# MechMath: Sorrifier-Driven Formal Decomposition Workflow for Automated Theorem Proving

arXiv: https://arxiv.org/abs/2603.24465 · HTML: https://mlsanity.com/paper/2603.24465/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Educational agents and math problem solving, one of 16 directions in LLM agents and tool use.
- Builds on 15 of its 26 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Placed in

- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 15 of 15)

- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction](https://mlsanity.com/paper/2508.03613/) (2025)
- [The Lean mathematical library](https://mlsanity.com/paper/1910.09336/) (2019)
- [Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving](https://mlsanity.com/paper/2502.07640/) (2025)
- [BFS-Prover: Scalable Best-First Tree Search for LLM-based Automatic Theorem Proving](https://mlsanity.com/paper/2502.03438/) (2025)
- [Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipeline](https://mlsanity.com/paper/2507.15855/) (2025)
- [Hilbert: Recursively Building Formal Proofs with Informal Reasoning](https://mlsanity.com/paper/2509.22819/) (2025)
- [Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics](https://mlsanity.com/paper/2601.14027/) (2026)
- [APOLLO: Automated LLM and Lean Collaboration for Advanced Formal Reasoning](https://mlsanity.com/paper/2505.05758/) (2025)
- [Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics](https://mlsanity.com/paper/2510.12787/) (2025)
- [Kimina Lean Server: A High-Performance Lean Server for Large-Scale Verification](https://mlsanity.com/paper/2504.21230/) (2025)
- [A Survey of Languages for Formalizing Mathematics](https://mlsanity.com/paper/2005.12876/) (2020)

## Built on by (most cited first, 1 of 1)

- [Automating Formal Verification with Agent-Guided Tree Search](https://mlsanity.com/paper/2605.27485/) (2026)

## Abstract (arXiv)

Recent advances in large language models (LLMs) and LLM-based agents have substantially improved the capabilities of automated theorem proving. However, for problems that require complex mathematical reasoning, current systems seldom succeed in their initial attempt, necessitating iterative adjustments to their proof strategies. Existing approaches for handling failed attempts typically either iteratively fix errors within the proof or discard the entire proof and regenerate it from scratch. The former leads to progressively longer contexts, which degrade the model's ability to attend to the remaining unresolved subproblems, while the latter is inefficient, as it may abandon mostly correct reasoning due to localized errors. To address this dilemma, we present MechMath, an agent system centered on a Sorrifier-driven formal decomposition paradigm. By leveraging the sorry placeholder in Lean to precisely isolate unresolved subgoals while preserving the surrounding verified proof structure, MechMath extracts each failed subproblem into a clean, self-contained context and resolves it independently. This avoids both the waste of full regeneration and the excessive context length induced by repeated repairs. Experimental results on challenging mathematical competition benchmarks, including IMO 2025, Putnam 2025, miniF2F, and a subset of ProverBench, demonstrate that our agent achieves significant advantages in proving efficiency.