Comment by rvz
2 months ago
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.
It's a Jacobian determinant and three points. You can check this yourself in Sage.
The author is a Princeton math doctorate.
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)
The talk page about the conjecture clarifies WP:RSSELF:
https://en.wikipedia.org/wiki/Wikipedia:Reliable_sources#Sel...
> 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?
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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.
See https://en.wikipedia.org/wiki/Wikipedia:No_original_research...
Wikipedia's editors won't be happy until the site has joined Stack Overflow in self-owned oblivion.
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.
Maybe have a seasoned mathematician check if the counterexample is really bogus before saying people fell for ai psychosis.
I'm pretty sure you can just check this for yourself. The Sage POC is like 8 lines.
This assumes that you already have Sage installed, and you have some working knowledge in using Sage.
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Looks like this has already been formalized: https://github.com/deancureton/jacobian
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.
It's a counterexample, not a proof. A schoolchild can confirm it.
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!