arXiv AI
What the Machine Invented: Mining New Mathematical Instruments from OpenAI's October 2026 Release of AI-Generated Mathematics
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arXiv AI
6d ago
Beyond Selected Breakthroughs: Evaluating Language Models on Randomly Sampled Mathematical Conjectures
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.
arXiv AI
Sep 11
A Human Audit of OpenAIs AI-Generated Mathematical Proofs
The article audits 18 chapter‑specific reviews of ten mathematical results announced by OpenAI, examining review standards, Lean formalizations, subsequent research, and references. No confirmed substantive errors remain in the principal results, though review depth varies and some dependencies are only partially checked. Chapter 8 raises the strongest reservation, requiring major revision of compressed analytic arguments, while Chapter 6’s polarity error was corrected after a PDF extraction issue.
arXiv AI
Oct 9
An Investigation of Robustness of LLMs in Mathematical Reasoning: Benchmarking with Mathematically-Equivalent Transformation of Advanced Mathematical Problems
The paper introduces GAP, a methodology that automatically generates mathematically equivalent variants of existing math problems using surface renames and kernel rewrites. Applying GAP to all 1,051 William Lowell Putnam Competition problems creates PutnamGAP, a 6,306-item dataset with 5,255 unseen variants. Evaluation of 18 commercial and open-source LLMs shows accuracy drops across all models, especially under kernel rewrites, indicating a persistent weakness in transferring proof plans to new mathematical settings.
arXiv AI
Jun 9
Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discovery
arXiv:2606. 08728v1 Announce Type: new Abstract: Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers.
arXiv Machine Learning
Sep 3
Towards Solving the Gilbert-Pollak Conjecture via Large Language Models
The paper announces a new lower bound of 0.8559 for the Steiner ratio, improving on the previous 0.824 bound for the Gilbert‑Pollak Conjecture. It introduces an AI system that uses large language models to generate rule‑constrained geometric lemmas, which are then turned into executable verification functions that certify the bound. The approach relies on only thousands of LLM calls, highlighting the feasibility of LLM‑based methods for advanced mathematical research.
arXiv AI
Sep 25
Learning to Discover Interesting Mathematics
The paper introduces a method for evaluating the intrinsic interestingness of mathematical theorems by comparing the length of their proofs to the length of their statements. It trains a 27B language model to predict proof difficulty, enabling the generation and selection of more interesting theorems while significantly reducing overlap with existing Mathlib. The approach allows iterative expansion of a self‑building, machine‑verified mathematical library guided by quantifiable metrics.