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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

#161

Post by awesome_dude »

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

>that could be a factor of intelligence

Could is carrying a lot of weight here.

Because, what's really happening is we're saying "Oh these things are what defines intelligence" then implementing them and /discovering/ "oh wait, there's more to this than we knew".

We've known, for decades, for example that an IQ test is not a measure of Intelligence, even though people still refer to it as though it is. A computer passing an IQ test, therefore, would have been thought of as possessing intelligence way back when, but would not now.

Oh, on the point of "creativity" - is a RNG "creative"? It creates a value unbounded by human intervention (in theory, yes Pseudo RNGs have limitations) - therefore it must be creative... right?

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

#162

Post by AndrewDucker »

blovescoffee wrote: post #152
AndrewDucker wrote: post #112

Earlier quoted context omitted.

Your brain is not just a stochastic generator.

what is it?

It also creates and updates models, uses those models to make predictions, and guides the stochastic generation by comparing the output to those models and reworks them in real time.

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

#163

Post by Zigurd »

There are plenty of high value endeavors where being a superhuman knowledge remixer is right on target. But even capturing all of the knowledge is proving elusive.

I use coding agents. I think they're pretty good overall. They save me a lot of tedious coding. For example I probably wouldn't spend the time to implement native splash screens for all the build targets of a Flutter app, but I'll have the coding agent do it.

Nevertheless, for all the time that we've had coding agents, it's still trivially easy to find the jagged edges of their training. For example, Gemini evidently doesn't know if the Xcode part of a Flutter tool chain is misconfigured. That's not exactly a Millennium Prize problem. But it is shaped wrong for a training set for a coding agent.

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

#164

Post by chongli »

a2ff6eeb0 wrote: post #151
chongli wrote: post #137

Earlier quoted context omitted.

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 .

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 dollars on LLMs to figure that out. Markov chains can do that job perfectly well.

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

#165

Post by tomrod »

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?

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

#166

Post by ben_w »

AustinDev wrote: post #73
EA-3167 wrote: post #59

Earlier quoted context omitted.

Robots in labs already exist, but mercifully they're not hooked up to anything as unpredictable as an LLM. Robots tend to work best as specialists doing high-throughput, extremely repetitive tasks which nonetheless require a degree of precision. Giving a robot a "human" body makes very little sense if we're talking about the needs and productivity of a non-human; humanoid robots are marketing for humans.

Humanoid robots are obviously more than marketing. The entirety of human civilization is human shaped. Making robots that are human shaped is easier and more efficient than redesigning and rebuilding everything that exists.

> The entirety of human civilization is human shaped.

That's the marketing pitch.

A plumbing robot doesn't need to be humanoid, an octopus shape may well be better for all the awkward corners. A robot police officer could be the municipality itself for sensory nodes (essentially the sales pitch of Flock etc.), plus some drones or robot dogs to perform arrests*.

The robot vacuum cleaners and lawnmowers we already have are nothing like a human. A robot taxi driver can be just the car. Robot dogs are already used for maintenance and security sweeps.

If you've got wheelchair access, you've got wheeled robot access. If you've got guide dog access, you've got access for Boston Dynamics' Spot.

* this may be a bad idea with current robotics, but I aver it's not improved by making those robotics humanoid.

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

#167

Post by jstummbillig »

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.

> It's also "out-brute forcing them."

That is also approximately what people have always done to succeed.

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

#168

Post by scarmig »

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?

There are plenty of artifacts that, if not impossible for humans to understand, then at least no human has ever completely understood. To start with, the universe as a whole. Despite that, we are able to choose legible pieces of it to model and perform useful actions from.

This will shift your argument--that doesn't count! etc., to the point where it's by construction unsatisfiable and vacuous. And it doesn't matter: an LLM might e.g. break some cryptographic algorithm in a way utterly unintelligible to humans, but the fact that it works would be sufficient on its own to make all of us choose to abandon that algorithm and choose different ones.

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

#169

Post by Reubend »

impendia wrote: post #83
smokel wrote: post #46

Earlier quoted context omitted.

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, m…

Mathematician here. There is a lot of recent work on the Lean project -- when a proof can be translated into Lean code, then it can be strictly and formally validated. https://lean-lang.org/ But otherwise, mathematical proofs are read and written by humans, and at the end of the day the relevant standard of proof is what other mathematicians will accept. Occasionally, mathematicians don't agree. For a prominent examp…

For that particular example, it's now been proved that Mochizuki's proof is incomplete: https://zeli.app/en/story/48963019

I guess whether he will eventually fix those gaps and resolve the issues remains to be seen.

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

#170

Post by Zigurd »

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

If you make that list comprehensive, there's probably a Nobel prize in it for you.
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