My big question with all these announcements is: How many other people were using the AI on problems like this, and, failing? Given the excitement around AI at the moment I think the answer is: a lot.
Then my second question is how much VC money did all those tokens cost.
I've tried my hand at a few of the Erdos problems and came up short, you didn't hear about them. But if a Mathematician at Harvard solved on, you would probably still hear about it a bit. Just the possibility that a pro subscription for 80 minutes solved an Erdos problem is astounding. Maybe we get some researchers to get a grant and burn a couple data centers worth of tokens for a day/week/month and see what it comes up with?
The question is how many people tried to solve this Erdos problem with AI and how many total minutes have been spent on it.
Why do you care about either of those questions?
Because it could be a massive waste of time and money.
Why do you think it's a waste of time and money? I really can't see it.
Capitalism already is a poor allocator of human effort, resources, and energy, why lock in on this specifically? There's entire professions that are essentially worthless to society that exist only to perpetuate the inherent contradictions of this system, why not focus more on all that wasted human effort? Or the fact that everyone has to do some arbitrary sellable labor in order to justify their existence, rather than something they might truly enjoy or might make the world better?
> Capitalism already is a poor allocator of human effort, resources, and energy, why lock in on this specifically?
It's absolutely best allocator of human effort there is. It has some problems but compared to alternatives it's almost perfect.
No it is the best of what we know.
There’s something else out there that nobody has the imagination to personally figure it out and get alignment toward it.
It can also be true that capitalism is transitory to get to a place where much of the capital one needs is invented.
Looking around, the evidence doesn't seem to support this conclusion. 50% of food thrown away, yet people go hungry. Every privatized industry diminishes in quality and reach. Selects and optimizes for profit rather than for human need.
> Looking around, the evidence doesn't seem to support this conclusion.
It absolutely does if you look at facts and not "vibes". There are less people starving now than ever now and it's a giant, giant difference. We are tackling more and more diseases thanks to big pharma. Even semi-socialist countries such as China have opened markets. Basically the only countries that do not implement capitalist solutions are the ones you'd never want to live in such as North Korea or Cuba (funny thing - even China urged Cuba to free their markets).
I think we should at least ask the latter, if it turned out it cost $100,000 to generate this solution, I would question the value of it. Erdős problems are usually pure math curiosities AFAIK. They often have no meaningful practical applications.
Also, it's one thing if the AI age means we all have to adopt to using AI as a tool, another thing entirely if it means the only people who can do useful research are the ones with huge budgets.
Your logic undoes your point, because the kid who "solved" this technically didn't even have to invest in a degree.
America should fund tertiary education better, and that would solve even more problems.
Getting off-topic, but as a successful high-school dropout I am compelled to remind anyone reading this that [the American] college [system] is a scam.
That's not to say that there aren't benefits to tertiary education, for many people in different contexts. It's just not the golden path that it's made out to be.
Many people currently in college are just wasting their money and should enroll in trades programs instead.
Meanwhile, nothing about being in or out of school is mutually exclusive to using LLMs as a force multiplier for learning - or solving math problems, apparently.
Neither does the Collatz conjecture, Fermat's last theorem, ....
(Of course, those problems are on another plane than this one.)
But that’s exactly my point.
These are absolutely worth studying, but being what they are, nobody should be dumping massive amounts of money on them. I would not find it persuasive if researchers used LLMs to solve the Collatz conjecture or finally decode Etruscan. These are extremely valuable, but it is unlikely to be worth it for an LLM just grinding tokens like crazy to do it.
If solving even the biggest problems in pure maths is not worth it for you, then I guess we should stop all the pure maths research - researchers are getting paid much more than potential token spend, frequently for decades and they frequently work on much less important and easier problems.
Is it worth it to buy a super-yacht?
No.
Maybe... but I would love if 1% of the investment in AI were redirected to the mathematics education and professional research that would allow progress on any of these problems...
I would question at $60k. At $100k is a steal.
No meaningful, practical applications? You realize that sounds incredibly naive in the history of mathematics, right? People thought this way about number theory in general, and many other things that turned out to have quite important practical applications. Your statement is also a bit odd in that researchers are already paid throughout their whole careers to solve such problems. I don't know.
> You realize that sounds incredibly naive in the history of mathematics, right?
This is after the fact justification. You are arguing that because a thing (number theory) showed practical applications we should have dumped a lot more effort into it. There is no basis for this argument whatsoever; it also seems to involve inventing a time machine. Number theory had no practical applications until the development of public-key cryptography, but you cannot make funding decisions based on the future since it’s unknowable.
Once we get something working, sure, you can justify more aggressive investment. This is not to say that we should not invest in pie-in-the-sky ideas. We absolutely should and need to. Moonshot research or even somewhat esoteric research is vital, but the current investment in AI is so far out of the ballpark of rational. There’s an energy of a fait accompli here, except it’s still very plausible this is all unsustainable and the market implodes instead.
> Number theory had no practical applications until the development of public-key cryptography, but you cannot make funding decisions based on the future since it’s unknowable.
You are completely missing the point. The point is that we should invest in pure maths because it has always been an investment with very good ROI. The funding should be focused on what experts believe will advance pure maths more (not whether we believe that in 100 years this specific area will find some application) and that's pretty much what we are doing right now. I think it's just your anti-AI sentiment that's clouding your judgement and since AI succeeded in proving pure maths results, you are inclined to downplay it by saying that well, pure maths is worthless anyway.
Can you imagine how many bags of chips we could buy if we stopped funding cancer research?
It's so expensive!
Can you imagine how much ChatGPT cancer research we could fund if we stopped funding cancer research?