# MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize

arXiv: https://arxiv.org/abs/2608.25449 · HTML: https://mlsanity.com/paper/2608.25449/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 44 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 23 of 23)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Learning the Difference that Makes a Difference with Counterfactually-Augmented Data](https://mlsanity.com/paper/1909.12434/) (2019)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction](https://mlsanity.com/paper/2508.03613/) (2025)
- [Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving](https://mlsanity.com/paper/2502.07640/) (2025)
- [Lean-STaR: Learning to Interleave Thinking and Proving](https://mlsanity.com/paper/2407.10040/) (2024)
- [TheoremLlama: Transforming General-Purpose LLMs into Lean4 Experts](https://mlsanity.com/paper/2407.03203/) (2024)
- [Herald: A Natural Language Annotated Lean 4 Dataset](https://mlsanity.com/paper/2410.10878/) (2024)
- [FIMO: A Challenge Formal Dataset for Automated Theorem Proving](https://mlsanity.com/paper/2309.04295/) (2023)
- [Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics](https://mlsanity.com/paper/2601.14027/) (2026)
- [FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models](https://mlsanity.com/paper/2505.02735/) (2025)
- [MA-LoT: Model-Collaboration Lean-based Long Chain-of-Thought Reasoning enhances Formal Theorem Proving](https://mlsanity.com/paper/2503.03205/) (2025)
- [REAL-Prover: Retrieval Augmented Lean Prover for Mathematical Reasoning](https://mlsanity.com/paper/2505.20613/) (2025)
- [AI scientists produce results without reasoning scientifically](https://mlsanity.com/paper/2604.18805/) (2026)
- [IndiMathBench: Autoformalizing Mathematical Reasoning Problems with a Human Touch](https://mlsanity.com/paper/2512.00997/) (2025)

## Abstract (arXiv)

Formal theorem proving enables machine-verifiable evaluation of mathematical reasoning, yet existing benchmarks often emphasize aggregate proof accuracy, concentrate on a narrow range of mathematics, and provide limited evidence of robustness to equivalent reformulations. We introduce MathAdv, a diagnostic benchmark spanning 13 domains across undergraduate- and graduate-level mathematics. Alongside Lean 4 theorem proving, MathAdv provides up to three auxiliary tasks: multiple-choice questions that probe mathematical knowledge, fill-in-the-blank problems that isolate informal reasoning, and expert-crafted transformations that test robustness to problem presentation. Our evaluation of contemporary theorem provers yields four findings: formalization remains a major bottleneck; performance varies substantially across mathematical domains; natural-language guidance helps general-purpose LLMs but can hinder proof-specialized models; and mathematically equivalent reformulations expose substantial robustness limitations. Together, these results show how component-wise evaluation can reveal model capabilities and failure modes that aggregate theorem-proving accuracy obscures. The dataset and evaluation scripts are available at https://github.com/margotyjx/MathAdv.git.