# BrokenMath: A Benchmark for Sycophancy in Theorem Proving with LLMs

arXiv: https://arxiv.org/abs/2510.04721 · HTML: https://mlsanity.com/paper/2510.04721/

## Key facts

- Cited by 23 papers in the map (data through 7 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 30 of 31)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [Simple synthetic data reduces sycophancy in large language models](https://mlsanity.com/paper/2308.03958/) (2023)
- [AbstentionBench: Reasoning LLMs Fail on Unanswerable Questions](https://mlsanity.com/paper/2506.09038/) (2025)
- [Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty](https://mlsanity.com/paper/2507.16806/) (2025)
- [Sycophancy in Large Language Models: Causes and Mitigations](https://mlsanity.com/paper/2411.15287/) (2024)
- [Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad](https://mlsanity.com/paper/2503.21934/) (2025)
- [When Large Language Models contradict humans? Large Language Models' Sycophantic Behaviour](https://mlsanity.com/paper/2311.09410/) (2023)
- [Benchmarking Hallucination in Large Language Models based on Unanswerable Math Word Problem](https://mlsanity.com/paper/2403.03558/) (2024)
- [Reasoning about Uncertainty: Do Reasoning Models Know When They Don't Know?](https://mlsanity.com/paper/2506.18183/) (2025)
- [The Open Proof Corpus: A Large-Scale Study of LLM-Generated Mathematical Proofs](https://mlsanity.com/paper/2506.21621/) (2025)
- [Linear Probe Penalties Reduce LLM Sycophancy](https://mlsanity.com/paper/2412.00967/) (2024)
- [MathSmith: Towards Extremely Hard Mathematical Reasoning by Forging Synthetic Problems with a Reinforced Policy](https://mlsanity.com/paper/2508.05592/) (2025)
- [Efficient Reasoning for Large Reasoning Language Models via Certainty-Guided Reflection Suppression](https://mlsanity.com/paper/2508.05337/) (2025)
- [Brains vs. Bytes: Evaluating LLM Proficiency in Olympiad Mathematics](https://mlsanity.com/paper/2504.01995/) (2025)
- [PromptCoT: Synthesizing Olympiad-level Problems for Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2503.02324/) (2025)
- [Confidence in the Reasoning of Large Language Models](https://mlsanity.com/paper/2412.15296/) (2024)
- [TreeCut: A Synthetic Unanswerable Math Word Problem Dataset for LLM Hallucination Evaluation](https://mlsanity.com/paper/2502.13442/) (2025)
- [SAND-Math: Using LLMs to Generate Novel, Difficult and Useful Mathematics Questions and Answers](https://mlsanity.com/paper/2507.20527/) (2025)
- [Read Your Own Mind: Reasoning Helps Surface Self-Confidence Signals in LLMs](https://mlsanity.com/paper/2505.23845/) (2025)
- [From Blind Solvers to Logical Thinkers: Benchmarking LLMs' Logical Integrity on Faulty Mathematical Problems](https://mlsanity.com/paper/2410.18921/) (2024)
- [ReliableMath: Benchmark of Reliable Mathematical Reasoning on Large Language Models](https://mlsanity.com/paper/2507.03133/) (2025)

