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

arXiv:2608.25449 · cs.CL, cs.AI, cs.LO · Submitted 2026-08-26 · Read on arXiv

cs.CL, cs.AI, cs.LO

Submitted: 2026-08-26

Updated: 2026-08-28

Code: https://github.com/margotyjx/MathAdv

Terminology

• Accuracy — 32× in this paper · explained in 1 episode
• Benchmark — 20× in this paper · explained in 2 episodes
• Robustness — 14× in this paper · explained in 5 episodes
• Verifier — 12× in this paper · explained in 2 episodes
• Reinforcement Learning — 5× in this paper · explained in 4 episodes
• Fidelity — 4× in this paper · explained in 2 episodes
• Human-in-the-Loop — 4× in this paper · explained in 3 episodes
• Adam — 3× in this paper · explained in 2 episodes
• Failure Modes — 3× in this paper · explained in 3 episodes
• Verification — 3× in this paper · explained in 2 episodes
• Benchmarking — 2× in this paper · explained in 3 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Redundancy — 2× in this paper · explained in 2 episodes
• Semantic Understanding — 2× in this paper · explained in 2 episodes
• Ablation — 1× in this paper · explained in 1 episode
• Agentic Reasoning — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Elias — 1× in this paper · explained in 2 episodes
• LLM judge — 1× in this paper · explained in 2 episodes
• Semantic Alignment — 1× in this paper · explained in 3 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics
• Llemma: An Open Language Model For Mathematics
• IndiMathBench: Autoformalizing Mathematical Reasoning Problems with a Human Touch
• DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models
• Herald: A Natural Language Annotated Lean 4 Dataset
• Solving Quantitative Reasoning Problems with Language Models
• Lean-STaR: Learning to Interleave Thinking and Proving
• Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Proving
• FIMO: A Challenge Formal Dataset for Automated Theorem Proving
• Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics
• WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct
• Generative Language Modeling for Automated Theorem Proving
• AI scientists produce results without reasoning scientifically
• REAL-Prover: Retrieval Augmented Lean Prover for Mathematical Reasoning
• OpenAI GPT-5 System Card
• PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition
• MA-LoT: Model-Collaboration Lean-based Long Chain-of-Thought Reasoning enhances Formal Theorem Proving
• InternLM2.5-StepProver: Advancing Automated Theorem Proving via Critic-Guided Search
• DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search
• FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Models

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