What was his Path to Math? Read on...

As a child, I did not know much about colleges and universities, but the presence of Stanford University about ten miles south exerted a tremendous influence. Through a sixth grade enrichment program I met Robert Borrelli, then an instructor at Stanford. He was very kind to me, and met with me on Saturdays to teach me advanced mathematics. Forty-three years later, we remain good friends. I was also lucky enough, a couple of years later, to hook up with Neal Binford of Stanford. He taught me the elements of formal logic.

These two wonderful mentors introduced me to many mathematical topics that I would never have seen in my ordinary classes. I am not sure that any of those topics has exerted a great influence over my professional career (although I do retain a strong love for logic). But what was important is that these men gave me much encouragement, and showed me that mathematics is a living, breathing subject. I suppose it was a harbinger of things to come when one day, when I was twelve years old, Borrelli asked me what I wanted to do when I grew up. I unhesitatingly replied that I wanted to create ``general proofs.''

I was an undergraduate at the University of California at Santa Cruz. That was an exciting place in the late 1960s---no grades, gifted students, and many innovative curricula. I think that what was most important about Santa Cruz for me is that the faculty was willing to lavish a great amount of time on me. I spent many a happy afternoon hanging out in faculty offices hashing through new ideas. My favorite undergraduate math course was real analysis. First of all, the subject became the love of my life. But the teacher, Stanton Philipp, was a remarkable man. He had learned much of basic mathematics in jail (he was thrown in the brig for disobeying orders in the army) and had a unique (and self-taught) approach to the subject. Stan dedicated himself to teaching me analysis. He spent hours and hours poring over the proofs I offered in my homework assignments and making copious remarks. I took away a great deal from his classes. Stan taught me both undergraduate analysis (from blue Rudin) and graduate analysis (from green Rudin). These six classes shaped my mathematical life.

My least favorite undergraduate courses were algebra. I always liked the material. But the teaching was very poor, and the courses tended to stifle my enthusiasm for the subject.

One stroke of luck during my sophomore year in college is that I began working with Robert A. Bonic. A Professor on leave from Northeastern University, Bonic was working on a very original calculus book. He made me a co-author---at the tender age of 18! This experience certainly has had a strong effect on my life. I also valued the fact (although I didn't consciously realize it at the time) that Bonic treated me as an equal. He was a good friend and an inspiring teacher.

I trust that the reader can see that what has been seminal in my intellectual development has been key people who gave of their time and effort and love to show me the way. I try, in my own career, to carry on this tradition.

I was a graduate student at Princeton University. Attending Princeton was the most important professional decision that I ever made. The mathematics department was fantastically stimulating, the faculty inspiring, and my fellow students helped to instill in me (and in all of us) a passion for excellence. I used to see John Nash every day when I was a graduate student. He was very ill at the time, and almost impossible to talk to. But he was a real presence in the Mathematics Department.

My thesis advisor was E. M. Stein, another great mentor. He is a tough cookie when dealing with his peers, but he is extraordinarily kind and patient with his students. He knew just when to push and when to pull, when to prod and when to cajole. And he got results.

Stein got me an Assistant Professorship at UCLA with a single phone call---no letters of recommendation, no teaching statement, no application, no nothing. Boy, those were the days. That was a good job, and put me into the context of a very strong and active analysis program that was led by John Garnett, Ted Gamelin, and Phil Curtis. These men taught me a lot---sometimes by being tough with me and pointing out my failings, and sometimes by showing me good problems. The analysis seminars at UCLA in those days were inspiring and just packed with good ideas. I still have my notes from those days, and still refer to them.

I did not get tenure at UCLA, partly because I was probably not good enough and partly because I won a distinguished teaching award so the faculty felt I was the wrong sort of person---not a dedicated researcher. Now that I have 150 citations on MathSciNet, including more than forty books, I like to think that I have proved them wrong. But I can say with certainty that getting fired at UCLA was a seminal event in my professional career. Al Neuharth (founder of "USA Today") says that everyone should have a big failure early in their career. As Nietzsche said, if it doesn't destroy you then it makes you stronger. Certainly I am more resilient and determined today because of the trials I went through after my demise at UCLA. And I am extremely grateful to my many graduate school mentors and friends who believed in me and stuck by me and helped me to land on my feet.

One great thing that happened at UCLA is that I became good friends with Robert Greene. We began a collaboration in 1979 that has proved to be extremely fruitful. It led to eleven papers, four books, and another book in development. Robert trained me anew in mathematics, and has turned me into something of a geometer. My interests have now wandered so far from classical analysis (in significant part due to Greene's influence) that people are astonished to hear that I am a student of Stein.

I think that one of the keys to success in life---not just in academics but in art and in any creative field---is to find the means to periodically re-invent yourself. If you don't then you atrophy, you want for ideas, and your creativity dries up. If you can manage to be re-born, then you get a fresh start with re-kindled enthusiasm and new viewpoints. You can jump-start your rebirth by changing jobs, or finding new collaborators, or switching fields. This is a key insight that you should always keep in view.

If I hadn't become a mathematician then I think I would have liked to be a rock star. Unfortunately, the competition there is quite stiff, and the chances of failure immense. It is a short life but a merry one. The great thing about being an academic mathematician is that you have huge chunks of time, you have security (tenure), and you have and a great deal of freedom and independence to explore your own thoughts and create your own intellectual path. With luck, you can have considerable influence over the development of others, just as my many fine mentors have had over me.