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OpenAI released hundreds of AI-generated solutions to hard math problems, but they fall short of the Advisory Group on Mathematics and Artificial Intelligence's standards, with gaps in formalization, chain-of-thought disclosure, and human understanding, as highlighted by a Cambridge and King's College paper on discrepancies between natural language proofs and Lean code.
Shopify 回归原生移动应用后，作者认为真正的转变不是性能问题，而是 AI 编码智能体让编写代码不再昂贵，从而把重心转向形式化验证等更难的工程环节。
Researchers are quickly surpassing OpenAI's recent AI-generated math results, with improved proofs formally verified in Lean, highlighting rapid progress in AI-assisted theorem proving.
OpenAI released 372 major mathematical breakthroughs, including a machine-generated proof of Subhash Khot's Unique Games Conjecture with a Lean certificate — the first results for which human mathematicians have not yet understood the proofs.
OpenAI released the openai/math repository containing 722 manuscripts in 372 research families — spanning results like integer multiplication below n log n, the irrationality exponent of π, and Mahler conjectures — produced by an unreleased internal model over ~4,000 problems, with many results formalized in Lean.
Astra and Claude helped prove that the best known packing of 11 squares is optimal, with the result fully formalized in the Lean proof assistant. This marks another milestone for AI-assisted mathematics and formal verification.
This paper introduces a theory of bidirectional type slicing, where selecting a term and querying its type information yields a minimal program slice sufficient to explain that type. The metatheory is mechanised in Agda and a linear-time approximation is implemented for the Hazel programming environment.
The paper introduces ReRoute, a framework for counterfactual 'what-if' prediction in scientific emulators that combines factual data with partial mechanistic knowledge—without needing controlled intervention data—achieving 18.2–31.8% lower climate error under CO2 distribution shifts. Its causal identification result is machine-checked in Lean, with applications to advection–diffusion systems, coupled-climate emulation, and ERA5-trained emulators.
A researcher reports spending three months running Claude Code and Codex on Erdős Problem #993 (unimodality of independent-set sequences in trees), only to learn that Tong Zhang and Wei Li posted a full proof last week, along with two Lean 4 formalizations that claim a clean build. The result is not yet peer-reviewed.
A developer shares a pessimistic prior that any software lacking formal verification or physical air-gapping will inevitably be exploited, in reply to a discussion about AI labs failing agent-containment security evaluations amid recent kernel CVEs and KVM escape vulnerabilities.
The authors introduce Choir, an open, modular protocol for distributed multi-agent autoformalization that decomposes projects into GitHub-based tasks with deterministic trust-gate verification, supporting Lean 4, Isabelle, and Rocq; it includes a preprint and an open-source repo funded by DARPA's expMath program.
The paper introduces LeanPolish, a symbolic Lean 4 pipeline releasing 33k+ verified proof edits and failed attempts, showing that verified supervision can suffer from search artifacts and that iterating the symbolic compression pass beats neural hybrids on miniF2F while modestly improving whole-proof rewriting on PutnamBench.
A tutorial-style walkthrough for software engineers that formalizes a constructive proof about regular languages in the Lean theorem prover, explaining specification, implementation, induction, and the anatomy of a formal proof step by step. The piece demonstrates how Mathlib's existing theorems make formalizing textbook automata theory accessible to developers.
A research team audits OpenAI's Lean 4 formal proof of 3D Navier-Stokes blow-up, showing that while mathematically valid, the solution physically breaks down at the atomic scale (fluid vaporizing at 0.7 nm) — a case of specification gaming. They propose adding a physics-boundary layer to neuro-symbolic AI systems and open-source their verification scripts.
Hillel Wayne explains what properties TLA+ can verify (safety invariants, action properties, liveness) and which limitations remain, tempering the hype around formal methods after Boris Cherny mentioned Claude's Opus finding race conditions with TLA+.
The team used TLA+ in their agent-swarm to achieve a 99.998% reduction in possible states and resolve 10 hard-to-find performance issues.
The irrationality of ζ(5) has been proved using an AI-assisted method, and the solution is marked as solved on FrontierMath despite not following the Apéry-style proof as initially sought.
This paper introduces a metric for the intrinsic interestingness of mathematical theorems and trains a 27B model to predict proof difficulty, enabling the generation of more interesting and novel mathematics with reduced overlap with existing libraries.
This paper introduces a framework for LLMs to discover and prove interesting mathematical theorems by optimizing for a metric based on proof difficulty, leading to more novel and useful mathematical knowledge with reduced overlap with existing libraries.
This paper introduces an approach for automatically generating generalized plans in Lean with formal proofs of completeness using LLMs, evaluated on benchmark domains showing significant advancements in automatic plan verification.