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kmaitreys a day ago

Maybe not?

https://en.wikipedia.org/w/index.php?title=Jacobian_conjectu...

Tiberium a day ago | parent | next [-]

I think the editor themselves misunderstood the conjecture.

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...

tptacek a day ago | parent | next [-]

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.

qsort a day ago | parent | next [-]

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.

jibal a day ago | parent | prev [-]

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.

kzrdude 16 hours ago | parent [-]

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.

handoflixue 8 hours ago | parent | next [-]

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.

tptacek 8 hours ago | parent [-]

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.

jibal 8 hours ago | parent | prev [-]

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.

verteu a day ago | parent | prev | next [-]

I agree, the conjecture never says anything about a proper map.

whimsicalism a day ago | parent | prev [-]

[flagged]

virgildotcodes a day ago | parent [-]

When you eat alphabet soup, do you take note of all the leftist messages bobbing in and out of existence in your bowl?

whimsicalism 18 hours ago | parent [-]

thanks for the productive reply, really contributing to HN here

tacomonstrous a day ago | parent | prev | next [-]

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.

Davidzheng a day ago | parent [-]

sure it does? two copies of the affine line? (I guess there's no galois group & no connected finite etale things tho)

tacomonstrous a day ago | parent [-]

I would call that a trivial finite etale cover :)

randompartytime a day ago | parent | prev | next [-]

[flagged]

rowbin a day ago | parent [-]

Anti-AI mentality claims another victim

slopinthebag a day ago | parent | prev | next [-]

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.

omaranto a day ago | parent | next [-]

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.)

nullc 8 hours ago | parent [-]

Irony in the message you're responding to likely suffering from slop-facts itself.

And indeed it's trivial to verify.

EagnaIonat a day ago | parent | prev [-]

[flagged]

meowface a day ago | parent [-]

I don't know why you're saying this, given this is not sycophancy and instead is an actual example of Claude Fable finding a real counterexample. I would get it if the mathematician had in fact posted something untrue or crankish, but he posted something true.

Frontier models have solved several major open problems in mathematics in the past few months, so this should not be a huge shock. "Anti-AI psychosis" will probably grow to outcompete AI psychosis by year's end.

Lerc a day ago | parent | next [-]

>"Anti-AI psychosis" will probably grow to outcompete AI psychosis by year's end.

Everyone has their own experiences making it hard to judge what attitudes are prevalent.

From what I have encountered the Anti-AI people have been more common and more outright scary.

I have heard some ideas from the Pro AI crowd and thought to myself "Yeah, that's not going to happen anytime soon", There was enthusiasm leading to overoptimism. A lot of them are going to be disappointed.

The Anti AI crowd, which I distinguish from those who want AI done responsibly, sustainably, and as safe as can be realistically be managed. There are real criticisms to be made on real issues here. The Anti AI crowd I see seem to want to scrub the world of it, they stand in the way of any responsible implementation because it would be accepting it.

Those people scare me, the vitriol and bad faith interpretation of everything as an indicator of the proof of their reality has the tone of the moral righteousness of a true believer. The outright endorsement of violent acts has me concerned that the more radical or emotionally unstable of the group will do some serious harm. It's not the bulk of a radical movement that causes atrocities, most of those involved just create an environment that normalises toxic attitudes. That environment can incubate a few individuals that act, either for phycological reasons, status, or simple the inability to empathise or consider consequences.

thin_carapace a day ago | parent | next [-]

I've seen plenty videos of locals being violently removed from town halls due to displaying of anti AI sentiment. I wouldnt consider it fair to use these examples to tar the entirety of the pro AI camp. the way objectivity and subjectivity are intertwined in your comment is spectacular, ever considered a career in propaganda?

handoflixue 8 hours ago | parent | next [-]

Accuse the enemy of propaganda; insist there's plenty of evidence without linking a single source...

Have you considered maybe reading this comment out loud in front of a mirror?

Lerc a day ago | parent | prev [-]

Do you have links to these videos?

You comment suggests you feel there is something wrong with what I said, could you elaborate?

EagnaIonat 4 hours ago | parent [-]

They are probably talking about data centres and town hall meetings where people are objecting and being removed.

Even a casual search you will find numerous videos.

The only issue I see with your comment (and this thread stems off the misreading of my post), is that despite your "I see the difference" it is still labelling one side.

In truth, there are crazy people everywhere.

Lerc 2 hours ago | parent [-]

I don't think it was a misunderstanding, the comment was not addressing the content of your post, but rather the descision to bring it up in a context where they thought it not relevant.

slopinthebag a day ago | parent | prev [-]

I initially wanted to downvote you but I can’t because you’re right.

I’d probably be called an anti-ai luddite on this site despite using it all the time for programming. I naturally gravitate to anti-ai viewpoints, but only because the breathless hype of the AI boosters is so nauseating. I have no moral qualms about AI (although I’d like nothing more than Anthropic/OAI/Google dismantled), but I really hate the idea that AI can replace artists, or humans as a whole. I think it’s anti-human to its core.

But AI is obviously useful and we could harness it for good. We shouldn’t give up on it entirely. And the people who are militantly against all usage are scarier than the boosters for sure.

jll29 20 hours ago | parent | next [-]

I understand you. As an AI research (actually, despite formally called professor of AI, I have historically always called myself more specifically NLP/IR/ML researcher rather than "AI" researcher, to avoid historic baggage).

I am intellectually curious whether "intelligence" and "consciousness" are simply layers that can be separated from the hardware they operate on or first emerged from, but I never had the urge or saw the point to practically replace human beings by machines.

Not everything that can be done should be done.

