Terence Tao: AI is ready for primetime in math and theoretical physics
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How Tao came to trust AI as an assistant in mathematical research
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翻訳
Renowned mathematician Terence Tao uses ChatGPT to generate images and code for his research, including his recent paper on prime factors of consecutive integers. He has spent the last year or so moving from cautious experiments with AI to regular use.
In September 2024, after testing an earlier OpenAI model on difficult math problems, he said it felt like advising “a mediocre, but not completely incompetent, graduate student.” Now the verdict is much warmer. At a conference at IPAM this week called “Accelerating Math and Theoretical Physics with AI,” Tao said that current models are now “ready for primetime,” because in math and theoretical physics, AI now “saves more time than it wastes.”
What changed his mind was the gradual widening of the tasks he can hand over. Tao now uses AI to search literature, write code, make plots and figures, run calculations, and test whether a possible approach is worth chasing. A literature search that once entailed hours or weeks of searching databases and libraries can now be shortened to a prompt that returns a useful map of relevant papers in minutes. Tao says this has enriched his research and given his papers more comprehensive references. He also uses AI for what he calls secondary tasks, including making plots and charts.
Tao says the lower cost of exploration due to AI lets him try “crazier things.” Instead of spending hours just to find out whether an idea fails immediately, he can ask AI to test it, run simulations, or carry out a long but routine calculation. He finds current models are useful assistants, but not peers: less helpful as sources of deep original ideas than as tireless systems for scanning known methods, connecting a problem to the right literature, and reporting back on what seems most promising.
Tao says that reliable verification of proofs is important as AI increases the number of proposed solutions to well-known problems. Most working math is still “informal mathematics,” meaning ordinary prose with equations rather than machine-checked proofs, which leaves room for subtle mistakes. Tao says AI can make this worse by producing arguments that look polished while hiding the weak step. His answer is formal verification using tools such as Lean, a tool that verifies a proof line by line and can keep AI honest.
The larger transformation Tao sees is a shift in what mathematicians spend their time on. As AI drives down the cost of routine problem-solving, the scarce skill becomes choosing the right problem, designing the workflow, and checking the result. He hopes for broader collaboration and more leadership from junior mathematicians. He does not expect the future to unfold in a smooth straight line.
AI is getting dramatically better in some directions, while remaining unreliable in others. But Tao uses AI for more mathematical tasks than he did a year ago, and he thinks the field will keep reorganizing around this new tool.
