Uncovering Writing

My rating: 5 of 5 stars

I remember sitting in an office with a friend and downloading his proof when it was published. I had a small background in abstract algebra and I was able to get through a few pages, but then became utterly lost. I was still enthralled and flipped through it like it was a gift for my birthday! Based on recommendations from two people, I jumped into Simon Singh’s book on Fermat’s Last Theorem.

Singh is a fantastic writer. His writing is lucid and fluid: never too many words, but also never too few. I enjoyed the mathematical background (and enjoyed working through the appendices), historical tidbits, how mathematicians work and the actual story of Wiles’s approach to the proof. It was a detective story with a touch of romance and history to it. It was exciting as each piece of the puzzle came together. I knew the ending and I still couldn’t wait to work through each page!

I enjoyed the history that Singh provided, from the classical Greek mathematic Pythagorus, up through the centuries to Fermat and then to the present. This was a lovely romp through my two true academic loves: mathematics and classical studies. I was happy that he incorporated the story of female mathematicians into his narrative, something I didn’t know and that rarely pops up in general discussion of great mathematicians. Also, I enjoyed the chapter devoted to Yutaka Taniyama and Goro Shimura, and their conjecture that sought to equate modular forms with elliptic equations. This conjecture was the ultimate lever that Wiles used to prove Fermat’s theorem.

Singh also builds a strong case for pure research, even into seemingly unimportant topics. Fermat’s theorem was a cool idea, but on its own, it really didn’t seem that crucial. Yet the Taniyama-Shimura conjecture, and the follow on work by Gerhard Frey and Ken Ribet, tied a solution to something that would unite disparate parts of very important contemporary mathematics. Fermat provided the motivation, originally by accident, to improving modern mathematics. Wiles said “the definition of a good mathematical problem is the mathematics it generates rather than the problem itself” (p. 163).

As for Wiles, he did amazing work and fulfilled his childhood dream. The book ends with a quote from him that I take to heart: “I had this very rare privilege of being able to pursue in my adult life what had been my childhood dream. I know it’s a rare privilege, but if you can tackle something in adult life that means that much to you then it’s more rewarding than anything imaginable” (p. 285).

My problem with Wiles is that his success was due to other people doing what he refused to do. I think Singh implies it occasionally. Wiles succeeded because he was able to look at the work and ideas that other mathematics published. Taniyama, Shimura, Frey, Ribet and others had interesting insights directly or indirectly related to Fermat’s Last Theorem. They could have kept those ideas secret, like Wiles did. But, that would have slowed, or possibly stopped him in his tracks. He kept his task secret for seven years, even going so far as to publish unrelated work to throw people ‘off the scent.’ I know this was his lifelong dream and he wanted to solve it on his own. But, mathematical progress seems fastest when ideas are put out into the community and others can add their points of view. This isn’t meant diminish Wiles’s intellect or accomplishment, but it makes me wonder if Fermat’s theorem and the Taniyama-Shimura conjecture could have been proved sooner. Most mathematicians, including Wiles, seemingly went into mathematics due to the beauty of the system, rather than for money or glory.

I highly recommend this book to everyone, from people with no interest in math up to PhD’s at the top of the field.