18 ms·
A little over 10 years ago I remember meeting a postdoc who believed he had something close to a counterexample to the Jacobian Conjecture. He and another perso
by koito17 2mo ago
A little over 10 years ago I remember meeting a postdoc who believed he had something close to a counterexample to the Jacobian Conjecture. He and another person was bruteforcing polynomials in about 16 variables, something like 80 - 700 terms each, using binary trees for mapping coefficients.
They were guessing, at the time, that the lower bound of a counterexample (P, Q) for max(deg(P), deg(Q)) would go up to 200.
To think that Claude Fable was able to find a counterexample in degree 7 is insane to me. We are truly in a new era.
- zaik 2mo agoWould this counterexample not be included in their search space?
- koito17 2mo agoThey were looking at 16 variables, degree of about 10 in each one. That search space is simply too big for a plain bruteforce. So they did some sort of filtering to reduce the search space to a pool containing "possible counterexamples". There was also a paper giving a lower bound of about 100 for possible counterexamples in that particular framework. Later raised to 108 in https://arxiv.org/abs/2204.14178 https://arxiv.org/abs/2204.14178 I don't remember the details very well since this was back in 2015 and wasn't really involved in the research. Consider this to be some sort of telephone game between what I heard in 2015 and what I remember today.
- jasonfarnon 2mo agobased on the approach described they were probably in dimension 2, this counterexample is 3 dimensional
- inigyou 2mo ago16 variables
- deleted 2mo ago[deleted]
- 0x1ceb00da 2mo ago[flagged]
- antirez 2mo agoSo many mathematicians over the years tried hard and failed, but now Anthropic just for some PR magically did it? And this after LLMs obtaining different math wins? What is your logic here really escapes my understanding.
- glimshe 2mo agoThe parent's absolutely nonsensical post highlights how polarized AI (as everything else) is today. I can understand someone being opposed to AI on moral, cost-benefit or productivity grounds. But we're seeing a lot of extremist "AI is good for nothing" posts out there nowadays.
- pred_ 2mo agoI don't think it is nonsensical at all. The author and his collaborator both appear to be bright people, so there's a good chance they had to offer non-trivial insights to guide the LLM, yet it's clearly in the interest of his employer to downplay whatever personal contribution they provided. Edit: Now the OP is flagged/dead for some reason. You could disagree on their take (calling it a marketing stunt is maybe a bit much), but I think the argument is sound, so flagging seems counterproductive to the discussion.
- glimshe 2mo agoI'm sure they had plenty of time to think about these insights without the LLM, as well as the many other mathematicians who tried to crack it over the years. Wether the LLM was simply an assistant or solved the problem entirely isn't as important as accepting than the LLM was the essential, previously missing piece in the solution.
- minimaxir 2mo ago> I think the argument is sound They got flagged because it is a literal conspiracy theory that assumes bad faith.
- NooneAtAll3 2mo agoyou might be confusing 2 variable case (which indeed was tested to 150+ degree) and 3 variable case (this counterexample)