Formula-One Prompting: Adaptive Reasoning Through Equations For Applied Mathematics
Existing prompting methods struggle to effectively generate or invoke governing equations when solving applied mathematical problems in domains such as finance and physics, thereby limiting the reasoning capabilities of large language models. This work proposes Formula-One Prompting (F-1), which introduces mathematical equations as an intermediate representation in prompt engineering for the first time. F-1 employs a two-stage framework: it first derives governing equations from the problem description and then adaptively selects among Chain-of-Thought (CoT), Program-of-Thought (PoT), or direct computation strategies for solution. The entire process—equation formulation and strategy selection—is completed within a single model call. Evaluated across five models and four benchmarks, F-1 outperforms CoT by 5.76% and PoT by 8.42% on average, with a notable 13.30% improvement on FinanceMath and particularly strong performance on physics-related problems.