I'd rather wait for independent seasoned mathematicians to verify such claims first before someone at said AI lab posting a claim about solving a proof online.
Let this be a lesson to those who fell for such AI psychosis and to not believe everything you see on the internet as real.
playing devil's advocate a little bit, but wikipedia does have a policy against original research. If you published an obviously correct counterexample to wikipedia which is not anywhere else on the internet (or in a book, etc), the rules are clear: the counterexample must be removed.
in this case it's not original research, because there's a tweet by someone with a good reputation, and plenty of comments on said tweet corroborating the result. But it's a more sketchy "secondary source" than most wikipedia references and some caution on the part of the editors is not out of place.
(saying this as the person who made the original edit to the wikipedia page adding the counterexample)
> Self-published expert sources may be considered reliable when produced by an established expert on the subject matter, whose work in the relevant field has previously been published by reliable, independent publications.
I'm not complaining about Wikipedia here, just noting for the thread: it's a vector of polynomials. It has a nonsingular Jacobian. Provided with it are 3 distinct points it sends to the same point; it can't be invertible.
What Wikipedia says about this doesn't matter, does it?
I think Wikipedia has very sane processes. I'm just saying that process isn't useful to this thread. It's like if I found a SHA2 collision. I'd probably have to be an absurdly talented (and lucky) cryptanalyst to do that, but anybody on the thread could trivially confirm my finding.
It's more like WP:BASICMATH. It's like someone showing a huge number isn't prime (proverbially hard to factor, trivial to check) and HN/WP users requesting a reputable source citation for the factor multiplication when anyone can input it in a calculator.
Verifying that counterexample is a trivial calculation for basically anyone qualified to make substantive changes in that category of article, it shouldn't be an issue in and of itself.
Discovering the counter example is research, validating it is basic calculations.
It's a Princeton math PhD who posted. The verification is quite straightforward and was posted by the tweet author. Wolfram would have to also be producing incorrect outputs for the counterexample to be false. The counterexample works as claimed and conjecture has been proven wrong.
To be clear, this is not the kind of thing where a Lean formalization provides any value at all. It's like formalizing the answer to a high school algebra problem. The counterexample is obviously correct.
Indeed. I was mainly responding to the comment about waiting for "independent seasoned mathematicians to verify", whereas in this case it is easy enough to convince oneself of the counterexample's correctness.
This topic really is a testament to people's willingness to opine on things they have absolutely no clue about.
A first year undergraduate can completely check this counterexample in ten minutes. The original post even linked Wolfram alpha for the calculations.
And if you genuinely try you can very quickly understand using only high school math and a bit of Wikipedia that this counterexample is vanishingly unlikely to be wrong, even if you don't do the calculations yourself.
Well, I mean, come on. There aren't that many minors who have taken basic multivariable calculus. But there are a lot of (technical) teenagers who could confirm it!
Let this be a lesson to those who fell for such AI psychosis and to not believe everything you see on the internet as real.