Burt Totaro on Terence Tao's blog: what math loses if AI brute-forces the Hodge conjecture
natanielruizg · x · 2026-09-12
Terence Tao's blog published a guest post by Burt Totaro examining what's at stake if AI companies burn vast resources to prove new results like the Hodge conjecture.
- The Hodge conjecture crystallizes the relation between topology and algebraic geometry — flexible real submanifolds vs. rigid complex ones — predicting which real submanifolds can be deformed into complex ones.
- Totaro warns about the value lost if problems are solved indiscriminately via "LLM semi-brute-force", urging mathematicians to always think about counterfactuals.
- The post doubles as a reflection on why extremely hard problems matter to the mathematical community, and how that value should be weighed in the AI era.
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