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In Memoriam: Freeman Dyson (1923–2020) George E

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In Memoriam: Freeman Dyson (1923–2020) George E In Memoriam: Freeman Dyson (1923–2020) George E. Andrews, Jürg Fröhlich, and Andrew V. Sills 1. A Brief Biography 1.1. Personal background. Freeman John Dyson was born in Crowthorne, Berkshire, in the United Kingdom, on December 15, 1923. His father was the musician and composer Sir George Dyson; his mother, Mildred Lucy, n´eeAtkey, was a lawyer who later became a social worker. Freeman had an older sister, Alice, who said that, as a boy, he was constantly calculating and was always surrounded by encyclopedias. According to his own testimony, Free- man became interested in mathematics and astronomy around age six. At the age of twelve, he won the first place in a scholar- ship examination to Winchester College, where his father was the Director of Music; one of the early manifestations of Freeman’s extraordinary talent. Dyson described his ed- ucation at Winchester as follows: the official curriculum at the College was more or less limited to imparting basic skills in languages and in mathematics; everything else was in the responsibility of the students. In the company of some of his fellow students, he thus tried to absorb what- ever he found interesting, wherever he could find it. That included, for example, basic Russian that he needed in or- der to be able to understand Vinogradov’s Introduction to Figure 1. the Theory of Numbers. George E. Andrews is Evan Pugh Professor of Mathematics at the Pennsylvania In 1941, Dyson won a scholarship to Trinity College in State University. His email address is [email protected]. Cambridge. He studied physics with Paul Dirac and Sir Jürg Fröhlich is a professor emeritus of theoretical physics at the Institute for The- Arthur Eddington and mathematics with G. H. Hardy, J. E. oretical Physics, ETH Zurich. His email address is [email protected]. Littlewood, and Abram Besikovich, the latter apparently Andrew V. Sills is a professor of mathematics at Georgia Southern University. having the strongest influence on his early development His email address is [email protected]. and scientific style. Dyson’s knowledge of Russian came Communicated by Notices Associate Editor William McCallum. in handy, as Besikovich preferred to converse with Dyson For permission to reprint this article, please contact: in Russian. Dyson published several excellent papers on [email protected]. problems in number theory, analysis, and algebraic topol- DOI: https://doi.org/10.1090/noti2323 ogy. Politically, he considered himself to be a socialist. 1140 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY VOLUME 68, NUMBER 7 During the war, at the age of nineteen, Dyson was as- at the Institute for Advanced Study. I loved Cor- signed to the Royal Air Force’s Bomber Command, where nell and I loved Hans Bethe, but I hated the Ph.D. he developed methods for calculating the optimal density system to which my students were tied. The Insti- of bombers in formations to hit German targets. In 1945, tute suited my style of work much better. The life- he was awarded a BA in mathematics. He became a fel- cycle of the Institute is one year long, with a fresh low of Trinity College (1946–1949), where he occupied a crowd of visiting members arriving each Septem- room just below the philosopher Ludwig Wittgenstein. Af- ber. The annual cycle is well matched to my short ter having read Heitler’s Quantum Theory of Radiation and attention-span. .. With some regret but more re- the Smyth Report on the Manhattan Project, Dyson con- lief, I left Cornell in June 1953 and took up my cluded that “Physics would be a major stream of scientific new position in Princeton in September. I was de- progress, during the next twenty five years,” and he decided lighted to have a position in which I would never to trade mathematics for theoretical physics. again be responsible for a Ph.D. For the rest of my In 1947, Dyson won a Commonwealth Fund Fellow- life I have been fighting ineffectually against the ship and applied to become a graduate student of Hans ever-tightening grip of the Ph.D. system on young Bethe at Cornell University. It may be surprising that people wishing to pursue careers in science. I am he decided to leave Cambridge, where Eddington, Kem- eternally grateful to Cornell for accepting me as a mer, and Dirac taught, and move to America. Dyson professor in 1951 without a Ph.D. Unfortunately, wrote [Dys07, Chapter 1]: the liberality with which Cornell treated me did not extend to my students. Scientists come in two varieties, hedgehogs and foxes. I borrow this terminology from Isaiah Dyson had married Verena Huber-Dyson in 1950. They Berlin, who borrowed it from the ancient Greek had two children (Esther and George), but the marriage poet Archilochus.... [F]oxes know many tricks, ended in divorce in 1958. In 1957, Dyson became a citizen hedgehogs only one. Foxes are broad, while of the United States. In 1958, he married Imme Jung, and hedgehogs are deep. Foxes are interested in ev- together they had four children (Dorothy, Mia, Rebecca, erything and move easily from one problem to and Emily). Dyson was a family man, and he seemed to another. Hedgehogs are only interested in a few greatly enjoy the company of his own six as well as other problems that they consider fundamental, and children. stick with the same problems for years or decades. 