would be too cheap. Nature gave us
these problems as tests of our imagination, and to havethem cheaply solved would be a loss of the mysteryand beauty of Nature. So I would choose a historicalquestion that deals with events that are lost in the past.
Where and when did the first life appear on our planet?
Where and when did the first human language emerge?
For a brief period of your life you lived in Zürich, whereyou also got to know W. Pauli. Would you like to say a
few words about your interaction with him?
I was lucky to live in Zürich in the summer of 1951 when
Pauli and I were the only two regular visitors at the ETH
institute of theoretical physics. Pauli liked to go for walks
after lunch and often invited me to join him. He loved toEMS Newsletter March 2020

talk about all kinds of problems from physics to psychoanalysis, and I loved to listen. Among many other topics, we discussed the question whether the perturbation
series expressing the interactions between particles inquantum electrodynamics are convergent or divergent.
If the series converges, it proves the theory to exist as awell-defined mathematical object. If the series diverges,
it proves that the theory is ill-defined and mathematically non-existent. I then believed that the series converged and Pauli believed that it diverged. As a result ofour conversations, I found a simple proof that Pauli wasright and I was wrong. I was profoundly grateful to Pauli
for forcing me to confront the unwelcome truth.
Since Pauli was a quantum physicist, this reminded meof another topic. What are your views on the possibility of creation of quantum computers, as well as on
the advent of areas such as quantum cryptography in
our efforts to be protected against the possible use ofquantum computers towards breaking current cryptosystems?
Quantum computers is not the right name for them. The
right name is quantum subroutines. They are physicalobjects with quantum behaviour that processes information faster than classical objects can do. They must
be connected to classical computer systems that provide
input and output and interaction with human operators.
The quantum subroutines are theoretically powerful andwill probably be practically useful. They still need a massive engineering development before we can set limits totheir capabilities. One of the important applications will
be to cryptography. A quantum crypto-system will betheoretically more secure than a classical crypto-system.
But that does not mean that the quantum crypto-system is more secure in the real world. In the real world,
crypto-systems are usually broken by exploiting human19Interview
later, physics has slowed down, while astronomy andbiology have speeded up. Now I talk with astronomers
and biologists more than I talk with physicists.
What is the first thing that comes to mind when you arethinking of the word “physics”?
When I think of physics today, I think of the monstrous
instruments like the Large Hadron Collider which costbillions of dollars to build and can only do one experiment in ten years. I also think of fashionable theories
that are never tested because they do not make verifiable predictions. If I were young today, I would notchoose physics as my line of work.

Freeman Dyson (left) at his office at the Institute for Advanced Study,Princeton, with Michael Th. Rassias, ca. March 2017.

errors in the day-to-day operations of the users. Humanerrors will probably be as prevalent in quantum systems
as they are in classical systems. So long as humans areinvolved in the practical use of crypto, no system will besecure against hackers.
An amusing thing you mentioned to me in a past discussion of ours related to the important physicist E.
Teller, whom you also knew, was that to be with Teller
one had to know how to act with children. Why is that?
Edward Teller worked with me on the design of a nuclear reactor called TRIGA, which was much safer thanother reactors. Teller was a brilliant scientist with anabundant supply of ideas. He was also a prima donna
who threw temper tantrums like a five-year-old if anyone dared to oppose him. So our collaboration worked
very well. Every day Edward would suggest a new crazyidea, I would explain why his idea would not work, andhe would throw a tantrum. Then the next day that idea
was forgotten and a new crazy idea was suggested. In thisway we converged on a design that actually worked. The
collaboration worked well because I had a lot of experience dealing with five-year-old kids at home. The reactor
was a commercial success and we sold 75 of them, someof them still working sixty years later.

One may state that mathematics has witnessed great
expansion during the last, say, one hundred years, withmany different areas emerging and various methods
discovered, bridging seemingly different fields. How doyou see the future of mathematics in that respect? Do
you think that interdisciplinarity might be the theme of
the future, for example?
The most beautiful feature of mathematics is its unpredictability. Progress comes in big jumps, sometimes unifying the whole subject with new ideas, sometimes diversifying the whole subject with new problems. The only
thing I know for sure about the future is that the next
big jump will be a surprise. I do not try to guess how itwill go.
Many scientists from a broad spectrum of areas haveexpressed various views, opinions and even fears about
the possible future consequences of the advancementof Artificial Intelligence (AI), in connection to theso-called “AI-control problem”. As someone who has
witnessed paradigm shifts in science which defined neweras, what are your views about the possible important
advances in AI which might affect human lives altogether?
Artificial Intelligence is a huge subject and I cannot
summarise the prospects for its future. The clearest
view of it was published in the book The Human Useof Human Beings’ by Norbert Wiener in 1950. Wiener
showed amazing insight in his vision of the good and bad
effects of AI. He predicted the failure of our society tofind benefits to humanity from the good effects and remedies for the evil. Seventy years later, his verdict, thathumans competing with machines will become slaves, isbeing proved correct. His remedies are nowhere being
applied on a scale adequate to the size of the problems.
I cannot do better in defining the problems than Wiener
did in 1950.

From all the people you have met in your life, who has
astonished you the most?
As it happens, the two people who impressed me themost were both scientists, Richard Feynman and Stephen Hawking. Both were physicists. This is probably
not an accident. They lived at a time when physics was
attracting a large fraction of the most brilliant youngpeople, with new experiments and theories and revolutionary discoveries rushing ahead. Now, seventy years

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EMS Newsletter March 2020