(Late) MathILy-Er Wrap-Up: Head Fakesby Shardul, 14 Aug 2017
It’s a Saturday morning, the last day of Root class, and all 25 MathILy-Er students are in the same room, busy at whiteboards and tables and incessant discussions. It’s crowded and you can hear everybody’s soft yet intense voices trying to prove, conjecture, disprove, convince, find, understand. A few friends and I have been working on a single proof for three hours; this particular problem has not been solved by either Root class for the last two weeks and is bugging everyone.
We think we have it! We try to explain to a bewildered passer-by. Not good enough, too confusing. Another couple of revisions—we drew some pictures, made some flowcharts—and we think it’s clear. Time to present to the class. And when it’s done, Jonah (our lead instructor) says to us (paraphrased): “That problem was posed in the 1980s, and that proof was discovered in 2003. Thank you for doing 20 years of mathematics in two weeks.” High-fives and grins all around.
Now that I think about it, MathILy-Er executed brilliant ‘head fakes’ on multiple levels. (A head fake is when you’re playing, say, basketball, and you turn your head one way but pass the ball a different way to confuse the player trying to intercept the ball. I use the word the same way Randy Pausch of The Last Lecture fame used it.)
The first head fake was the way we did math in class. We thought we were just playing around with those funny matrices who only had zeroes and ones in them. We thought it was just wishful thinking when we hoped to play seemingly disparate games in parallel and treat them as a single, unified game. We thought color-gradient spreadsheets just made our guesswork look pretty. And there, thrice were we wrong, and again a dozen times throughout MathILy-Er were we wrong. For lack of a better word in my vocabulary, we were conned by our instructors into discovering key aspects of mathematical theory, deceived by the apparent lack of structure into building very concrete concepts that we would keep developing throughout MathILy-Er, and this particular head fake is so effective that although we caught on to what was happening after the first two weeks or so, it was impossible to not fall for the trick again when a new curiosity presented itself—or was it hinted into our subconscious minds by our instructors?
The second head fake was all the absurd humor. If you haven’t encountered this particular genre of entertainment yet—more likely, you have, but you don’t know what it’s called—I think the evergreen Monty Python and David Malki’s webcomic Wondermark are quintessential. It’s hard to put MathILy-Er’s general atmosphere of absurdity in words, but all throughout those five weeks—in class, at lunch, in the dorm, at the programfire (MathILy-Er isn’t a ‘summer camp’ but rather a ‘summer program’), everywhere—it was the hardest thing to tell whether someone was being funny or serious, even when what you were discussing was far beyond what you felt could be true. (The trend was set by our instructors early on and everbody caught on soon enough, woe to those who took their friends too literally. We had a perfectly reasonable argument about whether Canada actually existed with the sole person from Canada declining to take a side because both were pretty convincing.) And what was the head fake? MathILy-Er let us open the metaphorical cans of worms and not be weirded out. In Branch class, when we first suspected that we’d found a number that was neither positive, nor negative, nor zero, very few people dismissed the idea outright and we could suspend our disbelief long enough to lead a meaningful investigation; but thinking back, I personally would have had a much narrower approach to such a situation before MathILy-Er. I now feel that discovering new mathematics is essentially trying to do things that nobody has even thought of doing before, because it’s simply too improbable that someone would just randomly think of them. It’s like the surprising construction that solves ‘the world’s hardest geometry problem’ but on a much deeper level. MathILy-Er taught me to not take anything, including myself, too seriously, but also to not dismiss the seemingly absurd or wrong without a little thought.
The third head fake—I’ve only discovered three, so this is the last one—is pretty deep. MathILy-Er turned its head as if it was teaching us math, or as if it was teaching us mathematical ways of thought. But MathILy-Er passed the ball to teach us how math is done. Math is seldom the stereotypical absent-minded genius (severely lacking in social life) scribbling away in solitude, publishing theorem after theorem or working on a single monumental proof for seven years or single-handedly writing the book on a niche incomprehensible topic. Quite on the contrary, math is a massively-multiplayer collaborative effort, where researchers from diverse areas of expertise (and areas of geography) pool their work together, building mathematics bit by bit, paper by paper, so that everyone understands what’s going on and everyone can at least try to contribute meaningfully. Mathematicians are friends, not recluses, and they share instead of competing, and they talk a lot with each other because there is no better way to gain new perspectives than to talk with someone who has one different from yours. Of course, since I’m not a mathematician [yet], I woudn’t know if this was true; but this is how it was at MathILy-Er where we were immensely productive, and this is how our instructors said productive math is done in the research world they come from, so I believe it is true and hope that I can some day become a part of it.