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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

#61

Post by fasterik »

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 could be right, but you're making a lot of assumptions about how complexity, scientific understanding, and explanations scale. One of the features of a good scientific discovery is that it often simplifies and compresses things that were previously a bunch of scattered facts. Also, as AI systems improve they'll get better not only at making scientific discoveries, but also at producing understandable explanations.

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

#62

Post by combobyte »

putlake wrote: post #24
EA-3167 wrote: post #18

Earlier quoted context omitted.

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.

It's not only going to be "connection maker". If and when robotics advance to a point where the LLMs are embodied, they can run experiments in the physical world and find new knowledge.

Being embodied is not the important barrier to running experiments. It's having access to a body of resources (i.e. funding and infrastructure).

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

#64

Post by chongli »

a2ff6eeb0 wrote: post #60
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…

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?

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

#65

Post by variadix »

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.

In the field of pure mathematics this might be true, but it has implications regardless for applied math, engineering, and physics.

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

#67

Post by a2ff6eeb0 »

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?

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 full, they just accepted the results as passed on by several layers of teacher.

I have a paper on routing algorithms, which I have attempted to read to my cat. I don't think my cat retained much, but they seem to be enjoying the cat food that got delivered using the results.

I'd suggest that we're going to be a lot closer to the cat than the author of the paper when AI takes off.

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

#68

Post by esafak »

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.

Is it the AI's fault we can't understand? If the GUT is beyond human comprehension does it matter less? We don't apply this reasoning to other animals or even to less capable humans. Besides, the robots may want to ponder maths for their pleasure.

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

#69

Post by ashleyn »

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=...

Wow, what a great comparison. LLMs are great at reasoning but absolute dogshit at simple arithmetic. If there's a raw calculation involved I always tell it to use python to add it all up.

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

#70

Post by esafak »

orphereus wrote: post #34
ianm218 wrote: post #23

Earlier quoted context omitted.

> That's something AI companies would really want you to believe. Why would I care what they want me to believe? Intuitively it would make sense that you can put math ability on a chart with a value for “general public” “smart high schooler” “smart undergrad” “smart PhD/ professional”. And you could place frontier AI somewhere on that chart over time from GPT 2 to now and see the trend. Then you’d have to consider th…

> Why would I care what they want me to believe? How would you not care? Are you a robot? They can say random stuff with the goal of increasing their shareholder value. Things they spit out do not have to be true. It is not easy to verify things they say, therefore, everything they say should be taken with a huge grain of salt.

He's saying he can connect the dots without their help.
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