3 ms·
If you ask me the relative rarity of computer assisted (brute force) proofs is because it is only useful in the unlikely scenario that the number of cases to ch
by contravariant 6y ago
If you ask me the relative rarity of computer assisted (brute force) proofs is because it is only useful in the unlikely scenario that the number of cases to check is too large for humans but small enough to be computationally tractable.
It's almost the contrapositive of the law of small numbers that any large numbers tend to be very large, placing most of them beyond the reach of ordinary computers.
- CJefferson 6y agoFurther, most interesting theorems work "for all" things (graphs, lists, integers, whatever), so it requires some clever work to even make the problem finite.
- nick_kline 6y agoActually a lot of things get proved first for narrower domains (because it can be easier to prove,) and then get generalized to larger sets and maybe get really general! eventually. This was a great insight one of my college profs gave me.