Differential geometry·OpenAI Math·Result 340
A counterexample to the nearby Lagrangian conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under differential geometry: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and embeds the animation.
In one line: OpenAI reports a counterexample to the nearby Lagrangian conjecture (differential geometry) in a preprint dated 23 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More, is on YouTube.
Chapter 35 of 84 in Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · starts at 11:51 · watch from there on YouTube →
What OpenAI claims
Disproves the unrestricted nearby Lagrangian conjecture. For some sufficiently large even N, constructs a closed exact embedded Lagrangian in T*(S9× SN-1) that is diffeomorphic to the base but not Hamiltonian isotopic to its zero section.
Paper
A counterexample to the nearby Lagrangian conjecture
OpenAI's abstract We disprove the unrestricted nearby Lagrangian conjecture. For some sufficiently large even integer N, we construct a closed exact smoothly embedded Lagrangian in T*(S9× SN-1) that is diffeomorphic to the base but is not Hamiltonian isotopic to the zero section.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 23 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- Disproves the unrestricted nearby Lagrangian conjecture. For some sufficiently large even N, constructs a closed exact embedded Lagrangian in T*(S9× SN-1) that is diffeomorphic to the base but not Hamiltonian isotopic to its zero section.
- Where is the proof?
- In the paper, A counterexample to the nearby Lagrangian conjecture (PDF).
- Is there a video?
- Yes, on YouTube (29:20, chapter 35).
Also in
- Chapter 5 of 10 in Yau's Uniformization Conjecture, Blaschke Conjecture and 8 More · starts at 1:22 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · Compilation · 29:20 · chapter 35 from 11:51 · description, sources and chapters →
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