arXiv:2608. 16118v1 Announce Type: new Abstract: How should we assess whether large language models can perform mathematical invention?
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.
arXiv:2608. 15979v1 Announce Type: new Abstract: Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules.
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.
arXiv:2605. 10574v3 Announce Type: replace Abstract: As artificial intelligence advances, models are not improving uniformly.
arXiv:2607. 05013v1 Announce Type: cross Abstract: Although LLMs have made significant progress in mathematical reasoning, determining whether a mathematical problem is solvable remains a fundamental yet challenging capability.
arXiv:2510. 20091v3 Announce Type: replace-cross Abstract: Creativity is often seen as a hallmark of human intelligence.
Although LLMs have made significant progress in mathematical reasoning, determining whether a mathematical problem is solvable remains a fundamental yet challenging capability. While recent studies have probed internal representations of model solvability beliefs, verbalization has primarily been studied behaviorally rather than as an internal representation, limiting its analysis and manipulation.
arXiv:2606. 04273v2 Announce Type: replace Abstract: For centuries, human mathematicians have written proofs to substantiate their mathematical arguments; yet, the ability to automatically verify the validity of proofs has long been a challenge.
arXiv:2606. 08532v5 Announce Type: replace Abstract: Modern artificial intelligence excels at prediction but cannot explain.
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:2607. 04505v1 Announce Type: new Abstract: 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.
arXiv:2606. 11762v1 Announce Type: cross Abstract: Large language models (LLMs) have achieved remarkable progress in language understanding, reasoning, and generation, sparking growing interest in their creative potential.