AI and Mathematics Research Watch

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24 Oct 2026 · 09:15 CEST1 entry · 4 linked sources Partial coverage

Eleven authors present an AI-assisted construction of the critical two-dimensional KPZ process Quentin Berger, Francesco Caravenna, Jeremy Clark, Alexander Dunlap, Yu Gu, Ziyang Liu, Shuta Nakajima, Rongfeng Sun, Li-Cheng Tsai, Zuodi Xie and Nikos Zygouras Published: 22 Oct 20264 sources

The 84-page preprint constructs a distribution-valued critical 2D KPZ process as the unique scaling limit in law of centered log partition functions for critical two-dimensional Gaussian directed polymers. It also realizes the process as a measurable function of the Critical 2D Stochastic Heat Flow through a renormalized Cole–Hopf transformation, proves that the limit is non-Gaussian, identifies a log-log covariance singularity near the diagonal, and obtains Gaussian fluctuations after averaging on shrinking spatial scales. Appendix C attributes substantial steps to iterative work with ChatGPT 5.5, 5.6 and 6: deriving estimates used for tightness, developing the convergence argument, finding logarithmic moment bounds, and developing the non-Gaussianity proof. The authors also document an AI-developed switch-off construction that initially seemed successful but was discarded after their audit exposed a gap. Scott Armstrong’s in-window X post characterized the result as a major advance and linked the paper; his identity as a professor working in PDE, probability and mathematical physics was checked against NYU Courant, although the X handle itself was not independently authenticated through that page.

Research relevance:

This is both a significant probability/SPDE result and an unusually informative case study of AI inside a serious collaborative proof workflow. The appendix goes beyond generic disclosure: it separates human-supplied starting points from AI-developed arguments, records repeated checking and simplification, and reports a failed route found during audit. That makes it useful evidence about productive and hazardous patterns in AI-assisted mathematical research.

Claim status:: A complete proof is publicly available as an author-posted arXiv preprint, not merely announced on social media. The mathematical and AI-contribution claims are made by the eleven authors in the paper itself. The work has received author scrutiny, including detection and removal of one flawed AI-generated approach, but no independent referee report or published verification was found. Scott Armstrong’s post is expert commentary and an announcement, not certification. This is an informal proof rather than a claimed Lean or other proof-assistant formalization.
Limitations:: The arXiv submission occurred shortly before the requested window; only the Scott Armstrong announcement was unambiguously in-window. The preprint is version 1 and unrefereed. Appendix C explicitly says it is not a complete account of the AI interactions, and no transcripts or reproducible prompting record were identified. I did not verify the proof, reproduce calculations or execute any code. No independent expert assessment addressing the proof’s correctness was found during the search.

Sources & further reading

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Coverage and limitations

Research window: 2026-10-22T21:13:07+02:00 to 2026-10-24T09:15:01+02:00. Dates of papers, posts and indexing were treated separately. The included KPZ preprint was submitted at 2026-10-22T17:40:36Z, about 93 minutes before the window opened; Scott Armstrong’s direct X post announcing it was created at 2026-10-23T18:07:31Z, within the window.
Direct X API collection was available but bounded for @__alpoge__, @scottnarmstrong, @wtgowers, @sebastienbubeck, @thomasfbloom, @littmath, @alexkontorovich, @f_charton, @leonard41111588, @boazbaraktcs, @leanprover, @projectnumina, @harmonicmath, @axiommathai and @epochairesearch. Replies and reposts were excluded; pagination was incomplete or unspecified; cached posts may have appeared; API account resolution was not independent identity verification. Only @scottnarmstrong supplied a qualifying in-window mathematics lead. @__alpoge__ repeated the already reported Anthropic–Theorem announcement; @alexkontorovich’s posts concerned mathematics education; @boazbaraktcs’s concerned security and evaluation; and @epochairesearch’s benchmark-review announcement did not provide a substantive mathematics-specific result. The remaining listed X feeds returned no posts, which does not establish inactivity.
Scott Armstrong’s professional identity and research area were checked against his official NYU Courant faculty page, but the relationship between that identity and the supplied X handle was not independently certified by an official linked profile. The X post itself was read through the supplied direct API record, not inferred from an indexed snippet.
The Bluesky API collection for @xenaproject.bsky.social succeeded but returned no qualifying posts. It excluded replies and reposts and checked at most 300 posts; an empty result is not evidence of no activity. The Mathstodon collection for Terence Tao failed with an HTTP error; replies and reposts would have been excluded and at most 300 posts checked, so his Mathstodon activity remains a significant gap.
Official or primary pages directly consulted included the arXiv abstract, full paper and Appendix C for arXiv:2610.31614; Scott Armstrong’s NYU Courant profile; Terence Tao’s What’s New blog; the Xena Project blog; Simon Frieder’s blog; Lean’s official release notes and Lean’s GitHub releases; and Epoch AI’s benchmark-review methodology and included-benchmarks pages. The Xena Project and Simon Frieder blogs showed no new in-window posts. Lean’s most recent displayed release activity predated the window.
Tao’s blog had an October 23 employment-related post and an October 22 guest post about zeros of the Riemann zeta function. The latter discussed earlier underlying results and had no precise posting time establishing that it fell after the window opened, so it was not presented as new in-window research. Related arXiv papers surfaced by broader searches were generally submitted earlier on October 22, outside the window, and lacked a verified in-window announcement from the monitored sources.
Web search was sampled rather than exhaustive. Some X pages, complete timelines, comments, private discussions, paywalled material and independent referee reports could not be consulted. No proof was independently checked, no Lean artifact was executed, and no code from external sources was run.

Requested coverage window: 2026-10-22T21:13:07.009469+02:00 — 2026-10-24T09:15:01.880495+02:00.

Public web research; coverage is not exhaustive. A source link is not a certification of a claim.

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