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

davidepiffer.com

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

#41

Post by nmstoker »

thaumasiotes wrote: post #13
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.

> 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. Your timelines are a bit unambitious. There's nobody expecting to make significant progress with a week of work.

They were just illustrating their point, I wouldn't take that literally.

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

#42

Post by flatline »

d--b wrote: post #3

It is obvious that super intelligence comes from more working memory. It is the scary thing actually. Cause once AI makes arguments that require a working memory of hundred items, then we as humans will have no way of understanding the arguments… We can decompose and write things but only up to a point. when Ai can have a working memory that spans hundreds of books, we are necessarily going to have to trust the syste…

This is why we have hierarchies of abstraction. Pretty much every field of mathematics relies on constructing notations, models, and other tools to simplify things in a way that is verifiable. LLMs rely on the same basic technique, they can just pull from a wide variety of these abstractions at once. So far we've been able to understand their proofs just fine. Computer-assisted proofs in the past that relied on brute-force is where we have run into trouble. We cannot reason about millions of possibilities at once, and we had to trust that the computer program that analyzed them was correct, which is a really hard problem and leaves humans fairly unsatisfied. I think we are actually progressing in terms of understandability in computerized proofs.

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

#43

Post by tired-turtle »

d--b wrote: post #3

It is obvious that super intelligence comes from more working memory. It is the scary thing actually. Cause once AI makes arguments that require a working memory of hundred items, then we as humans will have no way of understanding the arguments… We can decompose and write things but only up to a point. when Ai can have a working memory that spans hundreds of books, we are necessarily going to have to trust the syste…

“is obvious” -- that’s what my Russian math professor said in college before skipping the rest of a proof.

But was it?

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

#44

Post by breadzeppelin__ »

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-utracode)

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

#45

Post by akiselev »

EA-3167 wrote: post #18
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.

The key here is that it’s depending on the human inability to connect the sum of relevant knowledge, but said knowledge comes from humans. Theres going to be this field day of low-hanging fruit that ML can round up, but after that I suspect it will be in fits and starts as a “connection maker” rather than some proof producer.

I think we're underestimating just how much low hanging fruit there is. I've been trying to apply this LLM research process to physics (QM and solid state) and there is so much missing in Physlib and the rest of the Lean ecosystem that most of my work has been trying to formalize the theories and validating them against the specification problem (and mostly failing badly).

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

#46

Post by smokel »

orphereus wrote: post #16

C'mon AI companies, pivot to lawyers or doctors already. Trying to convince us that mathematics and software engineering are "solved" is getting very tiring. The pushback would probably be too much for the soon-to-be IPO-ed companies.

Mathematics is typically concerned with "proofs" [1], which similarly to code, often allow for strict validation. Thanks to reinforcement learning techniques, it is now possible to train LLMs to perform very well on code generation, and mathematical proof generation.

Law and medicine are fundamentally harder fields to obtain decent training data for, and LLM results are therefore expected to be less powerful. Also, making mistakes in these fields is costly, but perhaps you were alluding to that already.

[1] https://en.wikipedia.org/wiki/Mathematical_proof

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

#47

Post by fsmv »

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.

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

#48

Post by ryeights »

rho138 wrote: post #38
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.

You’re prescribing elegance to a stochastic generator trained on the wealth of humanity, including 4chan. Let’s set our expectations a bit.

Your brain is a stochastic generator. Have you read 4chan?

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

#49

Post by a2ff6eeb0 »

tene80i wrote: post #28
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.

It’s possible, but there’s a difference between vastness and difficulty. Humans can’t compete with AIs on vastness of material they are familiar with, or the depth of effort they are willing and able to throw at a problem. But scale isn’t the only aspect of difficult scientific endeavours. There’s also theory. And advancements sometimes come through hard graft of knotting together many things. And sometimes they come…

I don't think that's true. Human intelligence is limited, and our brains are inefficient machines.

The tools we built to replace muscles have mostly obsoleted raw strength for tasks like excavating earth.

There's no reason to think we can't do the same for brains. And then we'll never need to think for a living again. Some people may want to do it as a commercially insignificant hobby, of course, the way people lift and compete in strongman competitions today.

We'll have AI taking care of our needs, the way a good mother takes care of their children.

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

#50

Post by dgellow »

orphereus wrote: post #39
dgellow wrote: post #32

Earlier quoted context omitted.

They can rely on compilers, solvers, theorem provers to validate the generated softwares and maths. That’s what makes it possible to iterate quickly in a loop and self correct. You cannot do that in soft industries like legal and medicine

That is not the point I was making. I am not talking about validating software or maths. It can generate stuff that is valid, but bad and incomprehensible.

What I’m saying is that AI labs are talking so much about software and maths because we already have tools that can say « it’s all good ». That makes it possible and worth it for them to spend 1 week of compute on a problem until the validator passes, then publish marketing pieces. You cannot do the same in medicine or laws (modulo some niche areas)
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