The Jacobian conjecture (JC) has been disproved in dimension 3 (and thus all higher dimensions), via the explicit counterexample announced in that X post.

The Jacobian conjecture (originally stated by Keller in 1939, with roots going back to Kraus in 1884) asserts the following over a field of characteristic zero be a polynomial map. If the Jacobian determinant det?(JF)det(JF)det(JF) is a nonzero constant, then (F) is invertible and its inverse is also a polynomial map (i.e., (F) is a polynomial automorphism of affine space).It is equivalent to saying that such a map is injective (or bijective). The conjecture was open for decades, with many partial positive results but also a history of flawed proofs. It remained unresolved even in low dimensions until this recent development.

This is a landmark negative result. It doesn't "break" all of algebraic geometry, but it cleanly resolves one of its famous open questions while opening new precise questions (especially in dimension 2) and illuminating connections across mathematics. The explicit, low-degree nature of the example makes it particularly valuable for further exploration.

It doesn't mean AI can now solve any open problem on demand.
It doesn't replace the need for deep mathematical understanding.
Dimension 2 of the Jacobian conjecture is still open — this counterexample didn't touch it.
Related conjectures that fell as consequences (Mathieu for SU(3), certain moments and vanishing conjectures) are now resolved negatively, but that's because of known logical connections, not because AI magically solved everything.

Overall Ranking

This JC disproof sits in the top tier of recent AI-assisted math discoveries — comparable to the OpenAI Erd?s unit distance result (the most celebrated single one) in difficulty and subfield impact, perhaps a bit behind in raw autonomy but ahead in explicitness and cascading consequences.Harder/more prestigious than: Most smaller Erd?s problems or the jamming conjecture.
Similar to: The flagship Erd?s unit distance disproof and a few other standout combinatorial/geometry results.