Terence Tao on How AI Is Changing Mathematics

TL;DR: Mathematician Terence Tao believes AI is reducing the "cognitive friction" in mathematical research, making experimentation and bold ideas possible, and is poised to become a mainstream tool. ## From Blackboard to AI Assistant: A New Paradigm for Mathematical Research As the Special Program Director at the Institute for Pure and Applied Mathematics (IPAM), Terence Tao is highly enthusiastic about the application of AI in mathematics. He noted: "The development of AI is indeed very rapid. It allows me to conduct various experiments and try bolder ideas. You can let your imagination run wild on the blackboard, and if we encounter calculations that none of us want to do, we can let AI tools handle them." This shift is not just reflected in personal workflows. Tao observed that AI is fundamentally changing how mathematicians interact with literature, collaboration, and problem-solving: "I search the literature with much higher accuracy and efficiency than before. As a result, I am now more engaged in AI-assisted mathematical research and collaborative projects. And I think it is ready for mainstream adoption." ## Reducing Cognitive Friction: From "Must Think" to "Zero Friction" Tao particularly emphasized the concept of "cognitive friction": "Until recently, we lived in a world full of cognitive friction, where every task required us to think. So we never seriously considered it; we just thought that was the price of intellectual work. But now, with AI and other technologies, we can reduce that friction to zero." In traditional mathematical research, many calculations, literature searches, and preliminary verifications had to be done by the mathematician themselves, which often limited the scope of exploration. With the involvement of AI, researchers can refocus their energy on more essential issues — proposing conjectures, designing experimental frameworks — while leaving repetitive and technical tasks to machines. ## Not Just a Tool: Enabling More Mathematicians to Reach Fields Medal Level OpenAI's focus is not only on inventing a technology, but also on transforming the entire mathematical ecosystem: "Fundamentally, at OpenAI, we are focused on being at the frontier of automating science, the economy, and ourselves. We are not so concerned with winning Nobel Prizes or Fields Medals; we are more concerned with enabling 100 mathematicians in the world to achieve those honors on their own." Tao believes that as AI lowers the barrier to entry into advanced mathematical fields, more mathematicians will be able to conduct high-quality research in a shorter time. Future competition may no longer be about who can perform the most complex calculations, but who can use AI to devise the most clever approaches. ## Future Mathematical Publishing: The Path Is More Valuable Than the Result Tao made an interesting prediction about publishing research results in the AI era: "I hope that when AI usage becomes more widespread, people will not only publish the final results, but also the various paths they took to reach them, because that information is also very valuable." In traditional mathematical papers, authors typically present only one elegant, concise proof path, hiding all the wrong branches and failed attempts. But in AI-assisted research, these "discarded paths" may contain rich mathematical wisdom — they record the intuition, trial-and-error, and adjustments that occurred during the interaction between the researcher and AI. Sharing these paths could help other mathematicians find correct solutions faster, or even extract new methods from them. ## Having It Both Ways: A New Mathematical Ecosystem with AI Assistance Tao is optimistic about the future of AI and mathematics: "I think we can find a way to have it both ways." He believes that AI can help mathematicians maintain creativity while significantly improving research efficiency, ultimately changing the face of this ancient discipline. Source: https://www.youtube.com/watch?v=cdflu9ZXZGE