Terence Tao argues AI has created proof abundance in math and calls for a Math 2.0 that looks past problem solving
- Tao argues mathematics has entered an era of proof abundance because proofs are objectively verifiable and digitizable, which makes them well suited to machine learning.
- Given enough compute and frontier models, many open problems that were thought difficult can now be solved in relatively short time, often without special expertise from the user.
- Tao says most problems at the current research frontier remain unsolved despite press releases and social media claims, and he calls for Math 2.0 that expands the frontier while decentering problem solving.
- Tao argues problem solving is only a proxy for long-term goals, and further blind optimization of it is now actively harmful to the long-term health of mathematics.
- Tao calls for transparent AI assessments that report resource consumption and negative results, and points to the First Proof effort as one example.
Hacker News opinions
Tao is out of his lane. Lots of medicines don't have understood mechanisms, and we don't even have the mechanism behind general anesthesia nailed down.
Medical trials are based on effects, not mechanisms. I'd take the medicine that's proven to work over the one that's interesting for academic reasons but doesn't actually work.
Not fully understood in clinical medicine is not the same as just guessing with a compound. Repurposed drugs often have partial mechanisms. AI boosters blur that with the LLM sense of 'not understood' and it's basically wordplay.
AI has been turning computer science into biology for a decade. Neural nets need empirical study now, and math gets that same reckoning. I'm not sure mathematicians are ready for it.
I'm still not sure about math-2.0. AI and computer use wear people down, and AI may find useless results like P==NP with O(n**4242424242424242) complexity.
Some monocrop problem in academia here. Globalization is flattening the diverse search paths that used to come from several schools and slower communication.
Honestly I'd take a cancer cure nobody understands. Medicine already works that way, and we find side effects decades later.
The problem is the cart before the horse. You need to validate the cure against all the other candidates, and that's the hard part when nobody has a coherent rationale for why it works.
We don't know how acetaminophen works, thousands get their livers destroyed every year, and we still haven't banned it. So how is this new?