When I go to a supermarket, I always avoid self check-out. Why? First, I enjoy human interaction, even if machines may be more efficient (not yet the case). Second, I don't want the people working at the checkout to lose their jobs.

When we purchased a GPU cluster, I felt bad when I learned that the electricity bill was going to be north of 60 000 EUR every year (that number apparently assumes no jobs are running - so 100% idle time).

Lerc 2 hours ago | parent [-]

>Not everything that can be done should be done.

My concern is that people are being cavalier about the possibility of creating things that should have rights.

There will always be people who will never accept that a machine has awareness or rights. I suspect the major AI companies are doing there best to not have this talked about. As soon as it becomes a broad topic of conversation, it becomes a religious issue. The Discovery Institute is already spending money on this.

People worry about a machine that wants to kill us. For that to happen, someone has to have made a machine that wants. That is not something that should be done carelessly.

Lerc a day ago | parent | prev | next [-]

> I really hate the idea that AI can replace artists, or humans as a whole. I think it’s anti-human to its core.

AI can no more replace artists, than other artists can.

A sunset can be nice to look at yet be created without meaning. Any non-conscious process that produces images can produce beauty that has worth without intentionality. Any conscious process that produces artworks is just another artist.

Most artists would rather there be more artists in the world than fewer. If AI can't make art, it can't replace artists. If AI can make art (of the conscious intent form) then there are more artists.

slopinthebag a day ago | parent [-]

Well, I think an AI model could replace artists in a meaningful way without being conscious. So you end up with less artists.

Art is about human expression, it's not about the reflection of light off a surface. But economically I could see a world in which human expression is replaced by a facsimile and the world would be worse off for it. And that is what scares me.

Brave new world indeed.

edit: whoever downvoted the person replying to me, shame on you. they make good points and makes for good discussion.

Lerc a day ago | parent [-]

I think the fundamental problem is that art is not economical. Banksy once made a comment about the advertising industry, more or less to the effect that for all the corrupting influence of Advertising, the thing he truly hates about it is that it consumes the most creative people to do so.

People will make things they don't care about to survive. This is how we get reality television.

Irrespective of what the short term future of AI is, sooner or later there will be technical means of sustaining yourself without needing to work. If we aim for a society that values working on something because they believe in it, then we could have a better world. Right now it seems the only thing a lot of people are aiming for is to undermine whatever their adversaries want.

handoflixue 8 hours ago | parent | prev [-]

> I really hate the idea that AI can replace artists, or humans as a whole. I think it’s anti-human to its core.

I've never understood this idea that art is some special, unique domain. We already replaced humans with cameras and yet I don't see a whole lot of "cameras sacrifice our humanity" discourse.

People still enjoy tons of hobbies where humans are clearly worse than machines - they ride horses, they do sewing, there's a whole industry of hand-crafted goods. I mean, goodness, the Olympics is a celebration human triumph, and yet cars make our sprinters look pathetic.

EagnaIonat 4 hours ago | parent | prev | next [-]

I was responding to the person, not the top post.

I find it funny to be "anti-ai" when I work in the field. Pointing out dangers that need to be addressed isn't being Anti-AI.

I didn't comment on the top post because it's not my area.

senraex a day ago | parent | prev [-]

This is just a form of mass stupidity by the non-intellectually curious people who massively overrate their own intelligence.

Sorry, but if the current models haven't shown you something amazing at this point that would make this of little surprise, it because the person is an intellectual bore and completely full of shit themselves.

rvz a day ago | parent | prev [-]

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.

tptacek a day ago | parent | next [-]

It's a Jacobian determinant and three points. You can check this yourself in Sage.

The author is a Princeton math doctorate.

markasoftware a day ago | parent [-]

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)

endgame a day ago | parent | next [-]

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.

tptacek a day ago | parent | prev | next [-]

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?

bonzini a day ago | parent [-]

Wikipedia does have a rule allowing "routine calculations"

https://en.wikipedia.org/wiki/Wikipedia:No_original_research...

Of course given the magnitude of the statement a bit of care is warranted, but the rules do allow it.

tptacek a day ago | parent | next [-]

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.

redsocksfan45 13 minutes ago | parent | prev [-]

[dead]

throwaway676712 7 hours ago | parent | prev | next [-]

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.

nullc 8 hours ago | parent | prev | next [-]

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.

jibal a day ago | parent | prev | next [-]

See https://en.wikipedia.org/wiki/Wikipedia:No_original_research...

CamperBob2 a day ago | parent | prev [-]

Wikipedia's editors won't be happy until the site has joined Stack Overflow in self-owned oblivion.

urams a day ago | parent | prev | next [-]

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.

rowbin a day ago | parent | prev | next [-]

Maybe have a seasoned mathematician check if the counterexample is really bogus before saying people fell for ai psychosis.

tptacek a day ago | parent | next [-]

I'm pretty sure you can just check this for yourself. The Sage POC is like 8 lines.

aleph_minus_one a day ago | parent [-]

This assumes that you already have Sage installed, and you have some working knowledge in using Sage.

tptacek 21 hours ago | parent [-]

You also have to know how to take a Jacobian, so I can see how this might be a live controversy on HN.

Larrikin a day ago | parent | prev [-]

[flagged]

Certhas 20 hours ago | parent | prev | next [-]

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.

sciyoshi a day ago | parent | prev | next [-]

Looks like this has already been formalized: https://github.com/deancureton/jacobian

bugufu8f83 a day ago | parent [-]

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.

sciyoshi a day ago | parent [-]

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.

jibal a day ago | parent | prev [-]

It's a counterexample, not a proof. A schoolchild can confirm it.

tptacek 16 hours ago | parent [-]

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!