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The hand wringing is premature. Thus far AI has only shown a superhuman aptitude for brute forcing proof of existence: - Disproof of the Jacobian conjecture by
by zarzavat 22d ago
The hand wringing is premature. Thus far AI has only shown a superhuman aptitude for brute forcing proof of existence:
- Disproof of the Jacobian conjecture by example
- Construction of a non-sofic group
- Existence of singularity in Navier-Stokes
Mathematical conjectures tend to be universally quantified, especially those conjectures that are used as building blocks (e.g. RH). If anything, AI models are currently performing a useful service by disproving false conjectures, a kind of mathematical weeding.
The good news from the last couple of years of coding agents is that while models have become more persistent and knowledgable, their creativity (defined as being able to escape their training distribution and synthesize completely novel ideas) is improving at a much slower rate.
AI will only become a threat to mathematics if/when it develops the capability for creative big-picture problem solving. If that happens, the impact on mathematics will be a footnote compared to the impacts on society at large, since creativity unlocks a host of new economic capabilities.
- robotpepi 22d ago> Disproof of the Jacobian conjecture by example It should be noted that there was a manuscript, available online since the beginning of 2025, with a solution to the Jacobian conjecture: "Adrian Vasiu claims that the 7 page AI paper on the 3D Jacobian conjecture counterexample used notation and concepts from a draft of a paper jointly written with Alexander Borisov and Ofer Gabber, dated to January 14, 2025 and made publicly available on January 16, 2025." The extract is from wikipedia, where the sources are given.
- contubernio 22d agoTha Jacobian conjecture is (was?) notorious for publication of false proofs. There have been many, not all by those who shouldn't have known better.
- robotpepi 22d agoWell the author of this one obtained a grant based on the work, the proof uses the same strategy as Anthropic's and even share some notation. I'm not an expert but this doesn't seem like one of those P!=NP proofs.
- qbit42 22d agoYou can also brute force the existence of a proof... It is true that the biggest splashes have been from counterexamples and such, but I have seen many smaller examples of proving positive results in my own field. Perhaps not superhuman yet but sufficient to completely upend the status quo. And I'm supposed to believe that this won't change in a year? or two?
- alansaber 22d agoExactly, people are jumping at the shadow on the wall- LLMs have achieved remarkable things regarding their limitations, but those limitations show no signs of yielding