alt Hacker NewsI don't think this is a valid counterpoint at all. Math is cooperative, and comprehension is the point: the proof has value exactly because (and only to that extent) it empowers humans to understand an abstract truth. Chess is competitive: the memorized line has value because it makes you incrementally more likely to defeat your opponent.
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The goals of Chess and Math may be different, but they follow the same principle of exploration large search space according to fixed rules. In case of Chess these are chess rules, in case of Math these rules of mathematical logic.
Memorized proof patterns have value because they lead you to a final proof.
Math that humans don't understand but nonetheless allows AI systems to develop breakthroughs in various fields of science, technology, physics, engineering, medicine, etc., would have great value to humanity even if it doesn't help humans understand abstract truth at all.
Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it, it initially seemed useless, then another AI system found a predictive model of electromagnetism using it.
I hope I'm remembering this right: a mathematician claims to have a proof for the ABC conjecture, but can't conceive any other mathematician it's right — it's "too weird", so the proof is rejected?
Yes, this. Comprehension is the point. We could map this to something like physics. If a man on a horse can shoot another man with a bow, empirically he makes correct predictions on gravity, wind and relative motion. But he can’t explain it. It’s not any different if your model has some “embodied” or demonstrable understanding; the model is not part of the discourse.
Math isn't "cooperative". Math is about truths. The length of circumference. The area of a triangle. The formulas for these are true in an objective sense irrespective of whether you understand them.
That said, without understanding, Math can't evolve. Comprehension of a proof is very important, but not what Math is fundamentally about.
Computer programs are Math. You can use them without understanding how they work.
Math is also useful. If someone showed that p = np tomorrow in a formally verified proof I don't care if no one can understand it.