Mathematics & AI

Mathematics & AI

Mathematics & AI is an open-access, peer-reviewed journal at the intersection of mathematics and artificial intelligence. The journal publishes original research in mathematical foundations of AI, machine learning theory, optimization, statistical learning, neural network analysis, computational mat...
Article #1020
Issue MathAI 2026 Selected Papers Special Issue
Received 30 Apr 2026
Accepted 15 May 2026
Published 22 May 2026

Explainable AI for Mathematics: Proofs as Code with Knowledge Graph and Domain Ontology Support

K
Khalov A.
T
Tuchkova N.
MathAI 2026 Selected Papers Special Issue
Mathematics & AI 2026, 1(2), 17
DOI: 10.66693/mathai.1020 Published: May 22, 2026 Accepted: May 15, 2026 Received: April 30, 2026
CC BY 4.0 Open access. This article is licensed under a Creative Commons Attribution 4.0 International Licence, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, provided you give appropriate credit to the authors and the source and indicate if changes were made. Copyright remains with the authors.

Abstract

We investigate whether structured knowledge retrieval from a mathematical library's dependency graph can improve neural theorem proving at inference time while maintaining explainability of the retrieved context. Through a controlled ablation study on the miniF2F-Test benchmark (197~tasks, 8~non-chain-of-thought modes, $K{=}8$ attempts per mode), we find that graph-based retrieval augmentation significantly improves proof generation on hard problems -- those where the base model's parametric knowledge is insufficient -- while having no measurable effect on problems the model already solves reliably. On 109~hard tasks, the best graph-augmented mode nearly triples the baseline success rate (pass@1: $3.56\% \to 10.42\%$, $+6.8$~percentage points, $p{=}0.001$, Wilcoxon signed-rank test). Deterministic pattern-based graph entry points outperform LLM-generated ones ($11\times$ faster, higher accuracy). The retrieved graph context is fully traceable: each hint maps to a specific edge in the Mathlib dependency graph, enabling the user to verify \emph{why} particular lemmas were suggested. The approach is training-free, composable with any base prover, and adds negligible computational overhead.

Cite this article

Khalov A.; Ataeva, O.; Tuchkova, N. Explainable AI for Mathematics: Proofs as Code with Knowledge Graph and Domain Ontology Support. Mathematics & AI 2026, 1(2), 17. https://doi.org/10.66693/mathai.1020

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