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What? A brute force computer simulation can show you that some finite conjecture holds...but an axiomatic proof surely is the only real concept of "why" we have
by smegel 13y ago
What? A brute force computer simulation can show you that some finite conjecture holds...but an axiomatic proof surely is the only real concept of "why" we have. Because if it is not true, then 1+1 != 2, or some such result.
- ColinWright 13y agoNot for me, and not for many of the mathematicians I have worked with. Sometimes with a theorem there is a sense of knowing why something is true, and in those cases the proof emerges fairly naturally from that. Sometimes, on the other hand, you have a proof, you know it's true[0], and yet there is no enlightenment, no sense of what's happening, no real understanding of why it's true. Some mathematicians don't have this point of view, but I always felt that sometimes, even when I really knew the proof, I still hadn't grokked a sense of the why. It just all felt like unmotivated symbol manipulation. [0] For some value of "true".