[Eufrat]

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.

[jasonfarnon]

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.

[peteforde]

Your logic undoes your point, because the kid who "solved" this technically didn't even have to invest in a degree.

[tomlockwood]

America should fund tertiary education better, and that would solve even more problems.

[peteforde]

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.

[anematode]

Neither does the Collatz conjecture, Fermat's last theorem, ....

(Of course, those problems are on another plane than this one.)

[Eufrat]

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.

[azan_]

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.

[mhb]

Is it worth it to buy a super-yacht?

[Eufrat]

No.

[anematode]

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...

[inerte]

I would question at $60k. At $100k is a steal.

[dinkumthinkum]

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.

[Eufrat]

> 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.

[azan_]

> 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.

[anthonyrstevens]

>> Number theory had no practical applications until the development of public-key cryptography

This is so wrong I don't even know where to begin. Modular arithmetic, numerical integration, pseudorandom number generation, error-correcting codes, predicting planetary orbits (!), etc.

[Eufrat]

At the risk of asserting the claim was obviously a bit facetious, number theory had the reputation of having very little practical applications and I don’t mean that silly quote by G. H. Hardy.

A lot of applications just required a lot more computing power to be practical. This all starts to happen around the same time (unsurprisingly) and if you’re going to make hay that Reed-Solomon coding was invented in 1960, I think it’s worth pointing the first big use of was on Voyager because the computing power was finally able to make these work. It’s not like people hadn’t started to notice some of this decades earlier.