Comment on November 2014 Monthly Bragging Thread

Fri, 14 Nov 2014 12:49:16 GMT

Going through every theorem in the book and proving it

This is how I study math. A result I've come across a few times is that trying a problem before learning how to do it, even if you fail, will result in you learning how to solve the problem better (this study (pdf), for instance). AoPS pedagogy reflects this; they encourage the reader to try each problem before reading how to solve it, even if they don't succeed. (I've been doing this long enough that I forget that this is a minority approach rather than common sense. Reminds my of this paper. tl;dr, most students study by rereading the book, even though this is completely ineffective, and very few practice retrieval, which is wildly effective.)

In this way, I don't see the dichotomy between learning new math and using already-learned math in new situations. Going off stuff I read here (written for popular audience, grain of salt, although it's used as a text for an upper-level psych course at Harvard), pushing your mind to its limit learning new math is going to increase your ability to learn new math and pushing your brain to its limit using known math in novel situations will increase your ability to use known math in novel situations (which feels kinda, sorta like buffing fluid intelligence)—but there's no reason you can't learn math by using it in novel situations because that's exactly what I do when learning math. So, when I talk about "[studying] math intensely", I'm referring to doing inventive things with old material to learn new material.

One more thing: there's no widely-accepted method for increasing fluid intelligence that I'm aware of. This is all based on fairly new research and personal experience. Fortunately, between the age distribution of the US population and how many diseases we can treat or cure, there's a lot of money going into research neuroscience because Alzheimer's, so hopefully this is changing quickly relative to the counterfactual.

One more thing: OP doesn't know calculus.

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