The application of physics formulas is a fundamental human capability in numerical reasoning. While existing datasets often rely on implicit mathematical knowledge, they rarely explicitate the underlying formulas. To address this, we introduce FormulaReasoning, a new benchmark for formula-based numerical reasoning comprising 5,324 questions requiring calculations grounded in external physics principles. We provide high-quality, fine-grained annotations in English and Chinese—including formula structures, parameter names, symbols, values, and units—curated through manual effort and LLM-assisted validation. Additionally, we provide a consolidated formula database as an external knowledge source. To further challenge model performance, we develop an extended version of the dataset by coupling multiple questions. We evaluate various architectural and methodological frameworks, including retrieval-augmented methods, modular reasoning (formula generation, parameter extraction, and calculation), and preference-based optimization. Our analysis identifies critical challenges in formula-based reasoning, highlighting significant opportunities for future methodological advancement.

While recent studies explore Large Language Models’ (LLMs) performance on Theory of Mind (ToM) reasoning tasks, research on ToM abilities that require more nuanced social context is limited, such as white lies. We introduce TactfulToM, a novel English benchmark designed to evaluate LLMs’ ability to understand white lies within real-life conversations and reason about prosocial motivations behind them, particularly when they are used to spare others’ feelings and maintain social harmony. Our benchmark is generated through a multi-stage human-in-the-loop pipeline where LLMs expand manually designed seed stories into conversations to maintain the information asymmetry between participants necessary for authentic white lies. We show that TactfulToM is challenging for state-of-the-art models, which perform substantially below humans, revealing shortcomings in their ability to fully comprehend the ToM reasoning that enables true understanding of white lies.