Terminal-style Mathematical Modeling Bench: The First Agentic and Verifiable Benchmark for Mathematical Modeling

Researchers introduced TB-MathModel, a terminal-style benchmark that makes 18 real CUMCM and MCM contest problems from 2023–2025 agentic and verifiable, scoring agents' single JSON artifacts against reproductions of Outstanding-award papers. The benchmark uses direction-aware one-sided scoring and two-layer feasibility verification — a programmatic gate over six decidable invariant forms plus 624 Lean 4 obligations, with a hard gate zeroing infeasible answers — and scores each task against a panel of human outstanding papers. Across seven multimodal models (three seeds each), the strongest reached a multi-reference O-Eval of 64.58%, while a $2.54 open model held 59.81% at 1/100 the cost; source code is at github.com/wxj630/terminal-bench-math-modeling.

arXiv:2611.08237v1 Announce Type: new Abstract: Mathematical modeling turns an open-ended real-world problem into assumptions, a model, a solution, and a defended recommendation, and its answers matter only if they are both close to a credible reference and physically feasible; existing benchmarks either score solver fragments or grade reports with an LLM judge, leaving those numbers unchecked. We introduce TB-MathModel the Terminal-style Mathematical Modeling Bench , the first benchmark to make complete contest-style modeling problems agentic, verifiable, and terminal at once, over 18 real CUMCM and MCM problems 2023--2025 . Each task ships the verbatim statement, official attachments, and figures in a containerized terminal; the agent returns one JSON artifact, scored on the numeric core of the final question against a reproduction of the Outstanding-award paper. Two design choices distinguish it: direction-aware, one-sided scoring, which never penalises beating the anchor, and two-layer feasibility verification---a programmatic gate over six decidable invariant forms plus 624 Lean~4 obligations---with a hard gate that zeroes infeasible answers. Each task is scored against a panel of human outstanding papers rather than one, so a model must be close to many accepted answers; across seven multimodal entries three seeds each the strongest reach a multi-reference O-Eval of 64.58\%, while the \$2.54 open model holds 59.81\% at $1/100$ the cost. TB-MathModel turns the numeric core of modeling into a reproducible, machine-checkable signal for measuring long-horizon modeling competence and for collecting agent trajectories. The source code is available at https://github.com/wxj630/terminal-bench-math-modeling.