Scaling Mathematical Proof Supervision from Structured Textbooks

Large language models are increasingly capable at closed-world mathematical reasoning, but research assistance also requires source-grounded use of the literature. When a proof reaches a non-trivial step, a useful assistant should determine whether the needed tool (e.g., a lemma) already exists, identify a suitable scholarly source, and verify that its assumptions align with the current proof context. To rigorously evaluate such capabilities, we introduce Re$^2$Math, a benchmark for tool-grounded retrieval from partial mathematical proofs. Each instance is built from a candidate instrumental citation in the proof of a main theorem, with hierarchical context and an optional leakage-controlled anchor hint. We also make the task source-grounded yet citation-agnostic in that any admissible theorem sufficient for the proof transition is accepted. Evaluation uses a release-frozen retrieval artifact, ensuring reproducibility, while the benchmark itself supports automatic, continual expansion with newly constructed instances. On the current benchmark test set, the best fixed-judge ToolAcc reaches 7.0%, despite substantially higher rates of source grounding, indicating that current systems often retrieve valid statements but fail to establish their applicability to the local proof step. By decoupling citation recall, grounding, and proof-gap sufficiency, Re$^2$Math transforms literature-grounded mathematical tool use into a controlled diagnostic task.

Large language models (LLMs) are increasingly capable of mathematical problem solving and can even assist with research-level proofs, yet we still lack a scalable and reproducible way to measure step-level reasoning in long proofs across diverse sources. This evaluation gap limits trustworthy AI assistance in proof-certified scientific progress. Existing evaluations often emphasize final answers or rely on costly expert grading, while end-to-end proof generation remains open-ended and hard to verify automatically. We introduce Mask-Proof, a pipeline that turns real proofs into automatically checkable masked-step tasks. It masks key formula steps, provides the necessary surrounding context, and evaluates model reconstructions with an LLM-based equivalence judge using repeated votes for stability. The resulting Mask-ProofBench contains 292 curated problems across diverse research areas. Experiments with 17 models show that reasoning-enhanced models outperform standard models by 12% to 27%. Our evaluator achieves 96.8% agreement with expert annotators, enabling faithful, reproducible, and comparable measurement of step-level mathematical reasoning. Benchmark, annotations, and code are available at https://github.com/weating/Mask-Proof.

We present a new approach for benchmarking Large Language Model (LLM) capabilities on research-level mathematics. Existing benchmarks largely rely on static, hand-curated sets of contest or textbook-style problems as proxies for mathematical research. Instead, we establish an updatable benchmark evaluating models directly on the latest research results in mathematics. This consists of an automatic pipeline that extracts lemmas from arXiv and rewrites them into self-contained statements by making all assumptions and required definitions explicit. It results in a benchmark that can be updated regularly with new problems taken directly from human mathematical research, while previous instances can be used for training without compromising future evaluations. We benchmark current state-of-the-art LLMs, which obtain around 10-15$\%$ accuracy in theorem proving (pass@1) depending on the model, showing that there is currently a large margin of progression for LLMs to reach human-level proving capabilities in a research context.