3 ms·
I think many mathematicians would argue that there's an additional component of aesthetics at play. It's not just that you want to know whether a theorem is tru
by j2kun 13y ago
I think many mathematicians would argue that there's an additional component of aesthetics at play. It's not just that you want to know whether a theorem is true (in fact, nobody cares whether the theorem is true). You want to know why, and you want the proof to be so trivial that in hindsight it's obvious.
This is why people build up grand theories, so that when they get to the mean value theorem they can just say "Tilt your head and apply Rolle's theorem!" It's proofs that mathematicians are after, not answers, and beautiful proofs at that.
- JadeNB 13y ago> You want to know why, and you want the proof to be so trivial that in hindsight it's obvious. Certainly I agree with the first part of this sentence, but I'm not sure about the second part. I think that, if this is accomplished, then it is viewed as a victory; but I don't think any mathematician would describe it as his or her mission. (Perhaps on a larger scale, the mission of mathematics is to find the right definitions that make previously difficult things obvious.)
- j2kun 13y agoThe parenthetical is what I meant by my sentence. But also to a lesser extent Paul Erdos was a famous proponent of always finding simpler and more obvious proofs.