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