I am sorry that I cannot be there, but pleased that I may share a few of my thoughts.
I arrived at Berkeley in 1983, already a dedicated and quite experienced teacher, determined to find a Ph.D. adviser whom I could respect both as a researcher and as an educator. In Emery I found this, as well as an incredible mentor and supporter.
I am particularly thankful that I was able to visit with Emery last year. He gave me a copy of his last paper, and explained to me how we, as mathematicians, have a responsibility as we grow older to look at and write papers on the “big picture” instead of on small, specific problems. He told me what was in his paper as an example of this. We then chatted about my frustrations with serving as Department Chair. When I mentioned that I was being pressured to extend my term by one year, he quite forcefully informed me that I had to say no; that I had done my full term and that I needed the time for my research. I smiled at the thought of telling the college administration that I couldn't be Chair because my adviser said so. But, of course, Emery was correct and, of course, I followed his advice and am very glad of it!
I remember that visit with great fondness and am comforted by the knowledge that Emery had never stopped being my advisor. I consider myself to be very lucky.
I am very sorry I am not able to be in Berkeley for Emery’s memorial. I have always thought that one of the high points in my career was to have Emery as my adviser and subsequently Emery and Jean as my friends.
I would like to relate two stories about Emery. None of them say much about Emery, the superb mathematician who made major contributions to homotopy theory and the geometry of vector fields, but rather say something about Emery’s human side.
The first story has to do with my deferment from the draft. These were the Vietnam War years, and I had been fortunate to be one of the last classes to enter graduate school with 5 years deferment. I explained to Emery that I would like to work at, shall we say, a leisurely pace. Emery was sympathetic to the idea. Unfortunately, not being very disciplined, I took advantage of California (and Berkeley in the ’60s) and did not spend as much time as I should have on my scholarly pursuits. Then came the lottery! I did quite well, and was no longer threatened by the draft. I was not aware that Emery knew more about his students than just their mathematics. He knew my birthday! A few weeks after the lottery I got one of those phone calls that are never forgotten. Emery asked: “How is that thesis going?” After I got over my shock, with Emery’s wonderful guidance, I did finally finish up.
The other story is also related to the war. Universities around the country were redirecting their energies to protest the war after Nixon initiated the bombing of Cambodia. Not to be outdone, some members of the math department held lengthy meetings discussing possible protests. After many hours discussing many proposals, not all realistic, Emery, with a twinkle in his eye (at least in my memory), suggested the mathematicians go on strike and refuse to prove theorems! Somehow this encapsulated the impracticality of the previous hours of discussion. The debate became more reasonable thereafter. I do not recall the form of protest endorsed by the group, but still recall Emery’s suggestion.
I guess the point of these stories is to show that Emery was more than a mathematician. He understood his role as a mentor during difficult political times. This became especially true as his illness progressed. He was still a mentor, but now teaching us the meaning of courage.
I am writing in appreciation of Emery’s work.
He was a mainstay of research in homotopy theory for many years, and his influence, particularly through his supervision of graduate students on mathematics in Berkeley, was considerable. I got to know him well through my visits to Berkeley and his reciprocal visits to the UK. Over six or seven years in the 1970s we were involved in a very active collaboration, applying cobordism theory to prove the rigidity of certain singularities in complex algebraic geometry. Throughout this work I was greatly impressed by his enthusiasm, energy and professionalism, and so he kept the project moving forward. He became a friend as well as a collaborator, and gave me valuable advice on a number of issues.
Emery unselfishly shared his love of mathematics. He was unstinting with his attention and his guidance. He always knew the right questions to ask: where further progress could be made, and also where something was not quite right. The way Emery continued to do mathematics even after being struck by Parkinson’s syndrome will always be an inspiration to me.
I had the privilege of taking graduate courses from Emery Thomas, and being a Ph.D. student of his. At that time he was about to start a new episode of his mathematical life: he was switching to number theory. He was thinking of applying topological techniques to number theory. Perhaps I was his last topology student. Only after I returned to my country, my real involvement with his earlier papers started, and I have regretted that I had insisted on doing what I had in mind during my Ph.D. studies, instead of working on his stuff. The flavor of his charming papers on vector fields, and his beautiful work on topics like the span of manifolds, Postnikov towers, and cohomology operations, affected my mathematical taste deeply. Afterward I have always sought this flavor, strength, richness in all the papers I read. It was an amazing coincidence that only one day before I heard the sad news of his passing away, he was the subject of a mathematical talk between me and Selman Akbulut on the phone. A theorem of Emery Thomas on the span of manifolds, that I could luckily remember, had greatly improved Selman’s results in his latest paper, and saved him from months of extra work. Two days later I talked about this irony of fate with Selman; “it must be his kind spirit”, he said.
Emery Thomas was a great advisor and a kind person. I will always remember our visits at Stanford for seminars in his car, his kind, fatherly gestures like inviting me to lunch at unexpected times.
I would like to send my condolences to his family and to the whole mathematical community.
I consider myself very fortunate to have been a doctoral student of Emery Thomas. At that time, Emery was publishing theorems on the span of manifolds, on the existence of immersions, submersions, embeddings, etc., utilizing the obstruction theory of modified Postnikov resolutions. His research showed his students the importance of applying algebraic topology to geometric problems. He was a great advisor and an excellent lecturer. Particularly memorable was a party at his residence for Beno Eckmann in 1967.
I send my condolences to his family.