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"Congratulations, you're learning to think like a mathematician." - Elf M. Sternberg
"Congratulations, you're learning to think like a mathematician."
Quentin Hardy is the "technology culture" writers for the New York Times. He graduated from Columbia with a degree in Journalism, which qualifies him to be a journalist, but not necessarily a mathematician. In a recent review of the new biopic about Alan Turing, Hardy makes a couple of interesting claims about how Hollywood depicts brilliant mathematicians as having a "cold relentlessness." He writes
We lesser mortals, we tell ourselves, feel more authentically, with something essential that they lack. In each of these movies, there is an emotional climax when the hero discovers the limitation of his analytic approach. He is saved, or ruined, in relation to his ability to learn how to feel... At some point in almost every math movie, the hero stares at formulas in the air, bewitched by a world the rest of us can’t see. Then he talks to regular people, and becomes an enchanted, but disconnected, visitor. ... The depiction of all these people, essentially diminishing inner lives almost certainly as rich as our own, signals our ambivalence toward living around computers.
He may be right about how Hollywood makes an emotional crisis the heart of such movies, and he may be right that Hollywood depicts these people as having "diminished inner lives" is essential to the shorthand of the mathematician.

I'm no amazing mathematician. I'm at best an okay programmer. A few years ago, for no reason other than curiousity, I started working my way through an understanding of the Church-Turing Theory, and there were times when, yes, I would stare into the air, enchanted by a world no one around me could see. It wasn't a new world; certainly, hundreds of developers before me, the ones who gave a damn about the theoretical basis of procedural computer science, had all seen similar visions, of how the universe actually works underneath all those layers, the basis of automata and complexity theory and all those wonders.

For the past year, I've been distracted by Category Theory, that terrifyingly new and clever layer on top of of Church-Turing that tells us about declarative computer science, that allows us to say exceptionally precise things about how we want our programs run, such that our tools can actually write much of the error-prone procedural stuff for us. My vocabulary is full of new words like morphism, endofunctor, and the terrifying monad. And all throughout the year, when I've hit on one of those inflection points where I can suddenly see how this thing has been put together, see how we can describe things to computers such that they do our bidding in new and powerful ways, see how the math becomes much more than just arithmetic... yes, I'll stare off into space, enchanted by a world I can't share with very many, disconnected for the time being from the ordinary world.

So, in some regard, Hollywood gets that right. We do see things that are different from ordinary people. We do spare off into space, enchanted by things most people will never see, have no interest in seeing. (For all the angry indifference fans have toward Iron Man 2, Downey's look when he's trying to solve the visualization problem his father left him is absolutely spot on.) And unlike any mystical variations on this theme, when we bring what we've seen back to Earth and apply it, the math works, and the world changes.

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From: (Anonymous) Date: December 6th, 2014 06:30 pm (UTC) (Link)


I tell my students this all the time - especially in introductory classes about proof (like Discrete Math, Theory of Calculus, and Abstract Algebra). The _entire_ world is full of these layers and abstractions, and when you _see_ it in front of you, you can just end up staring at the images on the chalkboard/whiteboard/screen in your mind watching the pieces fall together. It's almost orgasmic when you _get_ it...
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