Post #1722096

2026-04-27 15:22 UTC

We are transitioning in mathematics from an era of proof scarcity to an era of proof abundance, but our mathematical infrastructure and culture has not yet adapted to this. As mentioned previously, there is now a strong (and growing) impedance mismatch between the three core components of mathematical problem solving: proof generation, proof verification, and proof digestion. An early sign of this transition could be seen in the chaotic response to the initial "First Proof" challenge, in which many more potentially viable solutions to the given problems were produced than could be readily verified or digested, either by experts or by automated tools. And now we are seeing the same impedance mismatch at the Erdos problem website, where (since the release of GPT 5.5, as well as the highly publicized recent solution to Erdos problem #1196) there is now an unprecedented backlog of nearly twenty claimed full or partial solutions "pending assessment": https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems . (Prior to this recent surge, this category contained one or two solutions at a time at best.) (1/5)

Replies (7)

@Mr0@privacysafe.social 2026-04-27 16:03

@tao@mathstodon.xyz Is there way to identify LLM generated proofs and reject them, if multiple proofs have already been found unless it gives new valuable insights and there is human written explanation that shows deep understanding Has "AI" helped with bridging different areas of mathematics or has it helped with simplification or at least making the mathematical terrain less dense

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@tao@mathstodon.xyz 2026-04-27 15:22

Perhaps surprisingly, this massive acceleration in proof generation has not actually produced significant acceleration in mathematical progress itself (with the possible exception of #1196, in which all three stages are largely carried out at this point, and for which some digested assessment of developments will soon be forthcoming). I can try to explain this counterintuitive situation using the culinary analogy from previous posts, in which the analogues of proof generation, proof verification, and proof digestion are food gathering, food cleaning and inspection, and food preparation (cooking). Societies that are used to food scarcity, and societies used to food abundance, handle communal meals in rather different ways. When there is food scarcity, the bottleneck is supplying the food in the first place; while the efforts of others in the community to clean and prepare the food, and stretch it to feed as many people as possible, are certainly appreciated, it is the hunters, gatherers, and farmers that actually "bring home the bacon" that are given the most acclaim and status, at least in popular culture renditions of such societies. Virtually any contribution of (non-toxic) meat or vegetables to a communal meal would be welcomed, and volunteers could readily be found to properly incorporate such contributions into that meal. (2/5)

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@Ardubal@mastodon.xyz 2026-04-27 15:31

@tao@mathstodon.xyz I wouldn't say »proof abundance«, rather »claim abundance«. The question is how much the failures in filtering the errors caused by not-actually-thinking will impact further actual progress.

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@yuhasz01@mastodon.social 2026-04-27 15:32

@tao@mathstodon.xyz AI math proofs focus on math *process* not new creative and original ideas and concepts,ie, repackaging content, circular reasoning

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@samirparikh@mastodon.social 2026-04-27 17:22

@tao@mathstodon.xyz The same thing is already happening in the field of computer security. Whereas we previously awarded prestige and compensation to those researchers who were able to find and disclose zero-day vulnerabilities, we now need to shift our focus and efforts to those who are able to classify, triage and remediate the large volumes of findings coming out of the various AI models. There is an abundance of things to fix while there is a dearth of people to fix them.

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@harrisonsweeney@mastodon.social 2026-04-29 22:46

@tao@mathstodon.xyz Is this something: Erdos 593: https://chatgpt.com/share/69f287c5-ec1c-8323-9fc6-a656cf8c1dae

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@mike@sauropods.win 2026-05-06 13:14

@tao@mathstodon.xyz Surely the output of mathematics is not proofs but understanding.

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