{"ID":2823854,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.00125","arxiv_id":"2601.00125","title":"Constructing a Neuro-Symbolic Mathematician from First Principles","abstract":"Large Language Models (LLMs) exhibit persistent logical failures in complex reasoning due to the lack of an internal axiomatic framework. We propose Mathesis, a neuro-symbolic architecture that encodes mathematical states as higher-order hypergraphs and uses a Symbolic Reasoning Kernel (SRK)--a differentiable logic engine that maps constraints to a continuous energy landscape. By defining a global energy function E(G), where zero energy implies logical consistency, the SRK yields gradient-based signals to train a Hypergraph Transformer Brain, turning proof search into energy minimization. Multi-step deduction is enabled via Monte Carlo Tree Search and Evolutionary Proof Search, guided by learned value functions and semantic unification.","short_abstract":"Large Language Models (LLMs) exhibit persistent logical failures in complex reasoning due to the lack of an internal axiomatic framework. We propose Mathesis, a neuro-symbolic architecture that encodes mathematical states as higher-order hypergraphs and uses a Symbolic Reasoning Kernel (SRK)--a differentiable logic eng...","url_abs":"https://arxiv.org/abs/2601.00125","url_pdf":"https://arxiv.org/pdf/2601.00125v1","authors":"[\"Keqin Xie\"]","published":"2025-12-31T22:02:02Z","proceeding":"cs.AI","tasks":"[\"cs.AI\"]","methods":"[\"Transformer\",\"Large Language Model\",\"Language Model\"]","has_code":false}