15 Sept 2026AI for ScienceBreakthrough
Independent mathematicians present GPT-6 Astra proof of the Erdős–Sós conjecture
Oliver Riordan and Alex Scott state that the Erdős–Sós conjecture was recently proved by GPT-6 Astra using a surprising argument and publish a simplified version, also determining extremal graphs and proving a related conjecture. David R. Wood separately publishes an exposition of the proof, likewise attributing its discovery to GPT-6 Astra. The multiple expert rewrites provide unusually strong independent validation of the AI-origin claim.
INDEPENDENTLY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.9/10evidence 97/100
14 Sept 2026AI for ScienceBreakthrough
ChatGPT 6 Astra supplies key strategies resolving 2D Le simplex conjecture
Chong Gu proves that triangles minimize the Monge–Ampère eigenvalue among bounded planar convex domains of fixed area, resolving the two-dimensional case of Le's simplex conjecture. The author states that the main results were obtained through a series of chats with ChatGPT 6 Astra and that the key strategies came from the model, after which he reworked and rewrote the article.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.3/10evidence 90/100
13 Sept 2026AI for ScienceBreakthrough
GPT-5.6 Pro-assisted proof closes Ryser (4,2) case
Patrick White proves that every 4-partite 4-uniform hypergraph with matching number two has vertex-cover number at most six, confirming Tuza's unpublished 1979 claim and closing the (r,ν)=(4,2) case of Ryser's conjecture. The author reports the proof was found through four rounds of GPT-5.6 Pro and that structural claims were checked by exact MILP and brute-force computation.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.2/10evidence 94/100
12 Sept 2026AI for ScienceBreakthrough
GPT-6 Astra-assisted proof settles Conway subprime-closure growth conjecture
Romain Popescu proves that the growth ratio of Conway's subprime closure converges to the golden ratio, settling the conjecture of Caragiu, Vicol and Zaki. The paper states that the underlying proof was constructed with algorithmic assistance from GPT-6 Astra and that its correctness was formally verified in Lean 4.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.0/10evidence 94/100
11 Sept 2026AI for ScienceBreakthrough
ChatGPT Sol 5.6 supplies core proof work settling undecidability of Medvedev logic
Rodrigo Nicolau Almeida and Søren Brinck Knudstorp prove Medvedev's logic of finite problems is undecidable, settling a longstanding open problem, and obtain related results for Skvortsov's logic. The paper states that the core idea and technical work of the undecidability proof were obtained using ChatGPT Sol 5.6 and formally verified in Lean by Claude Opus 5.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.5/10evidence 95/100
10 Sept 2026AI for ScienceBreakthrough
GPT-6 Astra-obtained proof settles core existence in approval-based committee elections
Patrick Becker, Matthias Greger and Dominik Peters prove that every approval-based multiwinner election admits a core-stable committee and that a Hare-core committee can be found in polynomial time, settling a central open question in the field. The arXiv record explicitly states that the proof was obtained with GPT-6 Astra. The paper also points to a Lean formalization of the core-existence theorem. This provides strong artifact-level support, but the result remains a new author-controlled preprint without independent external expert reproduction.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.5/10evidence 94/100
10 Sept 2026AI for ScienceBreakthrough
GPT-6 Astra obtains counterexample disproving the wrapping number conjecture
Qiuyu Ren exhibits an annular knot with wrapping number four whose Kauffman bracket has annular degree at most two, disproving the wrapping number conjecture. The arXiv comments explicitly state that the main result was obtained by GPT-6 Astra. The theorem and provenance are primary-source confirmed, but the four-page preprint has not yet received independent expert verification or reproduction.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.3/10evidence 87/100
10 Sept 2026AI for ScienceBreakthrough
ChatGPT Pro 6.0-assisted paper settles a conjecture on II1 factors of Fuchsian groups
Dimitri Shlyakhtenko proves that the von Neumann algebra of the fundamental group of any closed orientable surface of genus at least two is a free group factor, and extends the conclusion to arbitrary finitely generated torsion-free non-elementary discrete subgroups of PSL2(R), settling a conjecture of de la Harpe and Voiculescu. The arXiv abstract explicitly states that the result was obtained using OpenAI's ChatGPT Pro 6.0. The mathematical claim and AI-role attribution are primary-source confirmed, but the proof is a new preprint without independent expert reproduction or peer review.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.3/10evidence 88/100
09 Sept 2026AI for ScienceBreakthrough
LLM-assisted example resolves zero-private-capacity superactivation problem
Chengkai Zhu and Xin Wang resolve a longstanding quantum-information question by constructing two channels that each have zero private capacity but jointly achieve positive private communication. The paper states that the initial activation example was identified through interactions with large language models and that the result has been formalized in Lean 4. The theorem has strong author-provided formal-verification support but has not yet been independently externally reproduced.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.5/10evidence 94/100
