Mathematician Terence Tao has warned that artificial intelligence could trigger a crisis in mathematics comparable to the foundational upheaval that occurred between 1900 and 1930. In an essay for the 2026 International Congress of Mathematicians, Tao argues that the math community should shift focus from debating AI's capabilities to addressing deeper questions about the goals of mathematical research. He suggests that the field is facing a new stress test, one that is not about mathematical truth but about the implicit values and practices that define the discipline. Tao's working hypothesis is that AI tools will soon be capable of performing a reasonable fraction of research-level mathematical tasks with reasonable levels of success, quality, supervision, and cost.
Tao points to the First-Proof Project as evidence, where ten never-published research problems were tested against four AI systems under controlled conditions. Seven of the ten received at least one passing grade from at least one system, meaning a solution judged essentially flawless or needing only minor revisions. The cost for each problem ranged from tens to hundreds of dollars. He argues that AI threatens to pull apart the many interconnected goals of mathematics, such as solving problems, building theories, fostering community, and training the next generation. Tao warns that AI could shift the field from proof scarcity to proof abundance, with AI-generated proofs piling up faster than they can be checked, read, or absorbed.
Tao emphasizes that the current crisis is not about the correctness of mathematical results but about the implicit framework of mathematical values and practices. He suggests that the field should adopt guidelines like the Leiden Declaration on Artificial Intelligence and Mathematics, published in June 2026, which calls for authors to be able to give a clear, expert-level talk on their results. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified. Training young mathematicians requires special care, as Tao argues that the field must protect the 'irreducibly human aspect' of mathematical work.
Source: thedecoder
