I hate to be the one to point this out but how have we gone to the point where one of the world's Premier mathematics thought leaders is communicating through a medium that requires clunkily reading and combining multiple distinct sections and 'read more'links just to get through the thought
Tao: Open math problems being non-renewably mined by AI
381–390 of 401 posts
Re: Tao: Open math problems being non-renewably mined by AI
#382In the comments:
> @tao curious to know what makes LLM fundamentally different compared to (other) automatic theorem provers?
It highlighted that "automatic" is a spectrum. And the norm is shifting toward "fully" (even if the process is chaotic).
Re: Tao: Open math problems being non-renewably mined by AI
#383Earlier quoted context omitted.
So when AI is also better at coming up with the tasks and already solving the frontier problems? 1M AI agents running full time thinking at 10M times faster than humans, with 100 times the intelligence in each agent? Any human ideas regarding "frontier problems" or "what the AI should focus on" are irrelevant. We have automated our own thinking and human cognition will be about as important as being "the best at abac…
Before AI, did you find that the existence of human expertise in the world far surpassing yours 'automated your thinking and cognition' or limited your intellectual scope to inventing party-tricks? I've always found greater intelligences than mine are like runways for curiosity. It's hard to believe anyone in their presence would fall into a stupor instead of being highly stimulated by them - and I can't see why it w…
I think the main point is the ubiquity of AI intelligence. If there is a human far surpassing me, but unavailable to me, then I have to work through it myself. If the answer is a prompt away, then why bother.
Re: Tao: Open math problems being non-renewably mined by AI
#384Hmm, can't we just keep a better track of who comes up with some idea/concept/problem, etc, not just "who published a proof"?
It seems like new age requires a new form of publication instead of sticking to 17th century concept of a "paper".
Re: Tao: Open math problems being non-renewably mined by AI
#385Tao's central point seems to be : "In short, the indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained. " I am no mathematician, may have misunderstood his point and would be delighted to receive any corrections.
Indeed it's as if we've harvested all the large oak trees and can no longer make trans-Atlantic wooden ships and now must move on to metal. And doing that actually required stumbling on coal which ultimately was old wood. And then metal enabled us to move past coal. None of this was necessarily visible at the time but is the arc of progress. Of course mathematics being a purely abstract thought medium may not have the benefit of the physical / material world's progression. However it is ironic that here mathematics is progressing specifically because of how far along our material world has come. We're already at the point where a tiny nearly nil percentage of the population can reason at the frontier in mathematics, Terrence Tao obviously included in that small number, and if in the future that number truly reaches nil and only computers can go forward it's not so clear how fundamentally different the world will be to me. The hope is that the innovative manifestations in the real world will be able to be enjoyed by all just as one hopes mathematicians' thought exercises do unlock real blapplications.
I think the deeper point Terrence is making is simply that the information revolution which is the culmination of the mathematics revolution has less low-hanging fruit today. That was true ever since Claude Shannon
Re: Tao: Open math problems being non-renewably mined by AI
#386Earlier quoted context omitted.
What do u think lean is? That's like saying a program that works, is inscrutable because it appeals to the oracle of "code test cases" to prove itself correct. You're either being intentionally obtuse, or unintentionally ignorant.
Have you tried to read the Lean proofs produced for any of the recent high-profile results? They're extremely long, terribly structured, and don't indicate which parts are restating known results from literature and which are unique to the proof at hand. That's what makes them inscrutable. It's similar to Mochizuki claiming to have proved the ABC conjecture, with a proof depending on ideas developed over a large numb…
Tldr.
For all your bombast, do take a moment to note that no mathematician has actually said openai has not produced a correct solution. Should make you think.
Re: Tao: Open math problems being non-renewably mined by AI
#387Earlier quoted context omitted.
>>which actually deals with the finiteness of the list of problems that a machine successfully exhausts. This is already the case with most DevOps jobs with Claude Code. There are only that many finite issues that need fixing in production, even for very large systems. So you don't need all that many people to run ops these days.
Yet as a customer I don't think I've got to endure as many outages in my life before 2026 as I did for the past 9 months… And it's not just github, everything seems to be down on a daily basis right now.
Seriously, it feels like services that were once rock solid are now trembling every time the wind blows.
Re: Tao: Open math problems being non-renewably mined by AI
#388I'm with @nilesh on this one, and not exactly sure how merely the existence of a solution precludes the advancement of human knowledge. If a problem is "solved" (say, symbolically verified) without any insights gained, it doesn't seem very interesting to the profession. Navier-Stokes is a bit different (because there's a prize attached, so "scooping" matters), but almost all interesting problems don't have any prizes…
> all interesting problems don't have any prizes attached.
prize is not just monetary
Re: Tao: Open math problems being non-renewably mined by AI
#389Earlier quoted context omitted.
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…
there's a book I read "The Practice Effect" such that technology becomes super advanced based on using something, it gets better and better, but the people regress and become more like a medieval society as they just care that using things improves them.
I think this is how Asgard worked.
The tech got so advanced people kind of used the advanced tech, but looked pretty much like a how medieval society would. Even their politics.
Re: Tao: Open math problems being non-renewably mined by AI
#390Tao's central point seems to be : "In short, the indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained. " I am no mathematician, may have misunderstood his point and would be delighted to receive any corrections.
Doesn't this seem to be where all domains are headed? I get kinda freaked out when I feel like all the AI "utopianists" haven't taken the next logical step of thinking about what society looks like when humans are subpar in every domain (and you may argue this won't happen, though I'm becoming more and more a believer that it will, but my point is the utopianists believe that this absolutely will happen, and that it'…
Obviously it is a ludicrous example, but there are books for this: The Culture novels by Iain. M. Banks.
I'd be quite happy as a citizen of The Culture.
But, on a more serious note, or more realistic, I find it vaguely insulting that you think that so many of us are just so shallow we'll not figure out how to live meaningful lives in an AI dominated future. The world is already meaningless. Some people live in the US, get tech jobs and live lives of almost indescribable luxury compared to someone born in South Sudan. There are beggars on the streets of most African countries, who are deformed of malnutrition and suffering in pain. There are children who will never know true happiness, and die in misery.
It's all fucking senseless and nasty, and as someone who originated from such a poor country it is infuriating to see spoiled developed world complaints sometimes.
We live, suffer, die. Some suffer less, some a lot more. We find out own meaning somehow, in this brief weird experience that we perceive as conscious life.
If an AI can bring a few billion 3rd world people out of misery, I don't think I'm going to shed tears if that means you have to somehow "find meaning" outside of a high paying tech job.