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points by stouset 2 days ago | 0 comments
> Why aren't you excited for pushing the frontier of knowledge.

In mathematics specifically, having answers to open problems is often not inherently all that useful. The value of open problems typically comes from new theories and techniques that mathematicians produce attempting to drive towards solutions. The open problems themselves are a means to an end.

Suddenly having the all the air sucked out of the room by having all of math’s open problems solved—without producing fruitful new areas of research—is not inherently a win.

[–] senderista 2 days ago
About the only general lesson I can extract so far from these announcements is that apparently we underestimated the extent to which major open problems are amenable to known approaches (possibly from very disparate fields), if they are combined judiciously by a virtually omniscient search engine. Frankly it's a little disappointing to me that these problems didn't require major new creative advances (e.g. the invention of new subfields) for their solution. And arguably that's a loss, if humans, with their inferior search and recall capabilities, would have been forced to resort to more creative solutions.
[–] caminmccluskey 2 days ago
It's still possible, and I suspect likely, that many more problems will require new creative advances. Creative advances that may have arisen in the regular course of attempting to solve these problems that were nevertheless amenable (often in a very alien brute-force way) to combination of existing techniques
[–] stouset 2 days ago
Maybe this is too pessimistic an attitude, but we may be ten years from it not even mattering.

I’ve heard Grant Sanderson’s take. But I suspect math is going down a dark road where humans have little reason to pursue it any more. We’ve crossed a threshold where computers are regularly solving problems that have remained open for decades. Humans barely stand a chance today; ten years from now we’ll be irrelevant in terms of pushing the field forward.

AI might be around to produce new techniques for other AI. But will it be relevant for humans? Will humans even need to be part of the loop? Will the new techniques be presented in ways that are intended to be conveyed to humans? Will there be humans interested in or capable enough to use them? I have my doubts.

[–] senderista 2 days ago
We seem to still be a long way from an AI equivalent of Grothendieck (i.e., creative system-builder). Maybe AI is close to replacing a problem-solver like Erdos.