I grew up loving math.
Probably from the time I was in 5th grade through my second year of graduate school I would wake up every day thinking about math. My interests varied over the years, obviously. In high school it was the joy of learning all sort of new math from Mr. Waterman as well as the fun of math contests. In college I began to get interested in mathematical physics (even convincing the MIT Physics Dept to start an undergraduate General Relativity class), but also really enjoyed learning amazing subjects ranging from number theory to combinatorics. My most memorable classroom experience in college was definitely learning abstract algebra from Mike Artin.
Towards the end of my third year in graduate school, though, I completely lost interest in math. It didn’t happen gradually, either – I just woke up one day and wasn’t interested in math anymore. I’ve never known why.
Fortunately teaching my kids over the last several years has brought back the love that I used to have for math. As a result I’ve been paying much more attention to math-relatd items both in the news and online. This year I’ve found two incredible descriptions of what it is like to do math research that I wish I’d seen in graduate school. Going through them both made me wonder if my life would be different had I come across similar descriptions 20 years ago.
The first was this Numberphile interview with Ken Ribet:
The description of Ribet’s journey to prove that the Weil-Taniyama-Shimura conjecture implied Fermat’s Last Theorem was riveting. It is such an amazing story of the ups and downs of mathematical research and totally different from what I imagined that research was like when I was in graduate school. His interaction with Harvard’s Barry Mazur was especially moving.
The second item from 2015 that I wish I would have seen in graduate school was Cédric Villani’s Birth of a Theorem. A truly incredible description of the journey from initial idea to final proof of a Fields Medal winning theorem. The collaborative effort with his partner (that essentially covered all parts of the globe!) is incredible. All of the ups and downs in the research process were fascinating to see. Even though I know better, I tend to think of Fields Medal winners as being math automatons, so I was especially grateful to hear Villani discuss the dead ends, frustrations, and failures. A the end of the book, how he handled the initial rejection of the paper was also tremendously instructive. Again, the whole process was just so different than what I imagined math research to be like when I was in graduate school.
As an aside, Villani seems like a pretty cool guy. I ran across his name for the first time in this old post from Patrick Honner:
If you are a Fields Medalist and take time to do public lectures and talk to math teachers, I’m definitely buying your book.
Even though it is way too late for me to turn the math research clock back, I’m really happy to have come across these two descriptions of math research this year. I’m also grateful to have had my kids rekindle my old love of math. I hope that I’m able to instill in them some of the new ideas about learning and doing math that I’ve just picked up in these pieces from Ribet and Villani.