The paper introduces TopoAlign, a framework that repurposes code repositories to train Math LLMs by decomposing code into docstrings, main functions, and dependency functions and reassembling them into structures that mirror formal mathematical statements. Using this approach, the authors train three state‑of‑the‑art models—DeepSeek‑Math, Qwen‑3, and Herald—and evaluate them on MiniF2F, Putnam, and ProofNet benchmarks. TopoAlign yields significant performance gains, notably a 17.77% improvement on BEq@10 and a 68.82% boost on typecheck@10 for DeepSeek‑Math, while also providing modest gains for Herald.
arXiv:2606. 31134v1 Announce Type: new Abstract: While Large Language Models (LLMs) have demonstrated exceptional capabilities in mathematical reasoning, they frequently produce subtle errors that evade human detection.
arXiv:2607. 19374v1 Announce Type: new Abstract: Recent formal reasoning systems have reached IMO-level performance, yet they leave a fragmented landscape: algebra and number theory are handled in Lean, while geometry still relies on domain-specific languages with limited formal guarantees.
arXiv:2608. 14221v1 Announce Type: new Abstract: Autoformalization is commonly framed as translating natural-language mathematical statements into machine-verifiable formal languages such as Lean 4.
arXiv:2606. 15972v1 Announce Type: cross Abstract: With large language models (LLMs) increasingly applied to mathematical reasoning, formal proof assistants such as Lean can be leveraged to verify reasoning outputs with machine-checkable rigor, enabling use cases such as answer selection in test-time scaling with K sampled candidate answers.
arXiv:2508.02208v3 Announce Type: replace-cross Abstract: Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short...
arXiv:2609.35790v1 Announce Type: cross Abstract: While neural theorem provers have achieved impressive milestones in formal mathematics, they largely operate on the assumption that faithful Lean 4 f...
arXiv:2607. 18642v1 Announce Type: new Abstract: Mined code corpora are abundant but uncontrolled: a snippet's semantics, surface "messiness," and difficulty are whatever the wild contained; there is no known-optimal reference to grade against; and any public sample may already sit in a model's training set.
FormalEvolve is a neuro‑symbolic evolutionary search framework that treats autoformalization as a budgeted test‑time search problem. It builds a compilation‑feasible archive of formal statements and expands it using LLM‑driven mutation, crossover, bounded patch repair, and symbolic AST rewrites to generate diverse, semantically accepted formalizations. In experiments on CombiBench and ProofNet, FormalEvolve achieves higher SH@100 scores and improves theorem‑complete proving under fixed prover budgets compared to no‑archive baselines.
arXiv:2509. 03059v2 Announce Type: replace-cross Abstract: Recent advances in Large Language Models (LLMs) have shown that their reasoning capabilities can be significantly improved through Reinforcement Learning with Verifiable Reward (RLVR), particularly in domains like mathematics and programming, where ground-truth correctness can be automatically evaluated.
The paper introduces GAP, a methodology that automatically generates mathematically equivalent variants of existing math problems using surface renames and kernel rewrites. Applying GAP to all 1,051 William Lowell Putnam Competition problems creates PutnamGAP, a 6,306-item dataset with 5,255 unseen variants. Evaluation of 18 commercial and open-source LLMs shows accuracy drops across all models, especially under kernel rewrites, indicating a persistent weakness in transferring proof plans to new mathematical settings.
The paper introduces an epistemically and formally grounded ensemble (EFG) of large language model judges to evaluate autoformalization tasks in formal mathematics. It defines four criteria—logical preservation, mathematical consistency, formal quality, and formal validity—to provide a transparent, multi‑granular assessment. Experiments show that this ensemble outperforms coarse‑grained models, offering a scalable and interpretable proxy for evaluating formal mathematical reasoning.
arXiv:2606. 08728v1 Announce Type: new Abstract: Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers.