Comment by musebox35
16 hours ago
You can find Tao’s arguments here: https://mathstodon.xyz/@tao/117237320796901560
He argues that the supply nay be very large indeed but the interesting subset is not. Figuring out the interesting problems is difficult so strip mining the good known problems may lead to scarcity. I am not a mathematician myself, can not judge this accurately.
A Swedish proverb says, "a fool may ask more than ten wise may answer". This fool is reporting for duty! I'm glad I may have something to contribute after all (and I'm only halfway joking)
i'd be curious to hear why he thinks ai couldn't help make it easier to discover interesting problems, ie to make the interesting subset less scarce.
I guess you can see this as an exploration problem, in pure maths, while the goal is to solve a conjecture, the limitation of humans on pure computational power led to the exploration of alternative paths. Sometimes, these paths weren't leading to solving the initial conjecture but opened new idea and new direction. Sometimes a less direct but more humanly natural path was taken to solve the conjecture which also led to new and humanly understandable questions. In some ways solving the question wasn't the most important part of the work, as this doesn't have direct impact on our life (as I saw people comparing this with drug discovery), but the path leading to the solution raised new conjectures and techniques that further developed the field.
I have a really hard time reading AI proof so this might be a biased statement, but most of them feels like having a superpowerfull machine, that would have bruteforce all the possible words of finite length in your logical syntax. You have the path to the solution, using tools that where already known and even direction that where abandoned because they seemed to fail for our human brain. But at the end, as a mathematician, you don't learn anything that is really new.
To me this is the main risk with AI and in general the one most mathematican try to explain but fail, we might miss a lot of alternative path that would have raised more interesting questions (I think this is already more or less what is happening). On top of that, we will run out of mathematicians as no one wants to pursue a career in the field anymore.
This relies on the idea that AIs will only ever do the thing they just did, and nothing more.
It's the same argument which is invariably wrong yet comes up over and over again.
There's no real reason to think AIs solving lots of problems will stop further work on alternative paths - certainly a machine which never tires and can be trained on its own solutions is going to continue to improve.
There's precedent for this: just look at any overconfident post regarding what China will clearly never be able to do, despite decades of steady if frequently flawed progress.
There's no persuasive argument being presented as to why machine mathematical research should have a limit beyond hardware capabilities.
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The most immediate answer is because the models are proprietary and only available to those who want to hype the big labs.
We can speculate on whether it can’t, but its plain to see that so far it hasn’t.
Given how new it is, it seems premature to draw any conclusions from that.
If a human had solved these problems, we'd expect it to take years for people to digest them and formulate significant new advances.
Given the demonstrated rate of improvement of AI in math this year, I don't understand the value of that latter observation.
That’s what we are doing with nature, seas (look up strip mining there, it’s a horrible practice), and now the industrial harvestors are strip mining problem spaces. How do we like our own medicine?
Developing solutions to mathematical problems generally leads to improvements in quality and quantity of life at roughly the speed they percolate from the ivory tower down to the shop floor. So "how do we like it" is probably going to be "we like it a lot, this is awesome".
Every company is about to have a staff Ops Researcher who has a better grasp of the underlying math and theory than any university professor. That is an unambiguous win.
I see no reason why every company would have a staff ops researcher, or why such a position would have a better grasp of underlying math beyond the narrow slice that directly benefits the company. Why do you think that would happen?
> virtually none of this stuff is possible with technology any normal citizen has access to.
Not sure about the unambiguous win. Are we entering the age in which mathematics is industry-dominated?
1) Any university professor can spend their 24 years on a problem with little progress. 2) company has sudden interests. 3) industrial resources brute force the Lean proof. 4) Max PR for AI company 5) professors are left to rewrite the AI Lean slop into real human-readable math? {disclaimer non-math university professor}
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Who is "we" in that sentence? Why are you not speaking for yourself?
AI math: "We believe this resolves all remaining questions on this topic. No further research is needed." https://xkcd.com/2268/
"Further research is needed to fully understand how we did such a good job."