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AI isn’t outthinking mathematicians, it’s out-remembering them

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Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#101

Post by greazy »

breadzeppelin__ wrote: post #44
Animats wrote: post #33

Yes. That's how LLMs do programming, mostly. It's also why LLMs don't need abstractions or parsimony as much as humans. They can work on something complicated without simplifying it first. This has major implications that haven't been fully realized yet. On the math side, there are long machine generated proofs. On the code side, there are high volumes of code with similar code not being folded into functions.

I've been working on generating a large code base for the last couple of weeks. Finally got around to generating a sort of code-duplication report and have spent the last week just having it de-duplicating logic that had been strewn all over the place (eg 11 different functions all doing date math to add x days to a date). dozens of items that had each been similar functions duplicated numerous times. crazy. (opus-5-…

Can LLMs not do this for you? Or would they go too far?

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#102

Post by philipfweiss »

One thing about human mathematicians is that they only publish positive results. Professors etc might have file drawers full of "negative results", but the incentives and bandwidth of human mathematicians makes publishing these useful results impossible.

But AI agents have no such limitations and can publish and re-use negative traces easily. There have been some recent projects (https://www.theoremdb.org) aimed at exploiting this fact. https://news.ycombinator.com/item?id=49227505

In general though, LLMs do not have the same limitations and incentives as human mathematicians, and the next year's tsunami of change will make this abundantly. clear.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#103

Post by nullc »

fsmv wrote: post #47
a2ff6eeb0 wrote: post #5

Does it matter? It's going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers. The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.

The entire point of writing proofs is for advancing human understanding. A giant dump of symbols that passes the lean compiler is meaningless besides human beings understanding it.

Sometimes the purpose of the proof is simply to demonstrate that some construct is a safe assumption for other more interesting work-- and could still serve that purpose even if it was entirely a black box.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#104

Post by chongli »

hilariously wrote: post #89
tengbretson wrote: post #82

Earlier quoted context omitted.

String theory is a great example of a dead end kept alive by ego and sunk cost fallacy. An AI would have declared it dead and moved on 10 years earlier.

Ok Sabina, everyone is string theory is all just a bunch of egotistical morons.

No, not morons, but people who have built a career on string theory. At this point, even if they regret their decisions, it’s too late to turn back now.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#105

Post by wongarsu »

password4321 wrote: post #77
bze12 wrote: post #57

Earlier quoted context omitted.

AI has sitzfleisch https://en.wikipedia.org/wiki/J._Robert_Oppenheimer#:~:text=...

My browser doesn't do the fancy URL text selection... sitzfleisch: the ability to endure or carry on with an activity Something Oppenheimer did not have, apparently.

loaned from German, where it's originally a way to say buttocks, literally "sitting flesh". If you have more Sitzfleisch you can sit for longer. Both in the literal sense (a bigger butt makes sitting more comfortable) and in the figurative sense (having the mental ability to sit for longer, get more desk work done)

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#106

Post by a2ff6eeb0 »

chongli wrote: post #90
a2ff6eeb0 wrote: post #67

Earlier quoted context omitted.

Yeah, how many people do you think understand the Linux kernel in full? What percentage of the people using it to great commercial effect can understand it? How's your understanding of Schroedingers "An Undulatory Theory of the Mechanics of Atoms and Molecules"? You seem to be using the results of it as applied to semiconductor engineering just fine. And, I promise you, most semiconductor engineers haven't read it in…

You've moved the goalposts. The original claim was about producing mathematics that are in principle impossible for any human to understand . All the stuff you've listed is understood by some person, and that understanding is the source of its value. Now that we've cleared that up, can you furnish an example that satisfies the original claim of incomprehensibility and value?

You asked for examples, for a technology that we're still building. Maybe you can see the issue with that?

Anyways, people benefitted greatly from Newton's laws of gravity, even though we still don't have a quantum-compatible set of laws for it. The laws of gravity are still incomprehensible for people, but the approximation that we've observed is still immensely valuable.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#107

Post by hn_throwaway_99 »

ralusek wrote: post #81
ComplexSystems wrote: post #9

It's also "out-brute forcing them." It just never gets tired. If a mathematician picks a research direction and spends a whole week on it and it doesn't pan out, they will likely be annoyed, need a break for a while, etc. This thing just does not ever get tired or discouraged or care; it's just onto the next thing until something ends up working.

We're just going to slowly deconstruct every element that could be a factor of intelligence. It's not out-thinking, it's just out-remembering It's not out-thinking, it's just out-working It's not out-thinking, it's just able to consider more things simultaneously It's not creative, it's just randomly generating things and then selecting viable ones

But the difference really does matter and is not just a case of "whittling down" what intelligence really is.

We have known for a very long time that computers and machines are much faster than humans, more accurate, are scalable in certain ways that humans aren't, and they don't tire. I think most people who are not in the "AI cult" would agree that LLMs and modern generative AI are really just an extension of those faster/more accurate/more scalable and never tiring traits. But there does seem to be (and I'm sure folks much smarter than I have quantified this or described it better than I can) a fundamental difference in how humans think, especially as it applies to what true "understanding" really entails, and for the ability to think up truly novel and unique things that are not just a rejiggering/recombination of training data. I believe those skills really are at the heart of human cognition, and as impressive as LLMs are in replicating what this looks like, there are plenty of "LLM failure modes" where it's clear that LLMs lack a true understanding of concepts or the ability to generate useful, completely novel ideas.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#108

Post by orphereus »

lowbloodsugar wrote: post #74
chongli wrote: post #64

Earlier quoted context omitted.

Can you give an example of an incomprehensible piece of writing (any writing, never mind a proof) that has commercial value commensurate with the costs involved here?

I know right? And there’s only a market for maybe 5 computers in the whole world. Paul Krugman (1998): predicted the internet’s economic impact would be no greater than the fax machine’s. The 1876 Western Union memo dismissing the telephone as having too many shortcomings, and the banker telling Horace Rackham not to invest in Ford because the automobile was a novelty. We are in good company!

Past performance does not guarantee future returns.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#109

Post by jansport123 »

a2ff6eeb0 wrote: post #5

Does it matter? It's going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers. The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.

That maybe true at some point, but i don't think we are there yet.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#110

Post by nomel »

B-Con wrote: post #99
ralusek wrote: post #81

Earlier quoted context omitted.

We're just going to slowly deconstruct every element that could be a factor of intelligence. It's not out-thinking, it's just out-remembering It's not out-thinking, it's just out-working It's not out-thinking, it's just able to consider more things simultaneously It's not creative, it's just randomly generating things and then selecting viable ones

It's almost as if we're building something that... mimics intelligence.

Can you mimic intelligence?
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