The paper introduces a new human‑AI collaboration paradigm for mathematical discovery, shifting from selecting individual problems to exploring broad research directions. It presents the Find, Attempt, and Recommend (FAR) pipeline, which automatically searches a literature corpus, filters candidate conjectures, and surfaces promising resolutions for expert review. In a combinatorics pilot, FAR processed over 5,000 papers, identified thousands of open conjectures, and ultimately highlighted 77 items that led to new discoveries.
By Zeyu Zheng, Shengtong Zhang, Jeremy Avigad, Prasad Tetali, Sean Welleck
The paper introduces the AI Mathematician (AIM) framework, which leverages Large Reasoning Models (LRMs) to tackle frontier mathematical research. AIM addresses the complexity and procedural rigor of research problems through an exploration mechanism for longer solution paths and a pessimistic reasonable verification method for reliability. Early experiments show AIM can autonomously construct significant proof components and uncover non‑trivial insights across real‑world mathematical topics.
By Yuanhang Liu, Yanxing Huang, Yanqiao Wang, Peng Li, Yang Liu
arXiv:2606. 18119v1 Announce Type: new Abstract: To assess the ability of current AI systems to correctly solve research-level mathematics problems, we tested several AI systems on a set of ten problems in a broad range of mathematical fields; these problems arose naturally in the research process of the contributors.
By Mohammed Abouzaid, Nikhil Srivastava, Rachel Ward, Lauren Williams
Automatically constructing well-specified and valuable mathematical conjectures remains a central challenge in AI-assisted mathematical discovery. Many existing open problems and conjectures are often too broad, underspecified, or difficult to connect to plausible proof or refutation strategies.
arXiv:2608. 11195v1 Announce Type: new Abstract: AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively.
By Alan Li, Rahul Saha, Anton Xue, Swarat Chaudhuri, Adam Klivans, Pravesh K Kothari, Raghu Meka
The paper argues that human cognitive constraints, often seen as limits, actually drive mathematical progress by creating bottlenecks that force the development of new abstractions. It proposes a resource‑rational theory of mathematical abstraction, showing how these bottlenecks can lead to novel formalisms with broader applications. The authors illustrate this with historical examples and suggest that incorporating similar constraints into machine learning could aid in discovering useful mathematical abstractions.