My mother, who grew up in Los Angeles, gave birth to me in Santa Barbara, California at 8:30 p.m. on February 21, 1974. My father, also a Southern California native, didn't trust the hospital so he carefully studied my ears in order to be sure that no switch occured when the nurse took me away. Like my brother, who was born 15 months later, I can be sure that my parents are my own.
Less than a year later, my parents converted an old school bus into a hippie-mobile, and moved north to Sweet Home, Oregon with hopes of living off the land. Soon after arriving, my mother gave birth to Dennis. In the interest of stability, my parents purchased a turn-of-the-century school house located deep in a forest ten miles down a narrow winding gravel road full of potholes.
For almost ten years I remember driving up and down that road: holding my breath so as not to choke on dust; gazing wistfully at passing blackberry bushes and trails with unknown destinations; and studying mathematics while wedged in the back of the school bus while AC/DC sang about being rocked all night long. I didn't have a large yard; I had thousands of acres of Forest Service wilderness. I didn't have carefully labeled fresh organic fruit; I had my mother's gardens which were filled with warm dusty tomatoes, carefully hidden rasberries, and forbidden almost ripe strawberries. My parents never took me to the playground; instead they took me on long walks to abandoned apple orchards, on horseback to secret ponds hidden deep in the forest, and to lookout towers atop high mountains where young women sunbath topless while watching for fires.
They didn't take me to the pet store; I found my pets in the rocks shedding their skin. I onced asked my father for a pet bird and together we brought home 15 homing pigeons from a farmer, and converted an old tree fort into their new home. At night the big bad wolves howled about how they would eat us if they could, so I wasn't surprised when they later murdered my poor pigeons.
Western Oregon is a rain forest, and we got all of our water from a spring that dumped enough water on our land to create a marsh complete with mudpits, frogs, salamanders, and giant green leaves. Instead of neighbors with BB guns and booze, my brother and I had a jungle to explore. At the end of the day the familar dinner bell always rang.
For my parents, living in our old school over the top of the hill must have been a fantastic amount of work. When they told me we were moving to Texas, I imagined a vast treeless dessert, perfectly flat, where the sky pressed down so hard that everyone crawled on the ground. I knew we had family there, but I could not believe that Texas could be anything but a barren wasteland; empty, except for a passing dust particle or wondering cloud, and as habitable as Mars.
NOTE: In September 2005, I visited Sweet Home and took pictures of our house (the one with the blue roof).
Our destination -- Granbury, a small town two hours west of Dallas. I remember Atari user group meetings and a strong skateboarding scene. I put a good deal of effort into becoming proficient at both.
After several years, we left Texas for the pristine mountain community of Flagstaff, Arizona, which is just an hour from the Grand Canyon. I started high school, but only remained one semester before dropping out.
I packed my bags, hopped on a motorcycle, and drove. First around Arizona, then a few feet towards Texas, then with purpose to San Diego.
Next I went to Corvallis, Oregon, and enjoyed the kind hospitality of my aunt and uncle, who own Thormahlen Harps.
Skating to LA with the sponsored am guy.
I found myself in veritable slave labor working at Taco Bell. less interesting than High School would have been.
My mother suggested that, with a Pell Grant and low in-state tuition, I would make as much money by going to college. At age 16, I took the GED in order to go directly to Northern Arizona University
As a child in Oregon, I learned to program in C before I touched my first compiler. My father built several houses with no outside help, because he loved to build; I loved to make software. Spending every waking moment of a week pushing code out of my fingers fills me with elation. I declared my major with the computer science and engineering department at NAU.
Two years later I had taken the core computer programming classes. One day I found a book on group theory in the local used book store, and could not put it down. I was inspired to take an excellent summer course (by algebraist turned statistician Peter Horn) on how to write proofs. The next semester I took a course on "Software Engineering" which convinced me to drop computer science in favor of mathematics. I discovered that software engineering is interesting only because of the problems it can be applied to, and without a background in mathematics I might spend my life helping other people solve miscellaneous problems, instead of solving my own.
