Thinking Machines: Mathematical Reasoning in the Age of LLMs

• URL: http://arxiv.org/abs/2508.00459v1
• Date: Fri, 01 Aug 2025 09:31:48 GMT
• Title: Thinking Machines: Mathematical Reasoning in the Age of LLMs
• Authors: Andrea Asperti, Alberto Naibo, Claudio Sacerdoti Coen,
• Abstract summary: Large Language Models (LLMs) have shown remarkable abilities in structured reasoning and symbolic tasks.<n>This article focuses on recent models and benchmarks, and explores three central issues at the intersection of machine learning and mathematical cognition.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large Language Models (LLMs) have shown remarkable abilities in structured reasoning and symbolic tasks, with coding emerging as a particular area of strength. This success has sparked growing interest in applying LLMs to mathematics, both in informal problem-solving and formal theorem proving. However, progress in formal mathematics has proven to be significantly more difficult, despite surface-level similarities between programming and proof construction. This discrepancy raises important questions about how LLMs ``reason'', how they are supervised, and whether they internally track a notion of computational or deductive state. In this article, we address the state-of-the-art of the discipline, focusing on recent models and benchmarks, and explore three central issues at the intersection of machine learning and mathematical cognition: (i) the trade-offs between formal and informal mathematics as training domains; (ii) the deeper reasons why proof generation remains more brittle than code synthesis; (iii) and the question of whether LLMs represent, or merely mimic, a notion of evolving logical state. Our goal is not to draw hard boundaries, but to identify where the current limits lie, and how they might be extended.

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