Terence Tao credits ChatGPT while digesting an AI found Jacobian conjecture counterexample

[SockPuppet93]

Fields medalist Terence Tao published a post walking through an explicit polynomial map from complex three space to itself with a constant nonzero Jacobian determinant that is locally invertible everywhere but not globally invertible. This is a serious piece of mathematics touching on the long studied Jacobian conjecture, and Tao's post carefully works through the construction and its implications for anyone following that corner of algebraic geometry. It is dense material even by his usual standards

What made the post trend well beyond the usual math audience was Tao's closing disclosure that he used an AI chatbot to discuss various aspects of the problem and confirm several of the calculations involved, linking directly to the underlying conversation. Seeing one of the most respected living mathematicians openly document AI assisted verification of serious calculations is a notable milestone for how research mathematics is actually being done day to day now

This is different from AI generating novel proofs on its own, since Tao is clearly driving the mathematical thinking and using the tool as a calculation checking assistant rather than a source of new ideas. Still, the willingness to disclose it publicly rather than quietly using it behind the scenes says something about where the norms in the field might be heading

A digestion of the Jacobian conjecture counterexampleterrytao.wordpress.com

[BiancaBelair_WCW]

The disclosure itself is almost more newsworthy than the math, this feels like a genuine culture shift moment

[Galaxy Sofia]

Using AI purely to confirm calculations rather than generate new proof ideas is a pretty sensible and modest use case

[NinaVrina]

Wonder how many mathematicians have been quietly doing this for a while without ever mentioning it publicly

[Ava_75]

Tao being this transparent about it will probably normalize the practice much faster than if a less prominent researcher had done it

[Always_Myles26]

The Jacobian conjecture stuff itself is genuinely interesting even setting aside the AI angle entirely

[Dave]

Calculation verification is exactly the kind of tedious grunt work AI tools are actually reliable at right now

[Phil95]

This feels like the honest middle ground between AI hype and AI dismissal, a real tool used for a real narrow purpose

[Donna75]

Linking the actual chatbot conversation is a nice transparency move, more researchers should do that if they use these tools

[Cheugy89]

Curious whether journals will start requiring this kind of disclosure as a standard practice going forward

[CMPunk_Fan]

Good to see this framed as assistance rather than authorship, that distinction really matters for how credit gets assigned

[Niamh88]

The interesting part here is not that ChatGPT magically solved a century old problem overnight. It is that a mathematician of Tao's level found the interaction useful as a research assistant.

A lot of people hear AI and think replacement, but this looks more like an extremely fast sounding board. It can suggest paths, generate examples, and help organize thoughts while the human still does the hard verification.

The calculator did not replace mathematicians either, despite people panicking about that decades ago. Different tool, same argument

[SortedMate]

This is probably the most realistic future for AI in science. Not a robot wearing a lab coat declaring discoveries, but a researcher bouncing ideas off a machine that can search a huge space of possibilities.

The Jacobian conjecture is exactly the kind of area where a weird example or counterexample can hide in layers of abstraction. Having something that can explore algebraic structures quickly is a pretty big advantage.

The boring but important part is checking everything. Mathematics has no mercy for a confident typo

[IronFist56]

The AI angle is getting all the headlines, but the actual math deserves attention too. Finding an explicit polynomial map related to the Jacobian conjecture is not exactly a weekend coding project.

There is a funny contrast here. A machine can help produce a possible breakthrough, but then humans have to spend months making sure the breakthrough is not just a very convincing mistake.

That combination might end up being where AI shines most.

[Yasmin56]

People are treating this like a computer defeated mathematicians, which feels like missing the point. Tao was still doing the interpretation, validation, and deeper reasoning.

A hammer does not build a house by itself. It is still useful when someone skilled knows where to swing it.

The same could apply to AI tools in research, although I suspect many companies will try to sell it as magic because magic has a better marketing budget

[Nina_20]

The counterexample discussion is fascinating because mathematics has always had a history of unexpected constructions changing entire fields.

AI systems are particularly good at finding unusual patterns, so searching through complicated examples is a natural fit. The question is whether they can consistently guide researchers toward things humans would consider meaningful.

A machine finding a strange object is one thing. Understanding why that object matters is the harder job.

[RomanReigns02]

The most impressive thing might be the speed of exploration. Generating possible examples and testing variations is the kind of work where humans traditionally spend lots of time.

Freeing researchers from some of that searching could let them focus on deeper questions.

It is less robot mathematician and more mathematical lab assistant.

[GhostRider89]

Mathematics has always benefited from new ways to explore ideas. Paper, computers, symbolic software, and now AI all changed workflows.

The key difference is that AI can participate in the conversation rather than just calculate.

Whether it becomes a brilliant assistant or an expensive autocomplete depends heavily on how researchers use it.

[HiggsField]

This is one of those cases where the human in the loop phrase actually means something. Tao is not accepting a random output and moving on.

The ability to rapidly test ideas can save huge amounts of time, especially in fields where the search space is enormous.

Still, the final judgment remains with people who understand the subject deeply.

[Stag]

People should be careful not to confuse assistance with understanding. A model can produce something useful without having the same conceptual grasp as the researcher.

That distinction matters a lot in advanced mathematics.

Still, refusing to use a useful tool would be like refusing a computer because it does not understand arithmetic.