Multilingual reasoning models are commonly evaluated by whether they arrive at the correct answer, but not by whether they preserve the intended language while reasoning and responding. This omission conceals important multilingual behaviors that emerge as tasks become harder. In this paper, we study task difficulty, task accuracy, thinking-language consistency (TC), and answer-language consistency (AC) across reasoning models using PolyMath benchmark in eight languages and four difficulty levels. We uncover four findings: (1) language consistency exhibits four difficulty-dependent behaviors: output-language consistency remains aligned with input, remains misaligned, degrades gradually, or collapses abruptly. (2) We identify the language consistency breakdown effect, where increasing difficulty can cause a sudden drop in output-language consistency, especially in less strongly represented and non-Latin-script languages. (3) Due to this breakdown effect, accuracy can be preserved or even improved at a harder difficulty level as the model shifts to its internal dominant language. (4) Quantization can improve or degrade output-language consistency independently of its effect on accuracy, with GPTQ and AWQ often outperforming AutoRound under tolerance-based voting with ε = 1.0. These results show that multilingual capability cannot be characterized by accuracy alone; reliable evaluation should jointly consider task accuracy, language consistency, and task difficulty for multilingual benchmarks.
Reinforcement learning has proven effective for enhancing multi-step reasoning in large language models (LLMs), yet its benefits have not fully translated to multilingual contexts. Existing methods struggle with a fundamental trade-off: prioritizing input-language consistency severely hampers reasoning quality, while prioritizing reasoning often leads to unintended language drift toward English. We address this challenge with LANG, a novel framework that leverages language-conditioned hints to guide exploration in non-English reasoning tasks. Our method incorporates two key mechanisms to prevent dependency on these hints: a progressive decay schedule that gradually withdraws scaffolding, and a language-adaptive switch that tailors learning horizons to specific language difficulties. Empirical results on challenging multilingual mathematical benchmarks reveal that LANG substantially enhances reasoning performance without compromising language consistency. Moreover, we show that our framework generalizes beyond mathematics, fostering more consistent language alignment across model layers