09 Sept 2026AI for ScienceBreakthrough
Multi-model AI setup finds counterexample to the Pierce-Birkhoff conjecture
Zehua Lai, Lek-Heng Lim and Junyu Ren provide a counterexample to the Pierce-Birkhoff conjecture using a continuous piecewise-quadratic semialgebraic function that cannot be expressed as a finite lattice combination of polynomials. The arXiv abstract explicitly states that the counterexample was found with a multi-agent, multi-model setup chaining GPT 5.6, GPT 6, Claude Opus 5 and Claude Fable 5.1. The result is primary-source confirmed but not independently reproduced or peer reviewed.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.7/10evidence 88/100
08 Sept 2026AI for ScienceBreakthrough
ChatGPT Astra finds initial proof resolving approval-voting complexity question
Chris Dong proves that computing a committee satisfying both justified representation and Pareto optimality is NP-hard on the unrestricted approval-profile domain, answering a stated open question negatively. The paper says an initial proof was found by ChatGPT Astra and was then verified and rewritten by the author. The result and AI provenance are primary-source confirmed; independent external proof verification is absent.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.1/10evidence 89/100
08 Sept 2026AI for ScienceBreakthrough
OpenAI multi-agent AI system produces Navier–Stokes Millennium solution
OpenAI reports that an internal model significantly more capable than GPT-6 Astra, deployed through roughly 10,000 concurrent research agents, produced an analytical proof that smooth three-dimensional Navier–Stokes dynamics can develop a finite-time singularity under the official Millennium-problem formulation. OpenAI released a proof write-up and Lean formalization. The Clay Mathematics Institute later said the problem has 'apparently been settled', while formal prize evaluation and broader community vetting remain ongoing.
INDEPENDENTLY CONFIRMEDOPENAI — ON THE NAVIER–STOKES MILLENNIUM PRIZE PROBLEMPrimary source ↗ Relevance10.0/10evidence 98/100
07 Sept 2026AI for ScienceBreakthrough
ChatGPT 5.6 Sol generates main proof content for sharp curvature-sign rigidity results
Minbo Gao, Yuhang Liu and Genyuan Zhang establish curvature-sign rigidity and sharp pointwise pinching thresholds for sectional and Ricci curvature, including the sharp Ricci threshold 1/(n-1) and matching subcritical examples. The abstract says the main content of the proof was generated by ChatGPT 5.6 Sol and verified by the authors. The results are primary-source confirmed but not independently externally reproduced or peer reviewed.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.0/10evidence 88/100
07 Sept 2026AI for ScienceBreakthrough
GPT-6 Astra generates most arguments in result on AMP and low-degree polynomial equivalence
Zhangsong Li proves an almost-sharp equivalence between approximate message passing and growing-degree polynomial estimation for the Bernoulli rank-one planted-submatrix setting, resolving the Bernoulli rank-one case of a growing-degree AMP-equivalence question. The arXiv abstract explicitly states that most arguments in the paper were generated using GPT-6 Astra. The theorem and AI-role attribution are primary-source confirmed; the paper is new and has no independent external proof verification in the canonical record.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.2/10evidence 88/100
06 Sept 2026AI for ScienceBreakthrough
ChatGPT 5.6 Pro-obtained proofs improve hypergraph vertex-cover hardness bounds
Karthik C. S. and Dor Minzer present new multilayered PCP constructions yielding improved NP-hardness bounds for minimum vertex cover in uniform hypergraphs, including a tight k-epsilon hardness factor for k at least four without relying on the Unique Games Conjecture. The arXiv abstract states that the proofs were obtained using ChatGPT 5.6 Pro and subsequently rewritten by the authors. The results are primary-source confirmed but not independently reproduced or peer reviewed.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.1/10evidence 88/100
06 Sept 2026AI for ScienceBreakthrough
ChatGPT 5.6 Pro-suggested strategy helps settle critical Schouten-flow existence problem
Giovanni Catino and Carlo Mantegazza prove short-time existence and uniqueness for the critical Ricci-Bourguignon, or Schouten, flow, resolving the case left open by previous theory. The authors state that the strategy leading to the main argument was suggested during interactions with ChatGPT 5.6 Pro, after which they checked and developed the mathematics and take responsibility for the manuscript. The result is primary-source confirmed but not independently externally reproduced or peer reviewed.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.1/10evidence 89/100
04 Sept 2026AI for ScienceBreakthrough
Claude produces a complete machine-checked Lean formalization of Fermat's Last Theorem
Anthropic reports that a Claude Code-based multi-agent system produced the first complete computer-checked formalization of Fermat's Last Theorem in 11 days. The public artifact contains about 13 million lines of Lean and 29,511 theorem pages; its final theorem was checked by Lean, comparator and a second independently implemented Lean kernel. The result formalizes an existing theorem rather than discovering new mathematics, and the end-to-end run has not yet been independently reproduced by an external team.
