131–140 of 340 posts
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This is literally why we need a functional copyright system To block progress. Got it.
This is the literal opposite of progress: stealing from people genuinely creating, and stealing the money they should earn
Copyright maximalism is a bad look on a site called "Hacker News." Perhaps other sites beckon.
> We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential. In other words, the "right" people need to solve it: the mathematicians who made it their job and not the people working to push AI models forward? Struggling to understand how a solution to a millennium proble…
This is not at all what he said? I'm not sure how you got this from anything he wrote, actually.
I didn't realize that open math problems were a finite resource. I recall a story about some famous mathematician (Gauss?) dismissing interest in Fermat's Last Theorem claiming that he could crank out problems of equivalent interest. Clearly Tao knows a hell of a lot more than I do about this, but I'm surprised that math that close to completion.
They aren't, but the problem is that open problems tend to emerge when people are working on other problems. If fewer people are spending time deeply thinking about current problems since a handful of labs are solving them with AI without an eye towards understanding and only on verification, the pool of open problems won't be continuously growing. There is a fear that there will be a chilling effect on the community…
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So we can let the ai generate some math problems based on the solutions found? Other fields (computer science, physics, ...) can generate math problems too.
There's an infinite number of possible math problems, but the things that make these open problems worthwhile is they're interesting to people who have worked in related areas. They're good to give to new mathematicians, and they're good to help humans understand the shape of the problem space and relative difficulty with the tools we have. Cheesing these problems with LLMs gets rid of both the training benefit and o…
But from paleontologists' perspective, they go out looking for dinosaur fossils when they have questions that digging up a fossil may answer. The metric they're focusing on isn't tons of fossil mined out of the ground, it's a developing understanding of extinct life.
> We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential. In other words, the "right" people need to solve it: the mathematicians who made it their job and not the people working to push AI models forward? Struggling to understand how a solution to a millennium proble…
If there are no incentives for mathematicians to work on and share progress in tough problems because they will get scooped, then they will end up quitting and in net we will see less progress overall.
Time to consider re-training to become a nurse, electrician, auto mechanic, or a plumber.
I didn't realize that open math problems were a finite resource. I recall a story about some famous mathematician (Gauss?) dismissing interest in Fermat's Last Theorem claiming that he could crank out problems of equivalent interest. Clearly Tao knows a hell of a lot more than I do about this, but I'm surprised that math that close to completion.
That is exactly what Tao is explaining in that tweet.
TLDR: Open Problems are infinite, but those which are at the boundary of easy and hard problems and are interesting are far more scarce
I didn't realize that open math problems were a finite resource. I recall a story about some famous mathematician (Gauss?) dismissing interest in Fermat's Last Theorem claiming that he could crank out problems of equivalent interest. Clearly Tao knows a hell of a lot more than I do about this, but I'm surprised that math that close to completion.
Earlier quoted context omitted.
Yes, and they will. But what's happening here is that the system that cultivates mathematics (and mathematicians) is recieving likely the biggest shock of its history. How do you reward merit and identify talen when people can't absorb the number of proofs being generated, much less understand them? Perleman's proof of the Poincare conjecture took several years for the mathematical community to digest; the proof of N…
So what happens to this world view when AI not only clears the forest of problems we couldn't solve but also in the future discovers more forest with trees bigger than anything we've ever seen before? Not sure what the point of this argument is. Do we have mathematics for the sake of mathematicians good mental health and career or to solve and discover novel problems? Why should we care if mathematicians can understa…