He remembered even then questioning a children's song that proclaimed Mussolini's infallibility and love for kids. "Ed knew as a 6 year old in Rome that Mussolini was lying. He always said he learned then and there to be a sceptic of any received truth, or authority for authority's sake."

Nonconformity also ran within Nelson's upbringing. His father was a Methodist minister, Rhodes Scholar, and Southerner who was an early activist for African American civil rights. His father encouraged each of his four sons - in the Jim Crow South - to be nonconformists willing to offer a tired African American woman the front seat of a bus.

I was introduced to probability theory in a graduate course taught by Irving Segal from galley proofs of Doob's "Stochastic Processes". Irving presented his own viewpoint in addition to Doob's, and it was an exciting course. Once he drove me down to Urbana so we could talk with Doob. It was a memorable trip. Maintaining that the probability of an accident is directly proportional to the time spent on the road, Irving drove in such a way as to minimise that time. Despite having Irving Segal as thesis adviser, I did not learn physics at the University of Chicago. I took one course in the physics department but was defeated by the lab; I didn't really know how to explain the 457 percent error in my result for the mechanical equivalent of heat.

This research was done while the author held a National Science Foundation Fellowship. The author is greatly indebted to Professor I E Segal for inspiration and many helpful suggestions during the course of this work. Thanks are also due to Professors Halmos and Bahadur for their patient and critical reading of the text.

Banach space techniques have long been applied to the study of Markov processes. Kakutani and Yosida obtained the best results on the Markov processes for which the uniform ergodic theorem holds by elegant operator-theoretic methods, and discovered the mean ergodic theorem on reflexive Banach spaces. More recently, the theory of semigroups has been applied to diffusion processes. In the following pages some applications of operator theory to Markov processes will be made in new directions.

... when I got to Princeton University, I attended several of Arthur Wightman's courses and pored over the papers of Richard Feynman and Kurt Symanzik, and after a while I began to learn the difference between a Lagrangian and a Hamiltonian.

In these papers he showed for the first time how to use the powerful tools of probability theory to attack the hard analytic questions of constructive quantum field theory, controlling renormalisations with $L^{p}$ estimates in the first paper and, in the second, turning Euclidean quantum field theory into a subset of the theory of stochastic processes.

These are the revised lecture notes of a course given in June, 1983 for the Troisième cycle de la physique en Suisse romande Ⓣ. This course was given at a time when my thinking about stochastic mechanics was in a state of flux.

This stimulating book is a concise survey of stochastic mechanics, a subject whose development was largely initiated by the author's earlier book [Dynamical theories of Brownian motion (1967)]. The present book is full of original approaches to problems old and new in both mathematics and physics.

For myself, this volume of lecture notes presents the foreground between stochastic mechanics and quantum mechanics with clarity, economy, and elegance - virtues that I have come to expect from Nelson's writing.

Ed served for a number of years as director of graduate studies, reflecting his deep commitment to graduate education. He polished four of his graduate courses into books published in the Mathematical Notes series by Princeton University Press. The books are truly marvellous but cannot capture the verve and originality of Ed's teaching. One of the books, 'Tensor Analysis', based on a course he gave on differential geometry, includes a theorem that says - literally - that it is possible to park in any parking space just slightly longer than your car if you use enough iterations of the parallel parking manoeuvre. To do this, one would like to be able to "slide" sideways into the parking place. Ed modelled the configuration space of the car as a certain four-dimensional manifold and studied the interactions of four vector fields on this manifold, showing how "steer" and "drive" could be used to produce "wriggle" and then "slide." It is enormously fun reading, for mathematicians anyhow, but it had a serious purpose as an introduction to the subject of "holonomy." As delightful as the version in the book is, the version in class was illustrated with a toy car Ed purchased at the Woolworth's, then on Nassau Street, for this purpose. He got a "sitting ovation" at the end of his lecture!

I must relate how I lost my faith in Pythagorean numbers. One morning at the 1976 Summer Meeting of the American Mathematical Society in Toronto, I woke early. As I lay meditating about numbers, I felt the momentary overwhelming presence of one who convicted me of arrogance for my belief in the real existence of an infinite world of numbers, leaving me like an infant in a crib reduced to counting on my fingers. Now I live in a world in which there are no numbers save those that human beings on occasion construct.

In terms of religion, I'm a Christian. Worship and prayer are very important to me. I experience religion more as a matter of faith than of a belief system, and I think there's one question where mathematics and monotheistic faith seemingly conflict, and that is in the nature of mathematical objects. Let's take the numbers, 1, 2, 3, 4, 5 and so forth - 0 too. But also more general mathematical objects, like exotic spheres and whatnot. Do these things exist? Well, as a formalist I believe that we make them. But if we believe that the numbers, 0, 1, 2, 3, 4 exist as a completed infinity, where did they come from? Have they existed as they were in the beginning or now and ever shall be? That sounds like a religious belief - not mine. If we believe they're created, that raises a problem, because I believe it's part of monotheistic faith that all of creation is contingent; it could have been created otherwise. How could the numbers have been created otherwise? I think there's a real problem here.
...
I describe myself as an extreme formalist. That means that David Hilbert, who is regarded as the founder of formalism, I think was in his heart a Platonist. I believe he adopted formalism as a strategy against his antagonist, the intuitionist, L E J Brouwer. For example, he set the programme of proving that mathematics was consistent, starting with number theory, to prove that number theory was consistent. Well, that's a mistake. The question is: is elementary number theory consistent or not? I believe it's not. I believe that we do not have certainty in mathematics. I believe that many of the things we regard as being established in mathematics will be overthrown. And I'm a crackpot in that respect.

I am writing up a proof that Peano arithmetic (P), and even a small fragment of primitive-recursive arithmetic (PRA), are inconsistent. This is posted as a Work in Progress ...

You are quite right, and my original response was wrong. Thank you for spotting my error. I withdraw my claim.

Teaching freshman calculus is fun, but it poses very different challenges from graduate teaching. ... The most rewarding kind of teaching is the direction of Ph.D. theses.

I was the department's first webmaster, constructing the protocols, all but the final step of getting an IP address, to connect us to the World Wide Web. But the most rewarding administrative experience I had was one year when I was director of graduate studies. I would interview each graduate student. Michael O'Nan was one of them; this was back in the old Fine Hall. Something in his demeanour prompted me to call him back as he was about to leave. It turned out that he was unhappy with the thesis problem in analysis he had been assigned; what he really wanted to work on was finite groups. There was no one in the department who could advise such a thesis. I made some phone calls (there was no email then) and arranged for him to work with Daniel Gorenstein. Michael's thesis was an essential step in the classification of finite simple groups.

He was a man full of convictions and a lot of things he did went against the grain of other mathematicians. Although Ed had an unassuming presence, you mustn't mistake that for softness. He had a will of steel. He was really courageous. He had a strong conviction and was a strong enough mathematician that he could put his ideas into practice.

Six years ago today, this world lost one of the greatest men (and minds) its ever seen. Amazing is an understatement when trying to describe Edward Nelson - his contributions to mathematics and science made him a legend to the world, his sheer awesomeness made him a legend to anyone who ever met him. I am the luckiest girl ever to have had a man of such greatness play one of the most influential roles in my life. I am grateful my children had the opportunity to know him. He taught me the meaning of compassion, humility, strength, determination and unconditional love. May you rest in peace dearest Granddad and celebrate eternity with your true love Mahnyo (Nancy Wong Nelson). I love you so much.