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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

#181

Post by paulpauper »

philipfweiss wrote: post #102

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…

Yeah, LLMs are great at generating negative results for math-related prompts "We scanned values {a,b,c} from 0-100 and no results" Great..too bad journals will not publish this. But good job, I guess. A negative result is only truly useful if it can be bounded, requiring an actual proof.

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

#182

Post by lokar »

aurareturn wrote: post #100
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.

When people make these comments about string theory, are they at the forefront of quantum physics theory and have spent years on modern string theory? Or did they just watch a YouTube video and then keep parroting this?

Or the just read Woit, uh, 20 years ago now, “not even wrong”.

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

#183

Post by chongli »

akiselev wrote: post #129
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?

> 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? It depends on what exactly you mean by "commercial value commensurate with the costs involved" but I'd volunteer the 3G/4G/5G specifications and the other documentation required to implement the mobile network protocols. 5G is currently sitting at ove…

Read the rest of the discussion. The claim is about text which is in principle incomprehensible to humans.

If there exists a text which only one person can understand, that person can communicate their understanding to others, even if that doesn't help them with the original text. That dissemination of knowledge is what provides the value, not the mere existence of the text. If that person forgets or dies before they can share their knowledge then it will be lost.

We have many examples of this from history: ancient texts written in a lost language. These texts provide us with no value until the day they can be deciphered, unless you count linguistic puzzle-solving as a virtue.

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

#184

Post by rho138 »

yen223 wrote: post #52
rho138 wrote: post #38

Earlier quoted context omitted.

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

Not sure if you're referring to LLMs or humans here

(¬_¬)

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

#185

Post by [deleted] »

chongli wrote: post #137
a2ff6eeb0 wrote: post #106

Earlier quoted context omitted.

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.

No, I gave you a lot more leeway than that. Take any utterly incomprehensible piece of writing from the entire history of civilization and demonstrate its value. You keep falling back on "incomprehensible for some people" but that wasn't the claim. It was about a text which is incomprehensible in principle ; that is, utterly impossible for any human to ever understand .

[deleted]

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

#186

Post by paulpauper »

fooker wrote: post #176
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.

It helps though if you have many problems to work on

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

#187

Post by KolmogorovComp »

nickysielicki wrote: post #172
atleastoptimal wrote: post #97

Earlier quoted context omitted.

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 chan…

It used to be the same with assembly. Programmers complained the one generated by compilers was not pretty, but now in 99.999% of the cases, it does not matter because nobody look at it.

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

#188

Post by tcp_handshaker »

tomrod wrote: post #165
philipfweiss wrote: post #102

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…

What is next years tsunami of change? Asics?

They are always out of stock, and you can never find your size..

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

#189

Post by nobodyandproud »

bze12 wrote: post #57
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.

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

We Americans call it grit.

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

#190

Post by okamiueru »

tossandthrow wrote: post #171
okamiueru wrote: post #156

Earlier quoted context omitted.

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 computat…

The thing about discussing or explaining constraints, is that it rarely is useful or productive if the other side does not accept (or understand) the reality of them.

Turing completeness is not exactly a high bar, and it's genuinely confusing as to why you bring it up. Your C++ precompiler is exactly as intelligent as whatever is your favorite agentic workflow with whatever harness you're referring to. Both might be Turing complete. Neither are intelligent. But one of them seems to be fooling you to think otherwise.

There have been many times that the C++ precompiler produced some output I couldn't understand. I might even at some point thought it was trying to tell me something profound I was too dumb to comprehend. Turns out it was just a missing semicolon.

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