We advance the hypothesis that human mathematical reasoning, constrained by both the undecidability and the computational intractability of even modest logical fragments, relies fundamentally on pattern matching from domains external to pure deduction. The most prolific reservoir of such patterns is the natural world, whose physical laws and biological systems have undergone billions of years of ``pre-computation'' and already exhibit surprisingly innovative solutions.
arXiv:2606. 08532v5 Announce Type: replace Abstract: Modern artificial intelligence excels at prediction but cannot explain.
By Lei Lin, Xinlong Pan, Ronghao Wang, Chunbao Zhou, Jue Wang, Yangang Wang, Ivana Rasovska
arXiv:2607. 05168v1 Announce Type: new Abstract: Why do intelligent systems need to perform explicit symbolic reasoning?
By Jun Sun
arXiv:2607. 01571v1 Announce Type: new Abstract: Chain-of-thought (CoT) reasoning enables large language models (LLMs) to solve complex problems by generating intermediate reasoning steps.
By Aria Masoomi, Mahsa Bazzaz, Adel Javanmard, Vahab Mirrokni
arXiv:2303. 04203v4 Announce Type: replace Abstract: The theory of computation was built to answer Turing's question: what is effectively calculable by an unbounded, immortal, disembodied agent following rules?
By Xin Li
arXiv:2606. 28841v1 Announce Type: cross Abstract: Large language models are increasingly capable of mathematical reasoning, but the proofs they generate are often unreliable and hard to verify.
By Santhana Srinivasan R, Maithilee Patawar
arXiv:2606. 17289v1 Announce Type: new Abstract: AI systems based on artificial neural networks are being developed with aspirations of pushing the boundary of human mathematical knowledge.
By Phoebe Zeng, Thomas L. Griffiths, Brenden M. Lake
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.
By Syed Rifat Raiyan, Mohsinul Kabir, Hasan Mahmud, Md Kamrul Hasan
arXiv:2606. 07410v1 Announce Type: cross Abstract: The emergence of "Aha moments" in large language models, particularly DeepSeek-R1-0120, has raised the question of whether these systems genuinely reason or merely imitate the appearance of reasoning.
By Yuxiang Chen, Jun Wang
arXiv:2603. 08322v2 Announce Type: replace Abstract: We study mathematical discovery through the lens of neurosymbolic reasoning, where an AI agent powered by a large language model (LLM), coupled with symbolic computation tools, and human strategic direction, jointly produced a new result in combinatorial design theory.
By Hai Xia, Carla P. Gomes, Bart Selman, Stefan Szeider
arXiv:2606. 31134v1 Announce Type: new Abstract: While Large Language Models (LLMs) have demonstrated exceptional capabilities in mathematical reasoning, they frequently produce subtle errors that evade human detection.
By Arshia Soltani Moakhar, Iman Gholami, Max Springer, Mahdi JafariRaviz, MohammadTaghi Hajiaghayi
arXiv:2606. 14688v1 Announce Type: cross Abstract: AI systems coupled to proof assistants now generate formal mathematics at scale, and the gap between what a checker can verify and what a mathematician would value has become the binding constraint.
By Xiaoyu Li, Andi Han, Dai Shi, Zheng Gao, Jiaojiao Jiang, Junbin Gao