By Tai-Danae Bradley
Welcome to part 2 of our series where we’re taking a candid peek into the world of mathematical research. Last time we chatted about the often laborious process of doing math which, as we heard from Andrew Wiles, is much like stumbling in a dark room while searching for a light switch. The late William Thurston also described math in a similar fashion in his Math Overflow profile. Perhaps you’ve seen it? Here’s a screenshot:
I love that first sentence of his second paragraph! In my own experience, I’ve found that perseverance really is key as I’m well acquainted with fog, muddle, and confusion. In fact, mathematical fog is one of the main reasons why I started my own blog. But if I’m to be honest, there are times when I’m not sure how much of that fog is simply “the nature of the beast” and how much of it is, well, “encouraged.”
Quite naturally, this brings me to mathematician Piper Harron’s epic thesis, without which no foray into mathematical candor would be complete. No doubt you know what I’m talking about. If you don’t, then you must go check it out. Seriously. Right now. Just browse through the table of contents. With numerous laysplanations (explanations for the layperson) and chapter titles like “Getting Mathy With It,” you can’t tell me you won’t want to read more! Harron’s thesis is quite the epitome of math-made-accessible, and I was especially drawn in by the transparent honesty in her prologue. There she states that her thesis was written for
People who, for instance, try to read a math paper and think, ‘Oh my goodness what on earth does any of this mean why can’t they just say what they mean????’ rather than, “Ah, what lovely results!” (I can’t even pretend to know how ‘normal’ mathematicians feel when they read math, but I know it’s not how I feel.)
This is SPOT ON! As I mentioned in our previous post, I’m often in the stumbling-in-the-dark-while-groping-for-the-light-switch phase. But there are times when it feels like the switch was installed in the most remote, most inaccessible location possible, like, I don’t know, behind the drywall of the ceiling in the attic. I can’t tell you how many times I’ve thought Geez! Why can’t mathematicians just say what they mean?! And since this happens so frequently, I can’t help but wonder if there’s a secret math-committee out there whose goal is to obfuscate math as best as they can. But of course that’s silly. (Right?) There is no such committee. (Right?!) But it really is nice to hear others voice the same thoughts that have crossed my mind.
And finally, I’d be remiss to close our discussion without mentioning Terry Tao’s excellent blog post wherein he answers the question, “Does one need to be a genius to do math?” with an emphatic “NO.” In it he writes,
In order to make good and useful contributions to mathematics, one does need to work hard, learn one’s field well, learn other fields and tools, ask questions, talk to other mathematicians, and think about the ‘big picture.’ And yes, a reasonable amount of intelligence, patience, and maturity is also required. But one does not need some sort of magic “genius gene” that spontaneously generates ex nihilo deep insights, unexpected solutions to problems, or other supernatural abilities (emphases original).
Since Tao is one whom most of us would without hesitation call a genius, I found his words to be even more significant.
And this brings me right back to that Slate article I referred to at the beginning of part 1 of this series. After the author reminds us that “no one is born knowing the axiom of completeness,” he goes on to say, “even the most accomplished mathematicians had to learn how to learn this stuff.” How true! And I especially love how math teacher and self-proclaimed bad-drawer Ben Orlin illustrates this in his ‘How to Edit your Math Pessimism’ series:
I think it’s comforting to know that we students can replace “negatives” with just about any mathematical concept we’ve struggled with today and be in such good company! Pretty neat, huh?
I’ll leave you now with a few more links that relate to the topics we’ve chatted about today. And to everyone about to enter final/qualifying exam season, I wish you all the best of luck!
- Not too long ago, Evelyn Lamb wrote a fantastic article in which she contrasts Piper Harron’s thesis with Shinichi Mochizuki’s proof of the abc conjecture. I can’t recommend it highly enough.
- In this article, Marcus du Sautoy points out that everyone – not just those whose brains are ‘wired’ mathematically – is capable of doing mathematics.
- In a similar vein, Benjamin Braun wrote this piece for the AMS Blog in which he addresses “the secret question (Are we actually good at math?).” At the same blog, Evelyn Lamb wrote about math and the genius myth. Both posts contain several great links.
- Over at Baking and Math, Yen Duong notes that students too often think they are too “stupid/slow/dense” to do math, while the problem is often in the communicator rather than the mental abilities of the student.