Memo regarding my time with Jerry Marsden
by Ralph Abraham, www.ralph-abraham.org
03 October, 2010.
August 17 was Jerry's 68th birthday. A month later, about 10 pm on September 21, he died -- just before the Fall Equinox at 8 pm on September 23. So today I am remembering our time together in Princeton in the 1960s.
In 1960, just before my 24th birthday, I got my Ph.D. at the University of Michigan. With my wife Caroline I moved to Berkeley for my first academic job. This was a golden era for math at Berkeley. I soon met Steve Smale and Moe Hirsch who were my closest friends at that time. Then I moved to Columbia in 1962. During all these early years of my career we were all working in a new area of math called global analysis, which included dynamical systems theory, later known as chaos theory.
In September 1964, 46 years ago, I moved from Columbia to Princeton, with Caroline and our new son Peter, age nine months. My first teaching assignment was an honors course in advanced calculus. The students were fantastic and we stayed together in a series of courses for four years, after which I moved to UC Santa Cruz, with Caroline, Peter, and second son John, ages five and three. Most of these great students and friends went on to become professors.
Early in my second year at Princeton I was approached by Arthur Wightman, a distinguished professor of mathematical physics. There were new results in celestial mechanics regarding the stability of the solar system, called KAM theory, after Kolmogorov, Arnold, and Moser. Arthur asked me to teach a course on these new results in the spring semester, beginning in February, 1966. KAM theory is quite difficult. I accepted the challenge, and began planning the lectures in January. My intention was to begin the course with a survey of the classical material, all transposed into the new language of global analysis, then move into the new results in the same frame. I had no idea how much new mathematical work would be required!
In the first week of the course the lectures were easy. There was a large crowd in the lecture hall, including many of the great grad students of math and physics who went on to notable academic fields, as well as visiting professors from Princeton University and the nearby Institute for Advanced Study. As there were no existing texts on the subject, people were asking for notes of the lectures. So at the end of one lecture I asked for volunteer note writers. My idea was that a team of good grad students could share out the considerable task. But only one student came up at the end of that period to volunteer. I asked if he thought he could handle the job alone. With a quiet little smile he said he thought he could. His name: Jerry Marsden.
And so we began this joint project. I put in long hours preparing each lecture. And the day after the lecture without fail he would hand me a thick sheaf of lined yellow legal pad, with faultless notes ready to duplicate for the large group of students and auditors. I revised and extended the text in the summer of 1966. I recall temperatures over one hundred degrees at midnight. Throughout this time Jerry and I would meet at the squash courts at 5 pm for an hour of high speed chaos. Arthur Wightman arranged for publication by his publisher, Bill Benjamin, who became a close friend. The finished book appeared in January of 1967, and is still in print. It contains an appendix on center manifolds, a difficult and important, by Al Kelley, who is yet my colleague and friend here in Santa Cruz.
Later, after my move to Santa Cruz in 1968, Steve Smale suggested that I extend the book to include mechanical problems with symmetry, a difficult new frontier on which he was currently working. I decided not to undertake this project, but Jerry -- who had by then finished his Ph.D. -- did accept this project, and thus was born the second and greatly expanded edition of our text.