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

**Authors:** Xiaojun Wu, Cehao Yang, Xuhui Jiang, Chengjin Xu, Jia Li, Jian Guo  
**Lab:** IDEA FinAI · **Published:** 5 Nov 2026 · **Upvotes:** 12  
**Links:** [arXiv](https://arxiv.org/abs/2611.08237) · [PDF](https://arxiv.org/pdf/2611.08237) · [Code](https://github.com/wxj630/terminal-bench-math-modeling) · [This page](https://omen-bit.github.io/ai-paper-daily/paper/2611.08237.html)

## Key numbers

- **59.81%**: while the \2.54 open model holds 59.81% at 1/100$ the cost
- **18**: over 18 real CUMCM and MCM problems

## 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.

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Notes written by AI from the paper, numbers copied from the abstract. Check the paper before you rely on them. From AI Papers Daily.