arXiv AI
Aug 19

The Problem Is the Problem: Towards Scalable Mathematical Discovery

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
arXiv AI
Oct 5

Continual Graph Memory for Mathematical Research Agents

The paper introduces Ansatz, a mathematical research agent that uses Continual Graph Memory to organize and reuse intermediate proof results across multiple problems. The system represents facts, plans, and counterexamples in a unified graph, enabling dependency-aware retrieval, evidence-sensitive curation, and scoped recall to guide long-horizon proof searches. Experiments show Ansatz solves all ten First Proof Second Batch problems, tackles the Jamison caterpillar conjecture, and makes progress on several Erdős problems without human help.

By Junyi Zhang, Jinxi Yu, Eric Hanchen Jiang, Jiachen Lu, Zhi Zhang, Xinjie He, Hyunsik Chae, Ethan Ji, Alexander K Taylor, Vigyan Sahai, Yiwen Kou, Kai-Wei Chang, Raghu Meka, Nanyun Peng, Amit Sahai, Terence Tao, Wei Wang