Terence Tao Critiques OpenAI Over 719 AI-Generated Mathematical Proofs
OpenAI published 719 AI-generated mathematical proofs covering 372 result families, but faced sharp criticism from Fields Medalist Terence Tao and the Advisory Group on Mathematics and AI (AGMAI) for failing to meet transparency and formalization standards. The controversy highlights a growing conflict between commercial AI benchmarks and the mathematical community's need for verifiable, human-comprehensible research. Tao warns that releasing massive volumes of AI proofs without human digestion degrades the collaborative, educational, and exploratory nature of mathematics. OpenAI relied on unreleased proprietary models and provided chain-of-thought reasoning for only 10 manuscripts, while roughly 42% of the proofs lacked formalization or machine-readable metadata. Additionally, three initial proofs were retracted shortly after publication due to a sign error and its cascading impacts.
## BACKGROUND
To guide AI integration in mathematical research, institutions formed the Advisory Group on Mathematics and Artificial Intelligence (AGMAI) to establish release standards, such as disclosing models, prompts, and compute costs. In modern AI-assisted mathematics, formalization involves translating natural language arguments into computer-verified languages like Lean to mathematically guarantee correctness.