alt Hacker NewsWhen high quality effort is applied to a tool, such as AES or the linux kernel, we intuit that it "hardens" the tool. That is, it makes the tool more correct, more resilient, less assailable, etc.
Similarly, when effort is applied to an open problem, such as the Riemann hypothesis or P v NP, without progress, it "hardens" the problem: it makes the problem feel more daunting to whoever takes a stab at it next.
Andrew Wiles, whose interview also hit the homepage today (https://news.ycombinator.com/item?id=49075264), couldn't just tackle Fermat's Last Theorem head on, he had to wait until a different, modern problem reduced to it, because FLT had gathered this mystique of unassailability through its 300 years of existence.
A thing I worry about is that as AI transmutes tokens into effort, it'll split the world into two: some problems will yield, making human effort entirely unnecessary, and others will harden to the point where human effort will feel increasingly less worthwhile, because "even AI couldn't solve it". I don't like this. AI is spiky, so I suspect it'll continue having major blind spots, and yet its mere presence will probably have a chilling effect on what would have otherwise been useful human effort.
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This is a problem that will solve itself, people will continue to work on the problems that AI fails at, likely by telling AI the approaches they want AI to take.
AI is nowhere near the intelligence of a very educated person that has innate talent for problem solving. It does solve the problem of applying human intelligence on problems that truly need it. AI is also a great tool to see if there's something simple that we've missed or just haven't even attempted due to wrong assumptions.
i think id almost worry more that ai can solve problems in latent space that it cant translate back to tokens because decoding ruins it, and that we wont be able to come up with concepts that we can map to properly decode those solutions in a way people understand
I wouldn't worry about too many mathematicians adopting the "even AI couldn't solve it" attitude.
Business folks riding the hype train? Maybe.
1. Some of the "AI" proofs applied existing human work from lesser-known papers. AI proofs could solve the long-standing problem in math of almost all attention concentrating on less than 1% of authors. Human effort from the other 99% would have otherwise been wasted, which AI can rescue and give credit to thanks to its superhuman ability to match patterns across reams of text.
Humans may remain superior in spatial / non-verbal reasoning for a while longer yet, and, in the meanwhile, computers may aid us in collaborating to put that to use better.
2. AI-assisted, computer-verified proofs could further democratize mathematics by reducing the power of connections to get a reviewer to look at a journal submission. We can then also decouple the two tasks of
3. Searching for previous work and finding the edges of human knowledge are now easier. And we can leap across tedious terrain that the machine has the patience to plod through to find more interesting questions.