BrokenMath (Inspect AI)

An Inspect AI implementation of BrokenMath — a benchmark for sycophancy in LLM theorem proving (Petrov et al., NeurIPS 2025 Datasets & Benchmarks, arXiv:2510.04721).

What it measures

BrokenMath takes 451 recent olympiad problems and adversarially modifies each into a false statement. The model is asked to prove the (false) theorem. A sycophantic model plays along and produces a bogus "proof" instead of flagging the flawed premise — a safety-relevant failure mode adjacent to deceptive alignment.

• Solver: single-turn generate() — the model is asked to prove the false statement (proof-writing instructions verbatim from the authors).
• Scorer: an LLM judge applies the authors' 4-way rubric and classifies each response as correct / detected / corrected / incorrect.
• Metric — sycophancy rate: the fraction judged incorrect (the model attempted a proof and detected no issue). Lower is better.

Running

uv sync
# solver = model under test; judge = model that applies the rubric
uv run inspect eval brokenmath \
  --model openrouter/deepseek/deepseek-chat-v3.1 \
  -T judge_model=anthropic/claude-sonnet-4-5-20250929

Set the relevant provider keys (OPENROUTER_API_KEY, ANTHROPIC_API_KEY, …).

Data & pinning

• Dataset: HF INSAIT-Institute/BrokenMath (benchmark split, 451 problems), CC-BY-4.0, loaded with a pinned revision=. All problems are fully public with original_problem + ground-truth solution.
• Judge prompt: the 4-way checker in src/brokenmath/prompts/checker.txt is vendored verbatim from insait-institute/broken-math (Apache-2.0).

Reproduction

See evaluation_report.md for a baseline reproduction. Note the metric is judge-dependent (as with any LLM-judge eval): the paper's published rates use a GPT-5-mini judge, so absolute numbers shift with the judge model. Model ranking and the methodology reproduce faithfully.

License

MIT (this implementation). Upstream data is CC-BY-4.0; the vendored judge prompt is Apache-2.0. See LICENSE and upstream attribution above.

Citation

@inproceedings{petrov2025brokenmath,
  title={BrokenMath: A Benchmark for Sycophancy in Theorem Proving with LLMs},
  author={Petrov, Ivo and Dekoninck, Jasper and Vechev, Martin},
  booktitle={NeurIPS Datasets and Benchmarks},
  year={2025}
}