PRIMARY CONFIRMEDANTHROPIC — FORMALIZING FERMAT'S LAST THEOREMPrimary source ↗ Relevance9.6/10evidence 96/100
02 Sept 2026AI for ScienceBreakthrough
ChatGPT Sol 5.6 materially contributes to Cartan-convexity and butterfly-realization results
J. E. Pascoe develops Cartan convexity for self-adjoint free functions, proves extension results using universal direct sums and noncommutative Kraus-butterfly arguments, and establishes analogous results for graph embeddings. The arXiv comments state that the article was generated with ChatGPT Sol 5.6 and that the author reviewed the results and references. The mathematics and AI provenance are primary-source confirmed, while independent specialist reproduction is not established.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.0/10evidence 86/100
31 Aug 2026AI for ScienceBreakthrough
ChatGPT 5.6 helps find counterexample to the stable forking conjecture
James Freitag and Scott Mutchnik report a counterexample to the stable forking conjecture, a long-standing problem in model theory discussed since 1996. The authors state in the abstract that they found the counterexample using ChatGPT 5.6. The result is currently an arXiv preprint: the theorem and AI role are primary-source confirmed, but no peer review or independent mathematical reproduction was identified in this pass.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.1/10evidence 84/100
27 Aug 2026AI for Science
Google extends Co-Scientist into closed-loop real-world scientific research
A Google-led preprint extends Gemini-based Co-Scientist from hypothesis generation into execution-grounded workflows spanning experiment planning, laboratory interaction, real-data validation and manuscript generation across materials science, biology and computer science.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.1/10evidence 80/100
23 Aug 2026AI for ScienceBreakthrough
Alpoge and Claude claim a complex structure on S^6
Levent Alpoge publicly claims a construction of a complex structure on the six-sphere, a classical long-standing open problem, and attributes substantial work to Claude/Opus 5. The claim is not yet independently verified and S^6 has a history of failed claimed solutions.
PRELIMINARYFIRST-PARTY SOCIALPrimary source ↗ Relevance9.2/10evidence 62/100
19 Aug 2026AI for ScienceBreakthrough
AI-led work claims disproof of the Yau–Tian–Donaldson conjecture
Jihao Liu presents a smooth polarized projective fivefold that is K-polystable but admits no constant-scalar-curvature Kähler metric, thereby disproving the original cscK Yau–Tian–Donaldson conjecture. The paper documents that GPT-5.6 Sol, Fable 5 and Danus produced the counterexample and proof; an improved Danus run starting only from the original problem reportedly reproduced a complete solution in 5h29m without the key human intervention used in the first run.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.5/10evidence 82/100
13 Aug 2026AI for ScienceBreakthrough
ChatGPT 5.6 Sol-assisted construction resolves elliptic regularity question negatively
Nam Q. Le, Qi Sun and Hung V. Tran construct uniformly elliptic nondivergence-form equations in dimension three whose bounded solutions have unbounded W1,1 variation, showing that no interior W1,p estimate depending only on ellipticity exists for p at least one and resolving negatively an open question raised by Nadirashvili, Tkachev and Vlăduţ. The authors state that the main results were obtained through chats with ChatGPT 5.6 Sol and that key strategies came from ChatGPT; they then reworked, rewrote and checked all arguments. The result remains without independent external proof reproduction.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.3/10evidence 89/100
11 Aug 2026AI for ScienceBreakthrough
Claude-assisted Riemann-related result improves a critical-line bound to 67.2%
A Claude-assisted research workflow reportedly improved the proportion of non-trivial simple zeros shown to lie on the critical line from about 41.6% to 67.2%. This was a substantial partial result, not a proof of the Riemann Hypothesis. The work used roughly 31M output tokens, about 60 sub-agents, around 650 discarded strategies, thousands of computational checks and Lean formalization.
PRIMARY CONFIRMEDANTHROPIC RESEARCH / VIBEMATHED
Relevance9.0/10
03 Aug 2026AI for ScienceBreakthrough
GPT-5.6 Sol-assisted construction gives counterexample to Connes' rigidity conjecture
Shuoxing Zhou constructs non-isomorphic ICC property-(T) groups with isomorphic group von Neumann algebras, giving a counterexample to Connes' rigidity conjecture for this class. The paper explicitly says the result was obtained with GPT-5.6 Sol assistance, independently of and concurrently with OpenAI work. The theorem and provenance are primary-source confirmed; independent specialist verification remains pending.
PRIMARY CONFIRMEDPREPRINTPrimary source ↗ Relevance9.4/10evidence 91/100