Comment by lordgrenville
17 hours ago
Haven't been following this debate closely, but what's the issue with "strip mining open problems"? Surely the supply of interesting mathematical problems is (in theory) infinite?
17 hours ago
Haven't been following this debate closely, but what's the issue with "strip mining open problems"? Surely the supply of interesting mathematical problems is (in theory) infinite?
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.
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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.
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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.
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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."
These are a specific set of interesting, compelling, human-sized problems curated to motivate clever people to engage with math.