Characterizing initial human-AI proof formalization workflows

For centuries, human mathematicians have written proofs to substantiate their mathematical arguments; yet, the ability to automatically verify the validity of proofs has long been a challenge. Advances in AI systems' ability to generate code and engage in increasingly high-level mathematical reasoning promise to transform people's ability to formalize and thereby verify proofs. While many works focus on benchmarking the current frontier, we instead study how people use these tools. We conduct a mixed-methods analysis into the initial impact of AI on people's formalization workflows: what people claim they want, what they see as the barriers to those visions, and how they actually use and adapt AI in practice. A qualitative survey shows that people's preferences are diverse, but with a general desire for AI assistance in formalization that preserves high-level human control over the proof discovery process. To assess how people actually engage with AI for formalization under such limitations, we conduct a controlled user study in which participants formalize informal math problems and their proofs, with and without AI, across a range of mathematical problems at varying levels of difficulty and domains. Despite limitations of the tools at the time for autoformalization, participants tend to attain higher formalization accuracy when allowed access to AI tools than when formalizing on their own, with most participants flexibly choosing to use multiple different AI tools. Taken together, our work sheds light on the early stages of AI integration into formalization workflows, involving an intimate interplay of human and AI engagement.

Humanity's Last Exam

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 3,000 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning

The suite of datasets commonly used to train and evaluate the mathematical capabilities of AI-based mathematical copilots (primarily large language models) exhibit several shortcomings. These limitations include a restricted scope of mathematical complexity, typically not exceeding lower undergraduate-level mathematics, binary rating protocols and other issues, which makes comprehensive proof-based evaluation suites difficult. We systematically explore these limitations and contend that enhancing the capabilities of large language models, or any forthcoming advancements in AI-based mathematical assistants (copilots or "thought partners"), necessitates a paradigm shift in the design of mathematical datasets and the evaluation criteria of mathematical ability: It is necessary to move away from result-based datasets (theorem statement to theorem proof) and convert the rich facets of mathematical research practice to data LLMs can train on. Examples of these are mathematical workflows (sequences of atomic, potentially subfield-dependent tasks that are often performed when creating new mathematics), which are an important part of the proof-discovery process. Additionally, we advocate for mathematical dataset developers to consider the concept of "motivated proof", introduced by G. P\'olya in 1949, which can serve as a blueprint for datasets that offer a better proof learning signal, alleviating some of the mentioned limitations. Lastly, we introduce math datasheets for datasets, extending the general, dataset-agnostic variants of datasheets: We provide a questionnaire designed specifically for math datasets that we urge dataset creators to include with their datasets. This will make creators aware of potential limitations of their datasets while at the same time making it easy for readers to assess it from the point of view of training and evaluating mathematical copilots.