The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2607. 28632v1 Announce Type: new Abstract: Major mathematical conjectures still depend heavily on expert intuition, so a unified method for the systematic generation and validation of conjectures with substantial mathematical potential remains unavailable.
arXiv:2607. 17388v1 Announce Type: cross Abstract: We investigate the capacity of current language models to contribute to mathematical research.
The paper introduces OpenConjecture, a dataset of mathematical conjectures from arXiv papers since February 2026, and evaluates frontier GPT models on 200 randomly sampled conjectures. The models generate candidate solutions for about 60% of the conjectures, with counterexamples occurring roughly 1.3 times more often than proofs. The study examines solution novelty, citation practices, and fidelity to the original statements, finding that some solutions deviate from authors’ intent and that many proofs closely follow existing results, though some exhibit moderate novelty.
MathAdv is a diagnostic benchmark for formal theorem proving that covers 13 undergraduate- and graduate-level mathematics domains. It includes Lean 4 proofs and up to three auxiliary tasks—multiple-choice questions, fill-in-the-blank problems, and expert-crafted transformations—to probe knowledge, informal reasoning, and robustness to problem presentation. Evaluation of current theorem provers shows formalization is a major bottleneck, performance varies by domain, natural-language guidance can help or hinder models, and equivalent reformulations reveal significant robustness gaps.
arXiv:2606. 10799v1 Announce Type: new Abstract: Large Language Models (LLMs) struggle to rigorously verify complex mathematical proofs.
arXiv:2606. 14838v1 Announce Type: new Abstract: How to define a good explanation is a long-standing philosophical debate which has found recent renewed interest in the context of AI outputs.