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MA-ProofBench: Evaluating LLMs on Advanced Mathematical Analysis
๐กCurrent LLMs struggle with advanced math; see why even top models fail at formal theorem proving in this new benchmark.
โก 30-Second TL;DR
What Changed
Features 200 formalized theorems across 6 core topics like measure, complex, and functional analysis.
Why It Matters
This benchmark highlights the current limitations of LLMs in high-level mathematical reasoning, suggesting that scaling alone may not solve formal verification challenges. It provides a rigorous standard for researchers to track progress in reliable, proof-based AI systems.
What To Do Next
If you are building math-heavy AI agents, incorporate formal verification tools like Lean or Isabelle to cross-check LLM-generated proofs.
Who should care:Researchers & Academics
Key Points
- โขFeatures 200 formalized theorems across 6 core topics like measure, complex, and functional analysis.
- โขDivided into undergraduate (Level I) and Ph.D. qualifying (Level II) difficulty levels.
- โขIdentified Mathlib hallucinations and incomplete proofs as primary failure modes for LLMs.
- โขReveals a significant performance gap between informal natural language reasoning and formal verification.
๐ง Deep Insight
Web-grounded analysis with 14 cited sources.
๐ Enhanced Key Takeaways
- โขMA-ProofBench is distinguished as the first formal theorem-proving benchmark specifically dedicated to Mathematical Analysis, filling a critical gap where prior benchmarks predominantly focused on areas like algebra and elementary number theory.
- โขThe benchmark's problems are meticulously crafted through a human-led, LLM-assisted formalization pipeline, which is then subjected to independent expert review to ensure the formal statements accurately reflect the original mathematical concepts.
- โขEven the most advanced models, such as GPT-5.5, demonstrated significant limitations, achieving only 16% Pass@8 on undergraduate-level problems (Level I) and a mere 5% on Ph.D. qualifying-level problems (Level II), underscoring the substantial challenges LLMs face in formal mathematical reasoning.
๐ Competitor Analysisโธ Show
Competitor Analysis: LLM Formal Theorem Proving Benchmarks
| Feature / Benchmark | MA-ProofBench | TheoremBench | FormalProofBench | IMProofBench | IMO-ProofBench (part of IMO-Bench) | ProofBench |
|---|---|---|---|---|---|---|
| Primary Focus | Advanced Mathematical Analysis (Measure, Complex, Functional Analysis) | Lean4 theorem proving beyond contest settings | Graduate-level mathematical proofs | Research-level mathematical proof generation | Olympiad-level mathematical proofs | Competition-level mathematical proof generation and verification |
| Formalization Language | Mathlib (Lean) | Lean4 | Lean4 | Not explicitly stated, but agentic framework with tools like SageMath | Lean 4 (for IMO-LeanProofBench) | Not explicitly stated, focuses on proof generation |
| Difficulty Levels | Undergraduate (Level I) & Ph.D. Qualifying (Level II) | Beyond contest settings, structured for diagnostic evaluation | Advanced undergraduate and graduate mathematics | Research-level problems, some open questions | Basic & Advanced Olympiad-level | Competition-level |
| Key Evaluation Metrics | Pass@8 | Theorem-level coverage, token-efficiency | Accuracy (e.g., best foundation model 33.5%) | Human expert grading, automated grading for subproblems (e.g., Grok-4 52% on subproblems, GPT-5 22% on proofs) | Human evaluation, automated scoring via ProofAutoGrader (e.g., Gemini Deep Think 65.7% on Advanced) | Expert ratings, detailed marking schemes |
| Key Findings/Insights | Mathlib hallucinations and incomplete proofs are dominant failure modes; clear gap between informal and formal reasoning | Explicit premises substantially improve performance for Lean4-capable models | Best foundation model achieved 33.5% accuracy; performance drops rapidly thereafter | Current LLMs succeed on accessible research questions but struggle with challenging ones | Significant performance disparity across problem types, potential overfitting in some models | LLM performance varies significantly across subtopics; consistent drop in scores on newer problems |
| Release Date | June 11, 2026 | June 8, 2026 | March 27, 2026 | September 30, 2025 / October 1, 2025 | November 4, 2025 (IMO-ProofBench) | March 1, 2026 (PROOFBENCH dataset) |
๐ ๏ธ Technical Deep Dive
- Problem Set Composition: MA-ProofBench comprises 200 formalized theorems, distributed across 6 core mathematical analysis topics and 27 finer-grained subcategories. These topics include measure and integration theory, complex analysis, and functional analysis.
- Difficulty Tiers: The benchmark is structured into two distinct difficulty levels: Level I, consisting of 100 undergraduate-level problems, and Level II, featuring 100 problems designed to mimic Ph.D. qualifying examination difficulty.
- Formalization Process: Each problem undergoes a rigorous construction process involving a human-led, LLM-assisted formalization pipeline. This is followed by independent expert review to ensure the formal statements accurately represent the original mathematical concepts.
- Underlying Formal System: The benchmark problems are formalized within the Mathlib library, which is a large formalization library for the Lean 4 proof assistant.
- Evaluation Metric: Performance of LLMs on MA-ProofBench is primarily evaluated using the Pass@8 metric.
- Identified Failure Modes: Analysis of LLM performance on the benchmark revealed that Mathlib hallucinations (generating formally incorrect statements within the Lean/Mathlib framework) and incomplete proofs are the two dominant failure modes.
๐ฎ Future ImplicationsAI analysis grounded in cited sources
Future LLMs will require more robust formal reasoning capabilities to tackle advanced mathematics.
MA-ProofBench exposes significant gaps, with top models achieving very low accuracy on undergraduate-level problems, indicating a need for fundamental improvements in formal verification rather than just informal reasoning.
Development of specialized LLMs or hybrid AI systems for formal theorem proving will accelerate.
The identified failure modes (Mathlib hallucinations, incomplete proofs) suggest that general-purpose LLMs are insufficient, necessitating models specifically trained or augmented for formal mathematical languages and rigorous proof generation.
Benchmarks like MA-ProofBench will become critical for guiding research and development in AI for scientific discovery.
By providing a reliable reference for tracking progress in advanced formal mathematical reasoning, MA-ProofBench will help researchers identify specific weaknesses and measure improvements in LLM capabilities for high-stakes scientific applications.
โณ Timeline
2026-06
MA-ProofBench: A Two-Tiered Evaluation of LLMs for Theorem Proving in Mathematical Analysis paper released on arXiv.
๐ Sources (14)
Factual claims are grounded in the sources below. Forward-looking analysis is AI-generated interpretation.
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