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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

#111

Post by LPisGood »

matheist wrote: post #109
LPisGood wrote: post #41

Earlier quoted context omitted.

One of the most famous mathematicians of all time studied number theory. He wrote an apology to humanity for all of the very smart and capable people wasting time studying number theory, since these things are clearly unless old puzzles with no practical use whatsoever. Now, 100 years later, these results underpin all of modern public key cryptography.

And then there's G. H. Hardy, famous number theorist, who wrote an "Apology" for mathematics in the sense of defending the study of number theory for its own sake because it's beautiful. Which one were you referring to?

It is one in the same! The apology is, of course, defending the beauty of the pursuit but at the same time the writing acknowledges the (alleged) utter lack of practicality.

Re: Why Erdős Problems Are Falling to AI

#112

Post by wongarsu »

stymaar wrote: post #46
Levitz wrote: post #33

Earlier quoted context omitted.

It's just really hard to affirm that something has "no practical use whatsoever". Maybe it doesn't have use "now", maybe it doesn't have "direct" use but can be used for another finding that is useful, Math has a long story of finding out stuff that turns useful later on.

True. Though ~99% is still useless in the end.

As they say: 80% of marketing is useless, you just don't know in advance which 80%. Same with math

Re: Why Erdős Problems Are Falling to AI

#113

Post by bluefirebrand »

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…

> Are we ready to just let go of our intellectual faculties and give them to a giant supercomputer nobody understands

An unsettling number of people do seem to be more than ready for this. In fact I'd say they seem almost gleeful about it. Thinking is hard and they don't seem to like doing it!

Re: Why Erdős Problems Are Falling to AI

#114

Post by layer8 »

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…

> How can we possibly make use of these breakthroughs if we don’t understand them?

I mean, arguably the development of LLMs matches that description.

Re: Why Erdős Problems Are Falling to AI

#115

Post by eru »

inigyou wrote: post #82
parineum wrote: post #53

Earlier quoted context omitted.

They're publishing machine checkable proofs because that's the only way they, themselves, can check them. They don't understand the math either.

For 3.5 days we had a machine checkable proof the Collatz conjecture was false. There turned out to be a bug in the machine checker.

Yes, however any LLM agent you asked about that proof could tell you that. (And even most humans who know a little bit about the bug.)

You are right that Lean isn't great in this respect, and people are working on proof formalisations that are less prone to bugs.

Re: Why Erdős Problems Are Falling to AI

#116

Post by eru »

oliculipolicula wrote: post #103
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'.

No. Mathematicians who considered themselves experts on exactly those conjectures were bewildered. > And then -- the kicker -- something that I personally spent a couple years on in grad school, leading to some of my proudest work: quantum parallel repetition theorems ... > Is there some broader context or theory within which this would've been the obvious thing to do? What other results can be proven using these tec…

> we can however be optimistic, oddly. If you believe Feynman when he says that you can't explain to a child something you don't understand.. then we can see that ChatGPT has no idea of just what it has done!

Why would that be optimistic? Seems like the pessimistic reading to me, if anything. Or are you having a bout of Schadenfreude?

Re: Why Erdős Problems Are Falling to AI

#117

Post by lstodd »

epiccoleman wrote: post #100
lstodd wrote: post #59

Earlier quoted context omitted.

I can explain what the void coefficient is, why it is a dangerous simplification, why neutron moderation is needed, how it is typically controlled, why BWR reactors are inherently less stable than PWR. etc. it's simple really. All the while I have never had anything to do with nuclear power professionally or studied specifically it. I might have overstated a bit, but by 9th grade (15 year old) this is what was taught…

Man you went to a way cooler high school than me. I definitely was not taught anything that would help me understand how a nuclear reactor work.

having a lab assignment detecting beta-emission from 40-K (potassium-40 salt) is of course unthinkable nowadays. or idk, assembling a interferometer out of a HeNe laser for example. Whoa, no! Kids can get hurt!

Re: Why Erdős Problems Are Falling to AI

#118

Post by eru »

epiccoleman wrote: post #100
lstodd wrote: post #59

Earlier quoted context omitted.

I can explain what the void coefficient is, why it is a dangerous simplification, why neutron moderation is needed, how it is typically controlled, why BWR reactors are inherently less stable than PWR. etc. it's simple really. All the while I have never had anything to do with nuclear power professionally or studied specifically it. I might have overstated a bit, but by 9th grade (15 year old) this is what was taught…

Man you went to a way cooler high school than me. I definitely was not taught anything that would help me understand how a nuclear reactor work.

Not even basic thermodynamics?

Re: Why Erdős Problems Are Falling to AI

#119

Post by eru »

goodmythical wrote: post #51
lstodd wrote: post #48

Earlier quoted context omitted.

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.

Being familiar with the basics of fission power generation does not put the design of a competitive plant within your wheelhouse.

Nor understanding and judging a proposed design, yes.

Re: Why Erdős Problems Are Falling to AI

#120

Post by [deleted] »

svachalek wrote: post #40
serial_dev wrote: post #10

Earlier quoted context omitted.

I think it's the scientist version of "I vibecoded ten apps this weekend (at one point I'll have real users too)" . Because it's math, it's all mysterious and genuinely impressive, but in the end, if no human cares about it (apart from attention grabbing "it's so over" tweets and articles), does it really matter?

Nah, people are vibe coding lots of apps that no one cares about, but this is more like going through Stack Overflow and answering the most upvoted issues that don't have answers. These are published problems that have prior interest, for decades usually, and a few snarky internet comments don't undo that.

[deleted]
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