Why Erdős Problems Are Falling to AI • Hacker News Board

Re: Why Erdős Problems Are Falling to AI

#21

Post by ComputerPerson » Wed, Aug 05, 2026, 1:57 PM UTC

e4325f wrote: post #19

ComputerPerson wrote: post #2

The mathematics are above my intellectual capacities, but I still find the man and his lifestyle fascinating. Though I admit his heart attack probably wasn't a coincidence, sadly. I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS. I often see comment…

> Though I admit his heart attack probably wasn't a coincidence, sadly. He died aged 83...

I didn't know that. A poor assumption I made that his amohetamine use shortened his life significantly.

Re: Why Erdős Problems Are Falling to AI

#22

Post by RandomLensman » Wed, Aug 05, 2026, 1:58 PM UTC

the_sleaze_ wrote: post #14

RandomLensman wrote: post #8

Earlier quoted context omitted.

Which fund would that be?

https://www.rentec.com/Home.action?index=true > The company is widely considered one of the most profitable hedge funds in history, generating an estimated $7 billion to $8 billion in annual revenue solely from management and performance fees If you don't know Ren you should!

I meant which fund is supposed to be AI heavy? RIEF? RIDA? Medallion? Aren't they all quant?

Re: Why Erdős Problems Are Falling to AI

#23

Post by ComputerPerson » Wed, Aug 05, 2026, 2:06 PM UTC

qsort wrote: post #7

ComputerPerson wrote: post #2

The mathematics are above my intellectual capacities, but I still find the man and his lifestyle fascinating. Though I admit his heart attack probably wasn't a coincidence, sadly. I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS. I often see comment…

> I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS. The problem is that Paul Erdos was eccentric but he was also Paul Erdos. I'm not saying you're implying that, but I feel it's a similar line of thinking to how popular culture often romanticizes au…

FWIW I've worked in two different academic labs, both of which would have benefited from a runaway worker barreling down random paths, as long as they were being productive in some capacity.

Re: Why Erdős Problems Are Falling to AI

#24

Post by m3kw9 » Wed, Aug 05, 2026, 2:07 PM UTC

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.

Re: Why Erdős Problems Are Falling to AI

#25

Post by wat10000 » Wed, Aug 05, 2026, 2:11 PM UTC

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…

This has been an ongoing debate since the computerized proof of the four color theorem fifty years ago.

Re: Why Erdős Problems Are Falling to AI

#26

Post by eru » Wed, Aug 05, 2026, 2:11 PM UTC

ComputerPerson wrote: post #23

qsort wrote: post #7

Earlier quoted context omitted.

> I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS. The problem is that Paul Erdos was eccentric but he was also Paul Erdos. I'm not saying you're implying that, but I feel it's a similar line of thinking to how popular culture often romanticizes au…

FWIW I've worked in two different academic labs, both of which would have benefited from a runaway worker barreling down random paths, as long as they were being productive in some capacity.

> [...] as long as they were being productive in some capacity.

I'm afraid you only know that after the fact.

You might also like TempleOS, or at least the context and history behind it.

Re: Why Erdős Problems Are Falling to AI

#27

Post by eru » Wed, Aug 05, 2026, 2:13 PM UTC

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…

> 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'.

Re: Why Erdős Problems Are Falling to AI

#28

Post by bsaul » Wed, Aug 05, 2026, 2:14 PM UTC

something i've just realized : today long-standing maths problems are falling. It's great intellectually but won't probably have an immediate impact on our lives.

Now, what will happen once long-standing physics ( and chemistry and biology) problems will start to fall and at the same rate ?

Then we're going to enter a totally different world.

Re: Why Erdős Problems Are Falling to AI

#29

Post by eru » Wed, Aug 05, 2026, 2:15 PM UTC

a_conservative wrote: post #18

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 have the same questions about human mathematicians! I can't tell if xkcd #435 is still true, or if math is just as mushy as everything else seems to be. When a math proof can only be understood by a handful of people, what does that mean about that proof? I think the LLMs are pushing a problem that existed already and pushing it further. [0] https://xkcd.com/435/

That's why OpenAI also published machine-checkable proofs.

The process is very, very faintly similar to running a typechecker over your software sources.

Re: Why Erdős Problems Are Falling to AI

#30

Post by pfdietz » Wed, Aug 05, 2026, 2:15 PM UTC

Non-Erdős problems are also falling.

The AIs seem to have some combination of very broad familiarity with math (enabling relevant things from other subfields to be brought in to the proof) as well as patience and "sitzfleisch" (stamina in working through details even if they aren't immediately obviously promising.)

An obvious area for improvement would be automated generation of new conjectures and attempts to prove (or disprove) them, with the discovered arguments then being used as training for refined models. This will require autoformalization to check the results as there will be too many for manual verification.