We're running out of math. Maybe the president needs to establish a Strategic Math Reserve.
Tao: Open math problems being non-renewably mined by AI
81–90 of 349 posts
Re: Tao: Open math problems being non-renewably mined by AI
#82It's the same pipeline problem coders have been talking about; once AI does all the work, how are people going to get the experience necessary to take part productively?
Re: Tao: Open math problems being non-renewably mined by AI
#83This to me is another level of dishonesty. Imagine if a company producing math software starts to hear "rumors" someone is using their software to prove an important result and start massive runs of that software to beat the team. That may not be illegal per se but it is incredibly deceitful. I wonder if the original mathematicians should start a lawsuit for theft of intelectual property.
Re: Tao: Open math problems being non-renewably mined by AI
#84I 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.
his whole point is that specifically problems that have been held as important by consensus in the field are a finite resource. obvious example being the Clay millennium prize problems. seems like they function to shape the direction of future research into useful directions. which is to say, the process of developing a solution itself generates more useful problems.
of course thrrr are tons of problems once you remove this social consensus based filter. if i’m not mistaken Ramanujan left a book of dozens of unproven theorems, for one quick example. i don’t think that that has opened up dozens of fields of mathematical research.
Re: Tao: Open math problems being non-renewably mined by AI
#85This is just the age of slop mathematics, if it doesnt lead to our lives neing improved none of this matters. Math peeps are being nerd sniped by AI in the same way SWEs (the worst ones) got sniped by claude code. Building solutions to problems that dont matter for the sake of doing it just because you can. You'll ultimately waste a ton of time and get lapped by people doing real world work that actually improves the…
alright, i'll bite: what real work did you put out there that has improved the lives of regular people in the past one year? (without the use of ai, needless to say)
Re: Tao: Open math problems being non-renewably mined by AI
#86I think this is where people will have to let go of the ego of being the "sole author" of a solution for us to move into the next era of human flourishing.
Re: Tao: Open math problems being non-renewably mined by AI
#87That’s not untrue. But it’s also a misstatement of mathematical history. Many leading mathematicians historically have been highly competitive — Gauss comes to mind. Woe betide the lesser intellect that sent Gauss some ideas. The Newton Leibniz controversy was very serious business at the time in the UK and the continent. It was considered at the least a sin to reveal that sqrt(2) was irrational to those outside Pyth…
Between people.
Re: Tao: Open math problems being non-renewably mined by AI
#88I 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.
I think "close to completion" is not the right framing. Creating good open problems was an achievement because these problems often sit at the edge of known techniques, and solutions require inventing "new math". It's hard to find these problems, and they take decades to mature as they withstand scrutiny by many people.
In another comment below, I likened this to clear-cutting a forest. Growing the forest takes a lifetime; destroying it could happen in the next few months.
Re: Tao: Open math problems being non-renewably mined by AI
#89I 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.
It's easy to come up with new open problems. It's hard to come up with new open problems that seem to teach us something fundamentally new about the world. Our current batch of problems went through a complex selection process over decades (or centuries) based not purely on difficulty but also on perceived insightfulness.
I studied math, but I am not a mathematician, so I think I have a slightly different perspective on this than Tao overall. This is certainly the definitive end of an era in mathematics, but I think he's wrong that insightful new open problems are truly non-renewable. They might be non-renewable by humans at the rate at which they are being closed, but I see no reason why AI systems could not also discover insightful new open problems. In fact, once we have Riemann-capable AI mathematicians, I'd personally love to see what the next Riemann hypothesis is, which even these AI systems cannot solve with any amount of available compute.
I think we're about to find that, on the spectrum of mathematical intelligence, the best human mathematicians were only a fraction of a percent forward from the very beginning, and there's a vast universe of mathematical depth that's beyond our ability to imagine or work on directly in any way. We're used to feeling like we're able to directly perceive the Platonic realm, but we're almost certainly going to discover that our own minds, even when joined together over centuries of deliberation, can only interact with a tiny little shadow within it.
Re: Tao: Open math problems being non-renewably mined by AI
#90I 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 if people are disincentivized from trying to solve deep problems or study them for understanding as opposed to simply focusing on verification. It's more of a social and community problem than a fundamental problem with mathematics itself becoming "completed".