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"Mathematics is lucky in that it's an entirely logical field where things can be absolutely proven." A professional mathematician should confirm this, but my i
by scarmig 14y ago
"Mathematics is lucky in that it's an entirely logical field where things can be absolutely proven."
A professional mathematician should confirm this, but my impression is that most of the interesting bits of math are fairly informal and creative--rigorous proofs only come long after the fact, if they come at all, and really just amount to dotting is and crossing ts that few people double check anyways. Absolutely proven is a bit stronger than is warranted, and at least some other fields can produce statements that have the level of "truth" that a mathematical statement has.
- SoftwareMaven 14y agoThe point is that the proofs are actually possible. Even physics requires "proof by statistics".
- scarmig 14y agoMy point, though, was that mathematics is also a field filled with minefields and gotchas where experience is very useful. Moreover, that mathematicians are more than glorified theorem provers.
- Locke1689 14y agoIt's true that mathematicians more often deal with proof sketches rather than base formal proofs, but that's just for brevity purposes. I don't think any professional mathematician would argue that their main goal isn't to produce proofs (or things that could be proved, i.e. hypotheses).