[MikkoFinell]

>"If nobody understands a mathematical proof, does it count?"

Just wait until general AI really kicks off, then all of new math will be like that. It's not that humans are bad at logical thinking, our weakness is memory. That won't be the case for an artificial agent with instantaneous perfect recall of everything it has ever seen.

[BucketSort]

lol. I think the resurgence of interest in constructionist mathematics via Homotopy Type Theory will lead to better proofs ( since all proofs in HoTT are like programs and can be computationally verified in a straightforward way ).

[LeifCarrotson]

Even an AI will have various levels of cache. Some memories will be register-level instant, some will be thousands of miles and quite a few servers away, and others in between.

[MikkoFinell]

That's a good point. Lets throw "instantaneous" out, having the ability to store and perfectly recall data is a critical advantage for any thinking entity.

[posterboy]

>instantaneous

as the memory will exceed ram and then disk-space, that will be less true.

[KGIII]

Mathematics is a language. You don't really need to memorize it, you can read it. Unfortunately, most people aren't exposed to anything higher than arithmetic.

[posterboy]

yeah, well, have fun reading e.g. the stacks project[1] of round about 4000 pages without remember the necessary steps leading up to a corollary.

[1] https://stacks.math.columbia.edu/browse - abstract algebra as far as I can tell

[KGIII]

You're sure as hell not going to memorize it.

[Koshkin]

I remember having to memorize the multiplication table. And that was just the beginning...