Wikipedia's gonna Wikipedia. Unless there's a material debate over the Jacobian Conjecture itself, there's really no open question here. This isn't a complicated proof; it's a straightforwardly checkable certificate of a solution.
I removed the "claimed" weasel wording, and now others have followed up. The editors that don't understand math and don't realize how easily this counterexample can be confirmed have lost the debate -- not that there really ever was one.
Wikipedia has policies and it needs to use reliable sources. This rule is often skirted and a lot of facts are cited to self-published and fast moving web sources. Those who are braking the progress on the article here are doing the right thing, trying to uphold the editorial standard.
Luckily there is now a New Scientist article to link to, so, the issue should now be resolved.
The problem is, "dozens of mathematicians have independently confirmed this, and no one in the community has made any credible objections" is actually a much more reliable source than a link to an article. It's just less legible to administrators.
It's not really the job of an encyclopedia to be an up-to-the-minute reliable news source. Over the long term, the benefits of the reliable sourcing policy likely outweigh temporary issues like this.
I know what the policies are and I followed them. I also read the entire discussion on the talk page before making my change ... I doubt that you did. WP:BASICMATH says that this is not OR.
If this were OR then even the "claimed" statement would have required RS. No one was willing to remove the counterexample altogether, so my edit to remove the "claimed" weasel word was perfectly valid.
It's tedious, but you could literally even do this by hand. I'm pretty sure I've done worse coordinate bash back when I did math competitions in high school.
This is nonsensical: Properness of the map is equivalent to its being an isomorphism (quick proof: Jacobian invertible implies that the map is etale, and properness would imply that it is finite etale, but affine space doesn't admit non-trivial finite etale covers), so the lack of properness is just another way of verifying that this is indeed a counterexample.
The author has a PhD in math from Cambridge. If it turns out to be a false claim it is an interesting case study on AI's sycophancy causing even experts to drop their guard and make mistakes.
Who do you mean? The author of the tweet is Levent Alpöge, who does not have a PhD in math from Cambridge... but does have a PhD in math from Princeton. And his advisor was Fields Medalist Manjul Bhargava.
Also, there is no way this counterexample is wrong. You can very easily check it for yourself. (I did, I don't know why, obviously Levent wouldn't be wrong about this, but I guess I was in shock.)
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!
UPD: The edit got reverted and there's this on the talk page now: https://en.wikipedia.org/wiki/Talk:Jacobian_conjecture#c-DaR...
UPD2: There are edit wars happening now: https://en.wikipedia.org/w/index.php?title=Jacobian_conjectu... https://en.wikipedia.org/wiki/Talk:Jacobian_conjecture#c-Sea...