2026-09-08 22:40 UTC
Replies (2)
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@drScott@mathstodon.xyz 2026-09-08 22:58
@nilesh@fosstodon.org @tao@mathstodon.xyz I understand the argument for that claim as follows: 1) If a mathematician is scooped on a problem, it is hard for them to disseminate their insights and tools. 2) AI can, with sufficient investment, convert a tractable problem into a solution (and thus a scoop). 3) Mathematicians can (only?) avoid being scooped by being secretive about their work. 4) Good open problems are hard to make without an open mathematics community. (2-3) have just been given a major example, and seem quite plausible. (1) has a long history in the field, no? Plenty of careers ended or interrupted, and several famous and messy fights over priority. I think Tao argues for (4) persuasively.
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@TobyBartels@mathstodon.xyz 2026-09-09 22:37
@nilesh@fosstodon.org @drScott@mathstodon.xyz @tao@mathstodon.xyz I think that this is correct in a well-functioning community, but I'm not sure that the mathematical community functions well enough for this. Ideally, knowing a bad, inscrutable proof still gives us the incentive to find a good, insightful proof (whether by understanding the known proof better or by taking another approach), while at the same time cutting off inevitably fruitless efforts at finding a counterexample, so it's only to the good. But the community that we have now is driven more by the search for new results than by better understanding old ones, so the bad, inscrutable proof can make a good, insightful proof harder to find in practice.