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.
Emergent Abilities in Large Language Models: A Survey reviews how scaling LLMs leads to previously unseen capabilities such as advanced reasoning, in-context learning, coding, and problem-solving. The paper critically examines definitions, inconsistencies, and the conditions that foster these abilities, including scaling laws, task complexity, pre‑training loss, quantization, and prompting strategies. It also discusses the extension to Large Reasoning Models and highlights safety concerns like deception, manipulation, and reward hacking, calling for improved evaluation and governance.
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.
Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules. Whether such an output that appears creative is truly original and effective is hard to establis...
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.
The paper introduces the AI Mathematician (AIM) framework, which leverages Large Reasoning Models (LRMs) to tackle frontier mathematical research. AIM addresses the complexity and procedural rigor of research problems through an exploration mechanism for longer solution paths and a pessimistic reasonable verification method for reliability. Early experiments show AIM can autonomously construct significant proof components and uncover non‑trivial insights across real‑world mathematical topics.
The paper investigates how large language models (LLMs) balance capability and efficiency when using Chain-of-Thought reasoning on arithmetic and algorithmic tasks. It finds that while larger models solve more problems correctly, the improvement follows an exponential decay that slows with scale, indicating diminishing returns. Additionally, the length of reasoning output grows with problem size but does not improve with larger models, suggesting efficiency does not benefit from scaling.
arXiv:2510. 20091v3 Announce Type: replace-cross Abstract: Creativity is often seen as a hallmark of human intelligence.
arXiv:2609.37635v1 Announce Type: new Abstract: LLMs have been studied in recent linguistics as potential models of humans' linguistic abilities. Here we discuss an entirely different use of AI, name...
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.