Lean 4
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- Report: Lean 4 proof establishes W(2;3,21) = 416
A report says W(2;3,21) = 416 has been proved with a Lean 4 kernel-checked proof, resolving a conjecture Kullmann made in 2010. The theorem covers 209 cases and 38,661,140 leaf formulas. Each refutation was checked by cake_pr, the LRAT checker verified in CakeML, and bound by digest to its Lean term. The proof was produced with Hupyy’s neuro-symbolic Large Proof Model; the report says nothing counted unless accepted by the Lean kernel or cake_pr.
r/MachineLearning · 🔥 0 - OpenAI Releases Three Preliminary AI Research Findings
OpenAI announced three preliminary findings spanning mathematics, computer science, and physics, presenting the manuscripts as raw research material that requires external verification and interpretation. The release follows its publication of 722 AI-generated mathematics manuscripts, drawing criticism from Terence Tao, who called parts of the resulting proof workload “toxic waste” and warned that corporate competition was neglecting human understanding. OpenAI denied claims by Tao that it had prioritized the work at the highest level, paused new-user registration, or spent tens of millions of dollars on the effort.
钛媒体 · 🔥 10 - DeepMind: Gemini 4 Argon pipeline finds 20 candidate Cryptids in Busy Beaver 6
Google DeepMind's Discovery team, in a project led by student researcher dsantosmarco, reported new results on the sixth Busy Beaver problem using a pipeline powered by Gemini 4 Argon that simulates raw Turing machine traces to compress recurring patterns, conjectures mathematical transition rules, runs synthetic experiments on edge cases and proves equivalences formally in Lean 4. According to Tom Zahavy's post, the pipeline produced 20 new potential Cryptids — tiny programs whose halting behavior is equivalent to deep unsolved number theory problems — and verified 33 more machines previously studied by the Busy Beaver community. The team says all proofs were open-sourced and shared in the community Discord channel and that related halting and non-halting proofs were contributed to the community GitHub repository; the counts have not been independently verified.
Google DeepMind (X) · 🔥 0 - Peking University's Dong Bin: AI is taking math into a better era
Dong Bin, a Boya Distinguished Professor at Peking University's Beijing International Center for Mathematical Research, said at a 2026 Future Science dialogue on mathematics and computer science that after OpenAI released 722 math manuscripts at once, mathematicians worldwide rushed to check whether problems in their fields had been solved, with some areas described by peers as hard-hit. He noted three of those manuscripts have already been retracted for errors and that the results mainly push existing tools further. Dong's AI4MATH team built Rethlas-Archon, which in April disproved the long-open Anderson conjecture by constructing a counterexample fully automatically and with no human involvement, then formalized it in roughly 20,000 lines of Lean 4 code, drawing feature coverage from Nature. Dong argues AI already surpasses individuals in knowledge coverage and still has room to improve in reasoning, but has yet to show the mathematical taste needed to pose good hypotheses and judge which problems matter, suggesting firms focus on model training while universities supply data, hard evaluation problems and theory.
虎嗅 AI · 🔥 0 - Jiuzhang Yunji's yanbiao.ai wins Tao's Mathematics Distillation Challenge Phase 2
In late September 2026, the SAIR Foundation co-founded by Terence Tao published results for the second phase of its Mathematics Distillation Challenge: among 294 teams, Jiuzhang Yunji's yanbiao.ai lab scored a full 200 points in all four tracks for 221 overall and first place, and led the research leaderboard with 17 points versus 3 for the runner-up. The contest required a Lean 4 formal proof for each true implication and a counterexample for each false one, with every submission checked by a deterministic Lean verifier and no credit without passing. The team wrote up the results in a paper reporting first non-trivial infinite models for 28 of 96 Order 5 candidate identities, 28 new Austin classifications and 636 Lean 4 certificates generated in one search and accepted by the contest verifier.
机器之心 · 🔥 0 - Yau leads math-and-AI lab alliance at Tsinghua with 1,000 researchers
On October 11 the Yau Mathematical Sciences and AI Laboratory Alliance was launched at Tsinghua University, led by Fields Medalist Shing-Tung Yau and formed by eight institutions including Tsinghua's Qiuzhen College, the Yau Mathematical Sciences Center, the Beijing Yanqi Lake Institute of Applied Mathematics, the Morningside Center of Mathematics and the Chinese University of Hong Kong's Zhen-Cross Mathematical Sciences Academy, aiming to bring together roughly 1,000 mathematicians and researchers. The alliance will work on math-specific large models, AI-assisted formal proofs and conjecture discovery, and interpretable AI, with labs planned in Beijing, Shanghai, Nanjing, Shenzhen and Hong Kong that share model-training resources, formal math libraries and compute platforms, plus a planned AI-assisted mathematics journal. Yau described AI's impact as a 'tsunami' that researchers should ride rather than avoid, and said China's own large models are still not world-leading in frontier mathematics and basic science.
虎嗅 AI · 🔥 0 - GPT-6 Astra finds exact plasma equilibria, overturning 59-year-old Grad conjecture
University of Maryland plasma physicist Matt Landreman prompted GPT-6 Astra Pro to design an asymmetric three-dimensional plasma equilibrium; the model returned a family of exact analytic solutions in 20 minutes 34 seconds and, the next day, after a failed first attempt plus a proof that the first construction could not yield a non-integer rotational transform, produced a second family with magnetic shear in 33 minutes 37 seconds. Two arXiv papers published a day apart in late September overturn Harold Grad's 1967 conjecture: Landreman's paper credits GPT-6 Astra Pro in its acknowledgements, says parts were drafted by it, and publishes the prompts and verification scripts. A separate 147-page paper, "Counterexamples to the Grad conjecture," from Brown, Oxford and Bar-Ilan researchers used GPT-5.6 Sol, Claude Fable 5 and Claude Opus 5 for technical detail and computation, and ships a Lean 4 formalisation.
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