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OpenAI and Anthropic both claimed to have disproved the 27-year-old exponential time hypothesis (ETH) using AI-generated, machine-checkable Lean proofs, threatening to render large swaths of theoretical computer science research obsolete and shaking up the research community.
This paper systematically studies LLM-based verification of Olympiad-level mathematical proofs, introducing a human-curated USAMO 2025 dataset (Trojan-Bench), an adversarial proof generation pipeline (TROJAN), and MABGrader, a Multi-Armed Bandit grading framework that outperforms ProofGrader by 26.4% in Quadratic Weighted Kappa across 20 evaluated models.
OpenAI released proofs claiming to refute the Exponential Time Hypothesis, prompting Anthropic to publish its own refutation and leading computer scientists to organize community review of the AI-generated results.
Scientific American details the inside story behind OpenAI's claimed solution to a million-dollar Millennium Problem (Navier-Stokes equations), including controversy over alleged appropriation of mathematician Tristan Buckmaster's work and the revelation that OpenAI's internal model solved it through an unexpected reasoning path.
科学家重新审视 OpenAI 于九月公布的 166 页 Navier-Stokes 问题解答，发现情况比最初想象的更为复杂——关于该证明涉嫌抄袭两位数学家成果的传言可能被夸大了。
A commentary discussing the mathematician backlash against OpenAI's released AI-generated mathematical proofs, arguing the real issue is not lack of human credit but the lack of comprehensibility — models only close proofs without conveying understanding needed to advance mathematics.
UT Austin Math Chair Francesco Maggi says OpenAI appears to be preparing to release around 400 AI-generated mathematical proofs at once, signaling that mathematical discovery may no longer be the scarce resource — human understanding is.
FaithSieve is a Lean-assisted framework for fine-grained evaluation of mathematical proofs that uses semantic alignment scoring to ensure faithful formal evidence, achieving higher accuracy than baseline methods on expert-verified datasets.
Astra, an unreleased AI system, produced machine-checkable Lean 4 proofs for 10 long-open math problems at roughly $2,000 inference cost, sparking debate about the true cost and significance of AI-discovered mathematics.
Introduces Mask-Proof, an LLM-based pipeline that converts mathematical proofs into masked-step tasks for automated evaluation, and presents MaskProofBench, a benchmark of 292 curated problems achieving 96.8% agreement with expert annotators.
This paper evaluates the robustness of proof autoformalization models in Lean 4 under global and local perturbations, finding that current LLM-based models are sensitive to perturbations and often fail to faithfully reflect local changes.
This paper introduces a strict step-level verification framework for evaluating research-level mathematical proofs using LLMs, addressing context poisoning and outperforming global evaluation. The approach shifts focus to deductive constraints and reveals that remaining errors are often due to pedantic hyper-rigor, exposing implicit ambiguities in benchmarks.
OpenAI submitted proof attempts for the First Proof challenge, a research-level math competition testing whether AI can produce correct, checkable proofs. The company's internal model successfully solved at least five of the ten problems, demonstrating significant progress in sustained reasoning and rigorous mathematical thinking.