E.T.H. Visits

## After my initial visit to the E.T.H. in 1968, over the years I have revisited countless times. These excursions took me on some occasions to the mathematics department, on others to the physics department, and often to both.

# Honorary Member:

## Shortly after my initial stay, I returned during the summers of 1969 and 1970. I especially treasure one memory from the 1970 visit: that summer Jim Glimm and I stopped to visit the Seminar für Theoretische Physik just before staying for two months at an intense summer school in Les Houches. During that visit Res Jost hosted a little ceremony in the Hochstrasse 60 seminar/tea room where he bestowed on us both the title "Honorary Member of the Seminar for Theoretical Physics." The privileges included an open invitation to return to the E.T.H. whenever possible.

# Three Dimensions:

## Those early visits came during the four years that I worked on proving stability of the quartic interaction in three dimensions—the break-through in perhaps the most difficult, subtle, and innovative paper I ever wrote, and one that still provides many open challenges. I spent many hours on the Florhof terrace and also in the University garden next door working on this. Sometimes I would climb through the garden afterwards and walk to the main E.T.H. building.

##

When Jim Glimm and I finally finished writing our paper with the proof, publication seemed almost an unimportant afterthought. We intended to submit the paper to the premier journal, *Communications in Mathematical Physics*. But I gave a seminar in Princeton on that work, and during lunch proposed this to my former teacher Arthur Wightman, then the editor for quantum field theory. We discussed the almost-completed paper in general terms, but without seeing it on paper. Arthur expressed his opinion that the work would be too long for CMP. (While in those days this may have been the case, today a 130 page typescript is not that unusual.) In any case, I thought that for important work the journal editor needed to be very postive, receptive, and welcoming. So we gave the manuscript to a sympathetic editor from Eastern Germany who, during a scientific meeting, had solicited any work we might have. Not only was the editor enormously surprised and grateful to receive that paper, but he gave the paper especially rapid publication. And in place of the authors' institution paying a publication fee, which was fairly universal for professional society journals at the time, his journal paid to the authors a token honorarium in U.S. dollars!

# The Stanford Connection:

## Shortly before leaving Zürich in 1969, I was walking along the Bahnhofstrasse and saw a familiar face approaching, whom I had got to know three years earlier at the Stanford University mathematics department.

## (Let me digress a bit, for how I got from Princeton to Stanford is funny. In fact I had been planning to go to U.C. Berkeley, where my graduate student friend Oscar Lanford had accepted a position as assistant professor. Those were the days when one did not apply for positions: they just seemed to appear. I had to choose between M.I.T. and Berkeley, and in the end the adventure of exploring California won out. Just about to leave on a trip to visit Berkeley and to look for an apartment, I telephoned Donald Spencer to let him know my plans. I had got to know Spencer in Princeton, when by luck I signed up for his course in advanced calculus. Don had encouraged me a great deal in my transition from chemistry to mathematics, and he was a great enthusiast about my choice of Cambridge, as he had studied there with Littlewood. He had also introduced me to Arthur Wightman when I returned to Princeton graduate school, so he played to role of a good friend, as he was also to many other students. Don had left Princeton shortly before because he felt that the Princeton faculty treated badly his long-time collaborator and office mate Kunihiko Kodaira. At that point Don became chairman of the Stanford mathematics department, bringing Kodaira as a professor. I could attend Kodaira's wonderful lectures at Stanford, before he returned to Japan as a National Treasure.

## On the telephone, Don insisited on my telling him which flight I would be on, and he promised to pick my up at the San Francisco airport. He did just that, and in the end rather than going to Berkeley, I ended up spending a wonderful year at Stanford! Don even helped me find a spectacular place to live, in a small house on Skyline Drive with a view of the entire San Francisco Bay area. His friend Charlie Rapley had lived in that place, across from his brother Jim's ranch. But Jim was taking care of the empty house as Charlie had moved to San Francisco.)

## At Stanford I became friends with many of the students and younger mathematicians. There was a student of Heinz Hopf who was visiting the mathematics department from Zürich, and we often spent evenings together as part of Don Spencer's circle.

#

# Einstein Coins:

## Some ten years later in January 1980 I passed through Zürich for an evening on my way to Chicago to receive the Heineman Prize. I dined at the Osterwalder's home with Konrad and Res, and their wives Vreni and Hilda. On that occasion Res presented me with a very special present: two five-Franc Swiss coins dated 1979, the hundreth anniversary of Einstein's birth. One coin shows two famous mathematical equations connected with general relativity, along with some material taken from a photograph of Einstein's blackboard. The second coin has a setting that was modern for the time, with a "computer" drawing of Einstein's face. These coins have a place of honor in my Cambridge study, and they bring back memories of Zürich and the people there every time I look at them.

# Fermat:

## During both 1992 and 1993 I spent time as a visitor in the Forschungsinstitut für Mathematik (in the Hauptgebaude). This had been founded in the 1960's by Beno Eckmann to foster mathematical reserach and to bring visitors to the E.T.H. Today in his 90's Eckmann still comes daily to his desk in the Forschungsinstitut.

## One day in 1993 as I was about to go to lunch, I read an email from Debbie Haimo that told me the previous day that Princeton mathematician Andrew Wiles had announced at a conference at the Newton Institute in Cambridge that he had proved Fermat's Theorem. As I made my way into the Dozentenfoyer I recognized a large table of mathematicians around Jürgen Moser (Director of the Forschungsinstitut at the time) with Gerd Faltings (then professor at the Institute for Advanced Study in Princeton). Faltings had come to the E.T.H. to give a lecture that afternoon. The lunch-table of mathematicians included John Mather and Sergio Kleinerman as well, two other visitors from Princeton.

## So I headed directly toward the table to speak with Faltings. An interesting exchange ensued:

Arthur: "I just received an email saying that Wiles announced a proof of the Fermat Theorem. Is that the case?"

Faltings (with disbelief): "André Weil?" (The room was packed and the background noise drowned out much conversation. So Faltings thought I mentioned the eminent, but then aging doyen of mathematics Weil.)

Arthur (more loudly): "No. Andrew Wiles."

Faltings leaned back, tilted his chair, and stared directly at the ceiling. A long interval of silence ensued. It was probably only ten or fifteen seconds, but at the time it seemed like an eternity. For Faltings had thought about Fermat's problem extensively. At the time he represented the number-one expert worldwide on that circle of ideas, having established a famous partial result with his proof of Mordell's conjecture. After the silence, the legs of Faltings chair came back to the ground. He burst out with laughter, exclaiming: "I'm sure its wrong!"

As it turned out, Faltings was right.

But about a year later Wiles found another variation of the proof with Richard Taylor, definitively solving the 350–year old Fermat problem.

## A couple of years later Jürgen Moser told me that he had been incredulous at the time —as was everyone else at the lunch table. For how could it be possible that neither Faltings, Mather, nor Klainerman had known about such important work being carried out in Princeton—work so close to Falting's interests, that must have been in progress for a long time. Moser told me that he was sure that I had been playing a practical joke on Faltings! What a good story it ended up being, he recounted with delight.