1.2. Some of Dyson’s key contributions to theoretical [...] Some periods in the history of science are physics. At the time Dyson started his career in physics, good times for hedgehogs, while other periods are quantum field theory was in a messy state. Dirac and good times for foxes. The beginning of the twen- Werner Heisenberg thought that, in a revolution similar tieth century was good for hedgehogs. [...] [I]n to the one that gave birth to quantum mechanics, relativis- the middle of the century, the foundations were tic quantum field theory (RQFT1) would eventually be su- firm and the universe was wide open for foxesto perseded by a mathematically meaningful theory unifying explore. quantum theory with relativity theory. Dyson concluded Obviously, Freeman Dyson was the archetypal “fox,” and that what was necessary was to clarify the intricacies of the the period in physics when he started to do research and existing formalism of RQFT and to then use it to do con- scored his first great successes was exactly right for foxes. crete calculations explaining new experimental data. In He was so much a fox that he never got around to getting Cambridge, Dyson had learned some quantum field the- his doctoral degree. Of course, he did not need to. He ory from his friend Nicholas Kemmer and from a book by was offered a professorship at Cornell University in 1951, Gregor Wentzel. Dyson wrote [Dys96, p. 12]: to work with Hans Bethe essentially as a replacement for It was my luck that I arrived with this gift from Eu- Richard Feynman, who had left for Caltech a year earlier. rope just at the moment when the new precise ex- Dyson wrote about the time he spent at Cornell [Dys96, periments of Lamb and others [...] required quan- p. 18]: tum field theory for their correct interpretation. I enjoyed teaching students in class-room courses, When I used quantum field theory to calculate an and I enjoyed talking to them individually about science, but I did not enjoy being responsible for 1One referee pointed out that many would prefer the abbreviation “QFT” over dragging them through the three-year treadmill of “RQFT” since although nonrelativistic quantum field theories do exist, the rela- Ph.D. thesis research. From this unhappy situa- tivistic variety is the standard, and certainly the kind on which Dirac, Feynman, tion, I was rescued by the offer of a Professorship and Dyson focused. AUGUST 2021 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1141 experimental number, the Lamb shift [.. .], Bethe group, an important paradigm developed primarily by Wil- was impressed. son, who greatly generalized ideas of Stückelberg and Pe- Dyson’s principal contribution to quantum field the- termann and of Gell-Mann and Low. Dyson generously ory was, however, to unify the approaches to quantum shared his understanding of quantum field theory with electrodynamics (QED), the quantum theory of electrons, Bethe and Feynman, and explained the latter’s ideas to positrons, and photons, that had been proposed by Feyn- people preferring Schwinger’s over Feynman’s approach to man, Julian Schwinger, and Shin’ichirˉoTomonaga, a lit- RQFT, such as J. Robert Oppenheimer, who had become tle earlier. This unification work was facilitated by a cross- the director of the Institute for Advanced Study. country road trip, from Ithaca, New York, to Albuquerque, Since Dyson was a “fox,” it is unimaginable that he New Mexico, that Dyson took with Feynman in June 1948, would work in the same field for more than a year orsoat joyfully recounted by Dyson in Chapter 6 of [Dys79]. After a time. Indeed, right after his initial successes with QED parting company with Feynman in Albuquerque, Dyson (and with meson theory), he moved on to work on prob- rode a sequence of Greyhound buses to Ann Arbor, Michi- lems in statistical mechanics and solid-state physics. gan, where he attended a series of lectures by Schwinger, Dyson’s ideas and results in statistical mechanics and and had many conversations with him over a five-week condensed matter physics, among them his proof, with period. From Ann Arbor, he took a Greyhound bus to Andrew Lenard, of “Stability of Matter,” inspired a tremen- California, where he spent ten days.
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