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
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:2610.32575v1 Announce Type: new
Abstract: Large language models and agents have shown significant power in advanced physical research. In this paper, We introduce PHYRD, a living benchmark for...
By Qituan Zhang, Guo Chen, Linfeng Zhang, Wenlong Zhang
arXiv:2610.33690v1 Announce Type: new
Abstract: Many mathematical research agents focus on solving problems with fixed statements. However, conjecture research, especially in applied mathematics, may...
By Shu Miao, Feiming Wang, Wentao Long, Chenyi Li, Kun Yuan, Zaiwen Wen
arXiv:2604. 19341v2 Announce Type: replace-cross Abstract: Scientific discovery often requires many cycles of proposing, testing, and refining candidate solutions.
By Haotian Ye, Haowei Lin, Jingyi Tang, Yizhen Luo, Rahul Thapa, Caiyin Yang, Chang Su, Rui Yang, Ruihua Liu, Rundao Li, Zeyu Li, Pengwei Sun, Chong Gao, Dachao Ding, Guangrong He, Miaolei Zhang, Lina Sun, Wenyang Wang, Yuchen Zhong, Zhuohao Shen, Puheng Li, Pan Lu, Bianxiao Cui, Di He, Jianzhu Ma, Junfeng Li, Hexi Baoyin, Yejin Choi, Stefano Ermon, Xiaowen Chu, Tongyang Li, Yuzhi Xu, James Zou
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.
By Alizer Wong, Zixin Zeng, Yi Tan, Wenyuan Li, Xuhang Chen, Xingru Lai, Yang Shi, Liangsi Lu, Yanhui Chen