- Conservation of proof energy. I think I heard of this from Robin Hartshorne when I was taking his graduate algebra course. The idea is that if you're trying to prove something hard, and there's a lemma that makes the result easy, then proving that lemma is going to be hard.
- In real analysis, if something seems intuitively true, there's probably a counterexample. For example, the existence of an unmeasurable set. (2 and 3 courtesy of Fang-Hua Lin during his complex variables course, if I remember right.)
- In complex analysis, if something seems too amazing to be true, it probably is true. For example, everything about holomorphic functions.
- In numerical analysis, if you are estimating complexity or error bounds, log(n) for n large is 7 (courtesy of Mike Shelley, I think).
Wednesday, December 18, 2013
Some mathematical principles
I was just thinking about the old days when I used to do math (although not particularly well), and I remember thinking that there are some principles in math. These are general "trueisms" in math that, unlike theorems, are neither provable nor even always true. Actually, I guess then they're "trueishisms". Anyway, here are a couple I know of: