“The proof presented in this paper is due to Claude Opus 5.5”
Alexis Drouot publishes Claude’s 40-minute elementary proof of his conjecture on geometric bulk conductances
Result confirmed
The takeaway
A mathematical physicist posted a paper whose proof he credits almost entirely to Claude Opus 5.5, which produced a 5-page solution in 40 minutes, and wrote that ‘LLMs can solve Ph.D.-suited projects in just a few prompts’.
Status
- Claim
Result confirmed
- Our reporting
- High confidence
- Verification
- Preprint only
- Importance
- 3 of 5
- Last verified
- 14 October 2026
Your AI and this story
- GPT-6 Astra165 days after its cutoff
- Claude Opus 5.5104 days after its cutoff
- Gemini 4 Argon195 days after its cutoff
- Grok 4.7134 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 104 days before it.
Key facts
- Paper: ‘Geometric bulk conductances in even dimensions’, Alexis Drouot (University of Washington; CPT Aix-Marseille), arXiv 2610.16208 [math-ph], 15 pages, 12 Oct 2026
- Result: for a short-range projector P on ℓ²(ℤ^{2n}, ℂ^m) and a transverse family U of open sets, Tr(P[P,1_{U1}] ∧ … ∧ [P,1_{U2n}]) is a topological integer X_U times the bulk conductance of P; the proof deforms a cochain (an idea due to Kitaev) instead of the sets
- Priority: an elementary proof of a recent result of Martinian–Stoiber, which Drouot learned of only ‘at terminal stages’; Claude found the reference when asked for a literature search, and Drouot believes Claude ‘did not base its response on it’
- AI role: ‘Early October 2026, I asked this question to Claude Opus 5.5 … Claude proposed a 5-page solution within 40 minutes. Even in dimension two, Claude’s proof is much simpler and more elegant than the one presented in [DZ26]. The present paper is Claude’s solution, together with a few of my own edits.’
- Human role (listed by the author): identify the question and formulate the conjecture; ask Claude with the relevant material; simplify Claude’s proof; expand technical details; organize and interpret; track down ownership of ideas
- Reflection: ‘While it is disturbing to see an LLM solve what could have been a full thesis in under an hour, I believe I learnt a lot from this project … I prefer to stay out of controversies and prepare for a brutal transformation of mathematics … How should we teach the next generation of researchers, now that LLMs can solve Ph.D.-suited projects in just a few prompts?’
What happened
On 12 Oct 2026 Alexis Drouot posted arXiv 2610.162081. In 2024 he and Xiaowen Zhu proved a bulk-edge result for 2D topological insulators along curved boundaries and he conjectured the even-dimensional analogue. In early October 2026 he gave Claude Opus 5.5 the 2D paper, a project description and the obstruction he saw in higher dimensions; “Claude proposed a 5-page solution within 40 minutes”, simpler than the original even in 2D. The paper is “Claude’s solution, together with a few of my own edits”, and the comments field says “The proof presented in this paper is due to Claude Opus 5.5”.
The statement itself had been proved shortly before by Martinian and Stoiber, which Drouot learned only near the end (through a literature search by Claude). The new contribution is the elementary proof.
Section 1.4 is a personal reflection: Drouot finds it “disturbing to see an LLM solve what could have been a full thesis in under an hour”, says he will “prepare for a brutal transformation of mathematics”, and asks how to train researchers “now that LLMs can solve Ph.D.-suited projects in just a few prompts”.
No reactions were found on 14 Oct (web search; X not searched directly).
Why it matters
This is a frank first-person record of an AI proof on a research-level question, with a clear credit line to the model and a list of what the human did. Drouot’s description of the work as thesis-sized is a data point for the debate on graduate training that Tao and others have opened.
Sources
1 source from 1 site. Numbers match the chips in the text.
1 source: 1 primary
Primary
- arXiv 2610.16208: Geometric bulk conductances in even dimensionsarxiv.org, paper
Changes
- Filed from the arXiv paper