## Built on by (most cited first, 23 of 23)

- [How RLHF Amplifies Sycophancy](https://mlsanity.com/paper/2602.01002/) (2026)
- [MemSyco-Bench: Benchmarking Sycophancy in Agent Memory](https://mlsanity.com/paper/2607.01071/) (2026)
- [Diagnosing and Mitigating Sycophancy and Skepticism in LLM Causal Judgment](https://mlsanity.com/paper/2601.08258/) (2026)
- [Not All Proofs Are Equal: Evaluating LLM Proof Quality Beyond Correctness](https://mlsanity.com/paper/2605.10379/) (2026)
- [TCS-BENCH: Benchmarking State-of-the-Art Generative AI Theoretical Computer Science Research Ability](https://mlsanity.com/paper/2608.09538/) (2026)
- [Beacon: Single-Turn Diagnosis and Mitigation of Latent Sycophancy in Large Language Models](https://mlsanity.com/paper/2510.16727/) (2025)
- [RAudit: A Blind Auditing Protocol for Large Language Model Reasoning](https://mlsanity.com/paper/2601.23133/) (2026)
- [Too Nice to Tell the Truth: Quantifying Agreeableness-Driven Sycophancy in Role-Playing Language Models](https://mlsanity.com/paper/2604.10733/) (2026)
- [How LLMs Are Persuaded: A Few Attention Heads, Rerouted](https://mlsanity.com/paper/2605.09314/) (2026)
- [To Whom Do Language Models Align? Measuring Principal Hierarchies Under High-Stakes Competing Demands](https://mlsanity.com/paper/2605.12120/) (2026)
- [Sycophantic Praise: Evaluating Excessive Praise in Language Models](https://mlsanity.com/paper/2606.07441/) (2026)
- [Tag Questions and the Generational Reversal of Sycophancy Across 45 Language Models](https://mlsanity.com/paper/2607.23976/) (2026)
- [Aletheia: Quantifying Cognitive Conviction in Reasoning Models via Regularized Inverse Confusion Matrix](https://mlsanity.com/paper/2601.01532/) (2026)
- [Feedback Indices to Evaluate LLM Responses to Rebuttals for Multiple Choice Type Questions](https://mlsanity.com/paper/2601.03285/) (2026)
- [ReCrit: Transition-Aware Reinforcement Learning for Scientific Critic Reasoning](https://mlsanity.com/paper/2605.18799/) (2026)
- [How reliable are LLMs when it comes to playing dice?](https://mlsanity.com/paper/2606.07515/) (2026)
- [Agents Don't Just Agree, They Remember: Benchmarking Persistent Sycophancy in Self-Improving Personal Agents](https://mlsanity.com/paper/2607.10526/) (2026)
- [Group Alignment-Induced Sycophancy: A Two-Sided Evaluation of Steerable Pluralistic Alignment](https://mlsanity.com/paper/2608.11528/) (2026)
- [INSPIRE: An Internalize-Then-Improve Approach for Example-Driven Mathematical Reasoning](https://mlsanity.com/paper/2608.27501/) (2026)
- [Sweet Talkers: How Query Formulation Shapes Sycophancy in Romantic Relationship Advice](https://mlsanity.com/paper/2609.13841/) (2026)
- [XYEval: Agents say yes to bad advice](https://mlsanity.com/paper/2609.23939/) (2026)
- [Are You Sure You're Sure? Two Confounds in a Sycophancy Benchmark](https://mlsanity.com/paper/2609.32867/) (2026)
- [TCSAlgBench: Benchmarking Automated Proving for Research-Level Theoretical Computer Science](https://mlsanity.com/paper/2609.35606/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have recently shown strong performance on mathematical benchmarks. At the same time, they are prone to hallucination and sycophancy, often providing convincing but flawed proofs for incorrect mathematical statements provided by users. This significantly limits the applicability of LLMs in theorem proving, as verification of these flawed proofs must be done manually by expert mathematicians. However, existing benchmarks that measure sycophancy in mathematics are limited: they focus solely on final-answer problems, rely on very simple and often contaminated datasets, and construct benchmark samples using synthetic modifications that create ill-posed questions rather than well-posed questions that are demonstrably false. To address these issues, we introduce BrokenMath, the first benchmark for evaluating sycophantic behavior in LLMs within the context of natural language theorem proving. BrokenMath is built from advanced 2025 competition problems, which are perturbed with an LLM to produce false statements and subsequently refined through expert review. Using an LLM-as-a-judge framework, we evaluate state-of-the-art LLMs and agentic systems and find that sycophancy is widespread, with the best model, GPT-5, producing sycophantic answers 29% of the time. We further investigate several mitigation strategies, including test-time interventions and supervised fine-tuning on curated sycophantic examples. These approaches substantially reduce, but do not eliminate, sycophantic behavior.