After my last semester in computer science ended, I took every interesting math course the NAU mathematics department offered, more than I could officially get credit for. It then occurred to me that I would enjoy life as a graduate student in mathematics, so I did some arithmetic and learned that I could graduate very quickly. And so I did, in August 1994, after 3 years and one semester.
The first order of business was to get into one of the United State's first rate graduate programs. A quick check and it seemed that the best university an NAU math undergraduate student had ever gone to for mathematics grad school was the University of Washington, and Steven Wilson, who studies regular maps, had gone there decades ago. My undergraduate adviser, Michael Falk, an algebraic topologist, convinced me that the GRE math subject test is very important. I decided to stay at NAU, as a mathematics graduate student, for one additional year. I wanted to learn how to do well on the GRE and apply to as many graduate schools as possible, in hopes of getting a good offer from at least one of them. I also thought that I could impress the professors who would write my letters of recommendation by doing well in a few more of their classes.
Patience and love paid off and a year later I landed at the University of California, Berkeley.
Berkeley shocked me. I arrived early, during the summer, in order to be more prepared for my first semester at this intimidating university. I took summer courses in Complex Analysis and Topology, which were both taught by recent Berkeley Ph.D.s Alexis Alevras, a functional analysist, and Fred Teti, a logician. I also studied for the so-called "preliminary exam". This is a six hour written exam whose stated purpose is test whether or incoming graduate students have an undergraduate math education; it's actual purpose is to "weed out the weak". I considered it a good opportunity to review my undergraduate material and problem solving skills. Would I pass?
I passed two weeks after the first semester began, and about half of the others who took the exam also passed.
During my first year I took two courses in algebraic geometry from Robin Hartshorne, who is the author of one of the standard textbooks on the subject. I took an algebraic number theory course from Robert Coleman who understands many aspects of p-adic modular forms better than anyone. And, in the wake of Andrew Wiles recent proof of Fermat's Last Theorem, I took a course from Ken Ribet. Ken's work has provided much of the foundational material on which applications of modular forms to number theoritic problems is now based. His course would turn out to be the most important one, and you can read some of my notes.
By my second semester I began to understand that I wanted to study modular forms, so I spent a lot of my money to go to a conference at the National Academy of Sciences in Washington D.C. It was hard to justify going at the time, except that I had a feeling that it would be a good idea. As it turns out, this was one of the best things I've done. Names like Shimura, Faltings, Mazur, Hida, and Kato became real people, some of whom I had the opportunity to talk mathematics with. I often remember the conference even now. Barry Mazur said compassionately to me, "it must be hard for you at this conference knowing so little about modular forms."
My brother had moved to Belgium to learn French and study business. I visited him in the summer 1996 and also went to conferences in Lille, France and Antwerp, Belgium. This was the first time I left the United States. Seeing places such as Rome, Amsterdam, London, and Brussels was incredible.
My next academic year was mostly drudgery. I took courses on homological algebra, class field theory, Lie groups, and Euler systems. Somehow I also became convinced that I would work on Galois cohomology with Lenstra for my Ph.D. research. My life was essentially unexciting until March of 1998 when I took a long trip.
My first stop was a conference in Arizona where Mazur talked about Tate-Shafarevich groups and the importance of computers in understanding modular abelian varieties. Here it was! It was the application of software engineering which I had hunted for so long. So long that I had forgot that I was even searching.
Next I went to a conference on arithmetic geometry at the Newton Institute in Cambridge, England. I talked with Merel who introduced me to Mestre who in turn told me about the algorithm he designed with Oesterle. I talked over high-table with Peter Swinnerton-Dyer about his work on the first programmable computers (such as EDSAC) in the 1960's, the work which led to some of the most important open conjectures in modular forms. I quickly became convinced that I would study modular forms, and began reading basic facts about them in the Newton Institute library. Kevin Buzzard also asked questions which required me to implement a few standard modular symbols algorithms.