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Why Erdős Problems Are Falling to AI

quantamagazine.org

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Re: Why Erdős Problems Are Falling to AI

#71

Post by dieselgate »

throwatdem12311 wrote: post #6

When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”. Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound? How can we possibly make use of these breakthroughs if we don’t understand them? How coul…

In college the punchline for all the engineer, physicist and mathematician jokes were something like "The mathematician says: Yes, there is a solution."

In all serious "I don't understand any of this it's way over my head."

Re: Why Erdős Problems Are Falling to AI

#73

Post by amberjack »

the_sleaze_ wrote: post #12
throwatdem12311 wrote: post #6

When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”. Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound? How can we possibly make use of these breakthroughs if we don’t understand them? How coul…

I don't mean to be dismissive, are these just old puzzles with no practical use whatsoever?

The problem is more that the puzzles had an original context and reasons why they arose from "real" problems directly or mathematical problems trying to solve "real" problems etc. but the presentation and abstraction hides this pretty well for people not "near" the problems.

Re: Why Erdős Problems Are Falling to AI

#74

Post by jbm »

lstodd wrote: post #48
eru wrote: post #27

Earlier quoted context omitted.

> When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”. Math is an incredibly broad field. I mean, you don't expect a traffic engineer to understand anything about nuclear reactors, do you? Yet, they are all 'career engineers'.

I would expect anyone calling themselves an engineer of any field to understand basics of fission power generation. Come on, it's 7th (school) grade material.

I went to a decent high school, this was not something covered in 7th grade. It isn't covered in my daughter's school either.

For the 2026 version of me out there, please ignore. It is nerd posturing, and as real as the boomers at your gym claiming to have benched 225/315/405 in high school, despite having terrible form while doing 185.

Re: Why Erdős Problems Are Falling to AI

#75

Post by torginus »

throwatdem12311 wrote: post #6

When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”. Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound? How can we possibly make use of these breakthroughs if we don’t understand them? How coul…

There's no honor in being stupid, yet I must admit I am stupid, as there's even less honor in being stupid and pretending otherwise.

A lot of people were super hyped about OpenAI's 10 discoveries, but I still don't understand what they mean, and even if I did, what are the implications.

Like, what are non-sofic groups, and what follows from the conclusion that they exist?

I mean in the sense that quantum mechanics might make my head spin, but it's because of that that we have stuff like semiconductors, which have been one of the most significant discoveries.

The Fourier transform is one of the reasons we have fast telecommunications and radars.

What practical things are possible or might be possible due to these results?

Re: Why Erdős Problems Are Falling to AI

#76

Post by ewidar »

m3kw9 wrote: post #24

is probably a mix of other math papers that combined can solve this, the ingredients were already out there and they got trained with it.

could be, I guess we'll see.

but even that, if done correctly, is quite impressive. It sure sounds very useful given the number of papers out there.

Re: Why Erdős Problems Are Falling to AI

#77

Post by stymaar »

nsxwolf wrote: post #44
throwatdem12311 wrote: post #6

When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”. Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound? How can we possibly make use of these breakthroughs if we don’t understand them? How coul…

Maybe the "beautiful, elegant" math is really just accidentally that way, just the tiny cross section our dumb human brains can understand. The vast majority of it could be inscrutable, ugly, chaotic and seemingly meaningless.

> The vast majority of it could be inscrutable, ugly, chaotic and seemingly meaningless.

It is, provably: per Curry–Howard correspondence, any program you write is a proof of a theorem, and it is indeed mathematically meaningless.

Re: Why Erdős Problems Are Falling to AI

#78

Post by randomizedalgs »

throwatdem12311 wrote: post #6

When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”. Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound? How can we possibly make use of these breakthroughs if we don’t understand them? How coul…

Even the experts on the problem being solved find the writeups nearly impossible to read.

Example: https://nitter.poast.org/henryquantum/status/208362369543662...

Seems like a disservice to the community that openai put so little effort into producing good writeups...

Re: Why Erdős Problems Are Falling to AI

#79

Post by gyomu »

the_sleaze_ wrote: post #12
throwatdem12311 wrote: post #6

When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”. Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound? How can we possibly make use of these breakthroughs if we don’t understand them? How coul…

I don't mean to be dismissive, are these just old puzzles with no practical use whatsoever?

The meaning of "practical use" is all about context - who/when/where/why/what - and so it would be kind of hard to definitely claim, in an intellectually honest way, that a piece of math is an old puzzle with "no practical use whatsoever".

Unless you want to be the guy in the 19th century making fun of Boole algebra for having no practical use. You might be right, but not for long.

Re: Why Erdős Problems Are Falling to AI

#80

Post by inigyou »

stymaar wrote: post #77
nsxwolf wrote: post #44

Earlier quoted context omitted.

Maybe the "beautiful, elegant" math is really just accidentally that way, just the tiny cross section our dumb human brains can understand. The vast majority of it could be inscrutable, ugly, chaotic and seemingly meaningless.

> The vast majority of it could be inscrutable, ugly, chaotic and seemingly meaningless. It is, provably: per Curry–Howard correspondence, any program you write is a proof of a theorem, and it is indeed mathematically meaningless.

Generating a value of type "Either (Int, String) Bool" is proving that there's at least one integer and at least one string, or there's at least one valid boolean value. Except in Haskell, where it could also be an infinite loop.
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