AI must spark a rapid revolution

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Why mathematician Terence Tao thinks AI must spark a rapid revolution
By Karmela Padavic-Callaghan

Terence Tao argues that mathematics is entering one of the most consequential crises in its modern history because AI is rapidly transforming the production of mathematical proofs. During 2026, AI systems have reportedly solved or substantially advanced numerous long-standing problems, sometimes after being prompted by non-specialists. Tao describes this as a transition from “proof scarcity” to “proof abundance”: producing candidate proofs may soon cease to be the main bottleneck. 

Instead, the scarce resources will become verification, explanation, interpretation and community acceptance. Existing mathematical institutions — peer review, journals, conferences and informal expert checking — were designed for a world in which proofs were difficult and relatively rare, and may become overwhelmed if AI can generate them at enormous scale.

For Tao, however, mathematics is much more than producing logically correct proofs. A complete mathematical contribution begins with choosing or formulating a worthwhile problem, finding a solution, verifying it, explaining the argument clearly, identifying what is genuinely new, connecting it with existing mathematics and, ultimately, having the result understood and absorbed by the mathematical community. 

AI is increasingly capable of solving and formally verifying problems, especially through tools such as Lean and AI-assisted formalisation, but Tao worries about mathematically correct results that no human truly understands. Such proofs could create a vast body of technically verified yet intellectually inaccessible mathematics. Human mathematical judgment — deciding what is interesting, elegant, useful or conceptually important — therefore becomes more valuable rather than less.

Tao believes mathematicians must rapidly adapt their culture, education and institutions rather than allowing technology companies to define mathematics simply as the production of solutions to difficult problems. Students should still develop mathematical intuition independently before relying heavily on AI, while researchers should develop better benchmarks for assessing AI systems transparently, including their failure rates and the number of attempts required to produce a solution. 

Projects such as First Proof, the Leiden Declaration on Artificial Intelligence and Mathematics, and Tao's new video journal Mathematical Discourse represent attempts to reshape this future. Tao also sees enormous opportunities: instead of using AI merely to chase prestigious famous problems, mathematicians could employ it to explore thousands of smaller questions, creating a more experimental and collaborative form of mathematics. His central message is therefore not that AI will destroy mathematics, but that mathematicians must urgently redefine what their profession values: understanding, explanation, judgment and the creation of meaningful mathematical knowledge, rather than proof generation alone.

Key takeaways

• Proof generation may no longer be the bottleneck. AI could make candidate mathematical proofs abundant, shifting the difficulty toward validation and understanding.
  
• A correct proof is not automatically valuable mathematics. Tao stresses explanation, insight, context and community acceptance.
  
• Human mathematical judgment may become more important. Choosing good problems and recognising significant ideas remain difficult to automate.
  
• Mathematics education must adapt carefully. Excessive AI dependence could prevent students from developing intuition and independent problem-solving ability.
  
• AI could still greatly expand mathematics if used for large-scale exploration rather than merely competing to solve famous open problems.
  
• Tao's deeper concern is who gets to define mathematics in the AI era: mathematicians themselves or technology companies.
  

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