Terence Tao proposes "Math 2.0" at Caltech as AI ends proof scarcity

Tao's starting point is that math research grew up assuming proofs were scarce. Finding an answer to an unsolved problem and proving it correct was extremely hard, demanding deep expertise and years of work, so the field's research structures, reward systems, and reputations were built around solving difficult problems. AI is now undercutting that premise. AI-generated math has a property few human activities share: it can be checked objectively, in part because research often needs no physical experiment and the vast literature is digitized and easy to learn from.

Math is shifting from an era of scarce proofs to an era of abundant proofs, Tao argues, and math happens to suit machine learning unusually well — which is why major AI labs such as OpenAI and Anthropic are investing heavily in mathematical problem-solving. With enough compute and strong models, solving many previously hard problems has become relatively quick, and the person operating the AI no longer needs deep mathematical expertise.

Yet Tao stresses that AI has not solved all of mathematics. Most frontier problems remain unsolved even with vast compute, and since mathematical problems are infinite and their difficulty has no ceiling, new research areas keep opening up as AI advances. He also warns that media and social feeds highlight only AI success stories, creating the illusion that AI solves everything, while many unpublished failures exist; accurate assessment, he says, requires transparency about failures and compute consumption. His deeper concern is that if AI easily produces answers, math's real value could be lost — unsolved problems serve as lighthouses for exploring the mathematical world around them, and the trial and error of solving them often generates new theories and methods worth more than the final answer. Even a mathematically correct answer may not be suitable for real-world use in medicine or engineering, where human understanding and judgment matter. Tao's proposal also points to practical directions, such as creating integrated teaching materials from research results and developing safe open-source AI models specialized for mathematics, and he says the biggest obstacle to Math 2.0 is not technology or institutional culture but imagination.