Freeman Dyson

By Freeman Dyson 

Freeman Dyson was awarded the 2012 Henri Poincaré Prize at the International Mathematical Physics Congress in August. On this occasion, he delivered the lecture “Is a Graviton Detectable?” a PDF of which is available at http://publications.ias.edu/poincare2012/dyson.pdf.

John Brockman, founder and proprietor of the Edge website, asks a question every New Year and invites the public to answer it. THE EDGE QUESTION 2012 was, “What is your favorite deep, elegant, or beautiful
explanation?” He got 150 answers that are published in a book, This Explains Everything (Harper Collins, 2013). Here is my contribution.

The situation that I am trying to explain is the existence side by side of two apparently incompatible pictures of the universe. One is the classical picture of our world as a collection of things and facts that we can see and feel, dominated by universal gravitation. The other is the quantum picture of atoms and radiation that behave in an unpredictable fashion, dominated by probabilities and uncertainties. Both pictures appear to be true, but the relationship between them is a mystery.

The orthodox view among physicists is that we must find a unified theory that includes both pictures as special cases. The unified theory must include a quantum theory of gravitation, so that particles called gravitons must exist, combining the properties of gravitation with quantum uncertainties.

After his teatime conversation with Hugh Montgomery, Freeman Dyson wrote this letter to Atle Selberg with references showing that the pair-correlation of the zeros of the zeta function is identical to that of the eigenvalues of a random matrix.

In early April 1972, Hugh Montgomery, who had been a Member in the School of Mathematics the previous year, stopped by the Institute to share a new result with Atle Selberg, a Professor in the School. The discussion between Montgomery and Selberg involved Montgomery’s work on the zeros of the Riemann zeta function, which is connected to the pattern of the prime numbers in number theory. Generations of mathematicians at the Institute and elsewhere have tried to prove the Riemann Hypothesis, which conjectures that the non-trivial zeros (those that are not easy to find) of the Riemann zeta function lie on the critical line with real part equal to 1⁄2.

Montgomery had found that the statistical distribution of the zeros on the critical line of the Riemann zeta function has a certain property, now called Montgomery’s pair correlation conjecture. He explained that the zeros tend to repel between neighboring levels. At teatime, Montgomery mentioned his result to Freeman Dyson, Professor in the School of Natural Sciences.

In the 1960s, Dyson had worked on random matrix theory, which was proposed by physicist Eugene Wigner in 1951 to describe nuclear physics. The quantum mechanics of a heavy nucleus is complex and poorly understood. Wigner made a bold conjecture that the statistics of the energy levels could be captured by random matrices. Because of Dyson’s work on random matrices, the distribution or the statistical behavior of the eigenvalues of these matrices has been understood since the 1960s.

By Dan Burt 

Freeman Dyson, Professor Emeritus in the School of Natural Sciences, Bloomberg Hall

A sign and eight low buildings pass
unnoticed in a field the size of Central
Park: a wall-flower by a college town.
Wandering its halls, one chair offices,
bare egg white walls, nothing stands out until
I reach a lounge where mathematical
notations – integers, fractions, powers,
roots, Greek letters, brackets, slashes – weave
arabesques of genesis and infant stars
for paper napkin audience and nibbled
chocolate bars, on slate where palimpsests
and marginalia in coloured chalks suggest
a coffee break authored this text
a plaque below it warns, DO NOT ERASE.

By George Dyson 

In this 1953 diagnostic photograph from the maintenance logs of the IAS Electronic Computer Project (ECP), a 32-by-32 array of charged spots––serving as working memory, not display––is visible on the face of a Williams cathode-ray memory tube. Starting in late 1945, John von Neumann, Professor in the School of Mathematics, and a group of engineers worked at the Institute to design, build, and program an electronic digital computer.

I am thinking about something much more important than bombs. I am thinking about computers.––John von Neumann, 1946 

By Cécile DeWitt-Morette 

Cécile DeWitt-Morette with (from left to right) Isadore Singer, Freeman Dyson, and Raoul Bott at the Institute in the 1950s

In Brief 

It all began with a cable from Oppenheimer that I received on March 10, 1948, in Trondheim, Norway: ON THE RECOMMENDATION OF BOHR AND HEITLER I AM GLAD TO OFFER YOU MEMBERSHIP SCHOOL OF MATHEMATICS FOR THE ACADEMIC YEAR 1948 – 1949 WITH STIPEND OF $3500. ROBERT OPPENHEIMER.

I did not know that this was a great offer. I did not even know where Princeton was, but as a general rule, I would rather say “yes” than “no.” I was then on leave from the French Centre National de la Recherche Scientifique (CNRS), having been awarded a Rask-Oersted Fellowship for the academic year 1947–48 at the Nordiska Institutet för Teoretisk Fysik in Copenhagen.

In retrospect, I think that in the days of the Marshall plan, Oppie was looking for a couple of European young postdocs who would benefit from a year at the Institute. Did I benefit? More than I could ever have imagined.
During my two-year stay, 1948–50, Bryce DeWitt, a postdoc at the Institute, 1949–50, asked me to marry him, and I conceived the Les Houches Summer School as my self-imposed condition for marrying a “foreigner.” Thanks to Freeman Dyson and Richard Feynman, I learned about functional integration and am still fascinated by it.