Terence Tao says AI is pushing mathematics into an era of proof abundance — and blindly solving more problems could hurt the field
Terence Tao just gave a talk called Math 2.0, arguing that AI is fundamentally changing how mathematical research works.
For most of modern mathematics, proofs were scarce.
Solving an important open problem could require years of specialized human work.
Tao says that assumption is starting to break.
With enough compute and access to frontier AI models, solutions to many previously difficult open problems can now be produced relatively quickly — sometimes without the person prompting the model having specialized expertise.
He calls this the beginning of an “era of proof abundance.”
But Tao’s warning is more interesting than the capability itself.
He argues that blindly optimizing AI to solve more open problems could become actively harmful to the long-term health of mathematics.
Why?
Because open problems aren’t just boxes mathematicians want checked.
Tao describes them as “lighthouses” that guide researchers through unexplored mathematical territory.
While trying to reach one, mathematicians often discover:
- New techniques
- Unexpected connections
- Better explanations
- New questions
- Deeper understanding of why something works
The final proof can sometimes be less valuable than everything discovered along the way.
If an AI jumps directly to the answer, Tao argues that it could effectively skip that exploration and “sterilize the surrounding field.”
He also warns about reporting bias.
Social media and AI lab announcements mostly show successful AI proofs, while failed attempts, compute costs, and problems that models still can’t solve often remain invisible.
Tao’s idea for “Math 2.0” isn’t to stop using AI.
It’s to use AI for more than just racing toward solutions — including explaining opaque proofs, mapping connections between research papers, exploring variations of theorems, building formal mathematics libraries, and helping humans discover new mathematical principles.
His bottom line is interesting:
The biggest bottleneck to Math 2.0 may no longer be technology.
It may be imagination.
If AI can eventually solve open problems faster than mathematicians can study them, should solving the problem still be the main goal of mathematical research?
Source:
https://teorth.github.io/tao-web/slides/math-2-0-caltech-2026.pdf