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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

#171

Post by tossandthrow »

okamiueru wrote: post #156
tossandthrow wrote: post #146

Earlier quoted context omitted.

Maybe you can enlighten us. In what way aren't LLMs able to make new contributions. LLMs in agentic harnesses are Turing complete. To my best knowledge, we don't know of any greater computational model that the brain is a part of, that LLMs are not.

First of all, the argument isn't that LLMs (with I assume some automation) cannot be used in searching a problem space. I'm assuming this is what you're referring to, in terms of contributions? That's the part where LLMs are used as tools. Which there are plenty of places where they are useful. Also, do you know what turning completeness is? Why are you bringing that up here? The crowd that AI psychosis has brought t…

> That sentiment makes me cringe. If you understand how LLMs work, you'd know

> But not in the "I'd love to learn more" kind

I hope you are able to see the problem in your own communication here.

Computation classes are interesting because they say something about fundamental capabilities.

Two machine that are Turing complete are in theory able to carry out the same computations. They are isomorph mediums of computation.

Regardless. Please keep it sober. If you think you know something, enlighten us. But don't just propagate out lies.

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

#172

Post by nickysielicki »

atleastoptimal wrote: post #97
chongli wrote: post #26

Earlier quoted context omitted.

We don’t trillions of dollars in LLM investment to build things mathematicians don’t understand. We already have plenty of those, even from ancient times. As to your second point, Terry Tao already has an answer [1]: the proof isn’t the contribution, shared understanding is. This issue was already raised back when the four-colour theorem was proved. Machine proving and machine proof checking are useful tools but they…

If humans have nothing to contribute then shared understanding is a pointless endeavor. It makes sense now in the "centaur" period where human + AI > AI alone, but when AI mathematicians are both more rigorous and more elegant, then taking the time dumbing down their proofs to a human level of understanding is like requiring that we ensure all our current proofs be understandable by a monkey.

> If humans have nothing to contribute then shared understanding is a pointless endeavor.

I agree, but as a software engineer this gives me pause because I keep trying to insist on coding standards but I’m unable to come up with a compelling reason why it matters. Ostensibly the reason we cared about things like DRY and code quality was so that it would be easy to understand and easy to maintain and easy to make changes to later. But it now seems like a shared understanding of the codebase is less important than ever, and it’s more about shoveling requirements in without breaking any existing functionality.

Is a well tested slopfest better? That seems to be the conclusion for mathematics, so why not software too?

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

#173

Post by fooker »

This misses a very important point.

It’s not just about out remembering, it’s about breadth.

Mathematicians are all about depth. It’s pretty much impossible to become an expert in more than one narrow field of mathematics.

AI is happily applying techniques and abstractions across these silos.

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

#174

Post by a2ff6eeb0 »

chongli wrote: post #164
a2ff6eeb0 wrote: post #151

Earlier quoted context omitted.

Can you give me an example single piece of writing that the author didn't claim they understood? I don't think that any utterly incomprehensible writing exists. If you want examples where nobody but the author understands it, examples are a dime a dozen.

So you concede the point then. The age of humans comprehending things is not coming to an end . And therein lies the rub. When it comes to intellectual labour: Understanding == Value If a mathematician produces something incomprehensible then it has no value. It's meaningless. Indistinguishable from random noise. An AI which produces incomprehensible text is producing no value. We didn't need to spend trillions of do…

You may have missed the present tense. I didn't say it's over, but that it will be. Please pay attention and don't make straw men.

Again, do you believe that there are documents, of any value, that humans don't understand?

Maybe an LLM could help you notice what I was saying, since it's clearly beyond at least one human's comprehension!

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

#175

Post by rowanG077 »

EA-3167 wrote: post #131
rowanG077 wrote: post #118

Earlier quoted context omitted.

For some research funding is mostly the salaries of the people doing the research.

What research works that way?

large parts of Computer science, mathematics, theoretical physics, economics, some humanities research and I'm probably missing a ton.

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

#176

Post by fooker »

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.

Mathematicians routinely spend years on a problem without getting anywhere.

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

#177

Post by nickysielicki »

chongli wrote: post #64
a2ff6eeb0 wrote: post #60

Earlier quoted context omitted.

Why not? We build cranes to hoist weights construction workers can't lift. We build electron microscopes to measure things physicists can't see. Why is it so hard to imagine we can build tools to think thoughts we can't comprehend? If there's commercial value, I think it's inevitable. We don't fund mathematicians because it's cute when they understand a problem, but because their work tends to have applications with…

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?

Can you give an example of a 4-wheeled vehicle that could move at tens of miles per hour before the automobile was invented?

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

#179

Post by nickysielicki »

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.

was. Not is. Was.
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