PWW-Bench: Probing Visual Mathematical Reasoning with Proofs Without Words

Human mathematics is profoundly visual at the level of intuition, discovery, and communication, yet current math vision benchmarks focus on shallow calculation-based tasks rather than deeper modes of visual reasoning. To address this critical gap, we introduce \textbf{PWW-Bench}, a benchmark for multimodal mathematical reasoning of vision-language models (VLMs) built from the \emph{Proofs Without Words} (PWW) collection--403 single-page diagrams that illustrate proofs of mathematical theorems with little or no prose. In particular, PWW-Bench tests whether a model can \textit{understand proof-based mathematical reasoning from a picture} by asking the model to identify the theorem, point to the geometric components that make the argument work, and recover the logical chain the figure encodes. To support VLM evaluation on PWW-Bench, we define a rubric-based grading system using an LLM judge. We then conduct pilot experiments on a balanced subset of PWW-Bench with human-calibrated rubrics, evaluating 8 frontier and open-weight VLMs. We find that all models exhibit profound visual understanding failures: even when provided the correct theorem, VLMs do not reconstruct the correct proof. Furthermore, we develop an interface for crowdsourcing rubric calibration across the entire benchmark.