I was an undergraduate math major, albeit not a clever one. Proofs were hard for me, and I found it increasingly difficult to focus as the courses moved on to more and more abstract problems. An embarrassing thought: just 6 years after graduating, I don’t know if I could navigate much of my homework assignments from back in the day.
But this is not to say my degree was totally in vain. At my current job, I get paid to look at numbers and calculate cool information with statistics. This type of work is math for the sake of application, as opposed to work in number theory or topology, which is more math for the sake of math. Although in its purest sense, math isn’t a part of my job, studying the idealized form of it taught me some important lessons.
First of all, proving things is really hard. It requires one to take a giant leap from our own world to the world of logic, where axioms and propositions live in stark contrast to our day-to-day notions of observations and hunches. I admire and strive for the kind of clarity this type of thinking requires.
Studying math also gave me an appreciation for its artistic merits. Contrary to stereotypes of being stern and rigid, pure mathematics is quite the opposite: playful and free-spirited. The uncanny ability of some mathematicians to invert a problem to find its solutions is baffling to say the least. Crazier still are the ornate hoops they craft to jump through the toughest of puzzles.
But what has stuck with me the most are the stories and biographical insights. Mathematicians obsess over discovering true things, or even capital T truths, and go to courageously great lengths to illuminate darkness. To put it shortly, math people love math. I find many of their adventures and personal struggles resonating in my daily life.
And so reading Fermat’s Enigma by Simon Singh was a trip down memory lane. It is a delightful little history of mathematics, with a focus on the riveting stories behind the Last Theorem of the titular character. From ancient Greece to the late 20th century, we hear of the wide-ranging accomplishments of the brave mathematicians who were, knowingly or not, related to Fermat’s famous question, from Pythagoras and Diophantes, to Euler and Sophie Germain, and all the way down to Taniyama, Shimura, Richard Taylor and Andrew Wiles himself. My big takeaway: the book’s interwoven nature is a reminder that we in the 21st century are, funny enough, living in a strange conversation with the people of yesterday.
Singh is also adept at linking complex technical ideas to friendly prose. We get a nice little introduction to symmetry and group theory, for example, just a few pages before learning about the deathly duel of Galois. And his linking of Gödel’s incompleteness theorem to Heisenberg’s uncertainty principle was really cool. I had never even thought of them that way before, as historical parallels. He’s even got an appendix of clever little proofs for those with mathematical curiosities.
So I am glad I read this one. It helped re-establish a conversation with my 2011 self, and offered solid evidence (not proof!) that exciting lives lie just below the surface of topics that many people consider boring.
God exists since mathematics is consistent, and the devil exists since we cannot prove it. - Andre Weil (page 255)
I was so obsessed by this problem that for eight years I was thinking about it all the time – when I woke up in the morning to when I went to sleep at night. That’s a long time to think about one thing. That particular odyssey is now over. My mind is at rest. - Andrew Wiles (page 285)