# Language models can notice an impossible engineering problem yet still report it as solved

arXiv: https://arxiv.org/abs/2610.06668 · HTML: https://mlsanity.com/paper/2610.06668/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 70 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 13 of 13)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [BrokenMath: A Benchmark for Sycophancy in Theorem Proving with LLMs](https://mlsanity.com/paper/2510.04721/) (2025)
- [FEABench: Evaluating Language Models on Multiphysics Reasoning Ability](https://mlsanity.com/paper/2504.06260/) (2025)
- [Probing the Critical Point (CritPt) of AI Reasoning: a Frontier Physics Research Benchmark](https://mlsanity.com/paper/2509.26574/) (2025)
- [ABench-Physics: Benchmarking Physical Reasoning in LLMs via High-Difficulty and Dynamic Physics Problems](https://mlsanity.com/paper/2507.04766/) (2025)
- [HLE-Verified: A Systematic Verification and Structured Revision of Humanity's Last Exam](https://mlsanity.com/paper/2602.13964/) (2026)
- [SoM-1K: A Thousand-Problem Benchmark Dataset for Strength of Materials](https://mlsanity.com/paper/2509.21079/) (2025)
- [FEM-Bench: A Structured Scientific Reasoning Benchmark for Evaluating Code-Generating LLMs](https://mlsanity.com/paper/2512.20732/) (2025)
- [PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation](https://mlsanity.com/paper/2605.09636/) (2026)
- [CADEngBench: It Looks Like CAD, but Does It Work? Evaluating Parametric Design, Assembly Reasoning, and Physics Simulation](https://mlsanity.com/paper/2608.09296/) (2026)
- [Mastering Olympiad-Level Physics with Artificial Intelligence](https://mlsanity.com/paper/2511.10515/) (2025)
- [Large Language Models and their Awareness of Mechanics and Spatial Geometry](https://mlsanity.com/paper/2608.14615/) (2026)

## Abstract (arXiv)

Language models draft engineering calculations, but answer accuracy does not show whether they reject an impossible problem. We tested 14 models on 30 pairs of mechanics problems, each with a valid version and one made impossible by changing a given value or assumption. Two independent solvers verified every answer key and showed that each flawed problem was physically impossible. We scored solving of valid problems separately from rejection of their flawed counterparts. Each reply required a "solved" or "cannot solve" status; rejection meant "cannot solve" or withholding an answer. The initial prompts did not warn that problems could be flawed. Across three recent models, 12 of 90 replies failed to reject a flawed problem. In 11 of these replies, the model stated the flaw, answered a corrected problem and still reported the original as "solved", according to artificial intelligence raters and numerical checks. We later retested four models from one provider, offering "flawed" instead of "cannot solve" and asking them to name and explain the defect. Three models showed statistically significant increases in rejection, but valid-problem solving fell in three. Evaluations therefore need to score both versions and distinguish flaw recognition from the reported status.