Contents
Terrance Tao
Terence Tao suggests that mathematics is entering a turbulent phase similar to the early 20th-century foundational crises. However, this time the challenge is not about mathematical truth but about the values, goals, and practices of mathematicians. With AI potentially capable of handling many research-level tasks, Tao moves the focus from AI capabilities to understanding what mathematicians aim to achieve—often implicitly. He observes that traditional aims, like solving problems, developing theories, training students, and sharing knowledge, have historically been aligned, using simple measures like “solving hard problems” as proxies. AI, however, disrupts this harmony, highlighting Goodhart’s law: focusing on a single metric, such as the number of problems solved, can distort core values.
Tao uses problem solving as a case study to demonstrate how the simple goal of “solve unsolved problems” expands into a complex, multi-stage process when implicit expectations are clarified. This process involves not only generating and verifying solutions but also writing them clearly, ensuring they are understood, accepted by the community, and integrated into formal mathematical theory. AI expedites the initial stages—proof creation and validation—but may overwhelm later stages like exposition, peer review, and canonicalization, which depend heavily on human effort. He warns of an “proof abundance,” where AI produces numerous correct yet opaque proofs faster than humans can interpret, potentially disrupting journals, refereeing, hiring, and the collective mathematical knowledge base.
Tao emphasizes recommendations from the Leiden Declaration, urging mathematicians to disclose AI tool usage, support reviewers, preserve human responsibility in authorship, and ensure proper attribution. He advocates for shifting cultural focus away from being “first to prove” and towards the slower, more deliberate human processes of digestion and canonicalization. The essay concludes by highlighting the need for similar value-based analyses across teaching, mentoring, hiring, and outreach. Tao advocates for open community discussions on both AI capabilities and mathematical values, stressing that mathematics will remain a human-driven field even as AI becomes a powerful collaborator.
Slides
Tao, Terence. “Mathematics in the age of Al.” Public lecture slides. International Congress of Mathematicians 2026. University of California. July 24, 2026. https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.pdf.
Essay
Tao, Terence. “Mathematics in the age of AI.” UCLA Department of Mathematics. arxiv, August 24, 2026. https://arxiv.org/html/2608.16753v1.
An essay, based on a public lecture delivered at the 2026 International Congress of Mathematicians, on how the mathematical community might respond to the arrival of artificial intelligence tools that are capable of performing research-level mathematical tasks. Rather than debating the capabilities of such tools, we condition on the hypothesis that these capabilities will arrive, and examine instead a question that is orthogonal to it: what the goals and values of mathematical research actually are. The problem-solving component of mathematics is used as a case study.
References
Leiden Declaration on Artificial Intelligence and Mathematics. “Leiden Declaration on Artificial Intelligence and Mathematics.” June 2, 2026. https://leidendeclaration.ai/.
Jamnik, Mateja. “The Leiden Declaration: Mathematics, AI, and Making Our Values Explicit.” Communications of the ACM, June 25, 2026. https://cacm.acm.org/blogcacm/the-leiden-declaration-mathematics-ai-and-making-our-values-explicit/.
MIT Report – AI and Education
The MIT report highlights that overreliance on AI can prevent students from experiencing genuine learning through effort and struggle. While AI can quickly solve problems, write essays, and debug code, relying on it for thinking diminishes opportunities to develop skills, confidence, and understanding. The report terms this tendency “cognitive surrender,” where students resort to AI whenever they encounter difficulty rather than learning to overcome challenges independently.
The report warns that heavy AI use is undermining the social side of learning. MIT classes have long relied on study groups, office hours, and teamwork. But when students use AI instead of talking with classmates or instructors, they become more isolated. This weakens the sense of community and shared effort that makes learning at MIT so powerful. The report stresses that learning is not just about getting answers — it’s about building relationships, asking questions, and growing together.
Another concern is trust. Instructors feel pressure to “police” AI use, while students worry about being falsely accused by unreliable AI‑detection tools. This creates tension and suspicion on both sides. The report argues that this atmosphere makes learning harder and undermines the respectful, collaborative environment MIT seeks to protect.
The report highlights that AI undermines the value of traditional assignments. When AI can handle most homework, essays, and take-home exams, these tasks no longer accurately show what a student truly understands. As a result, grades lose their meaning, and students may focus more on efficiency than learning. The report recommends that instructors redesign assessments to evaluate genuine understanding rather than AI-polished responses.
The report concludes that education involves more than just learning facts; it aims to develop individuals who are thoughtful, capable, and able to collaborate, make good decisions, and grow from experience.` Overdependence on AI might cause students to miss vital human experiences such as mentorship, teamwork, creativity, and identity formation, all of which are crucial for their development into confident adults and future leaders.
MIT’s Ad Hoc Committee on AI Use in Teaching, Learning, and Research Training. “Report – AI and Education.” AI and Education, August 13, 2026. https://aiandeducation.mit.edu/report/.
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