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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

#21

Post by logicchains »

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.

>produce proofs far more intricate than humans can understand

Math is not magic, a proof is just a series of applications of a set of rules on some axioms. A mathematician could understand any proof given enough time to study it; the only way for AI to make proofs that a human couldn't understand is by making really, really long proofs.

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

#22

Post by dgellow »

user982 wrote: post #2

Metacommentary: how did this post get to #5 on the front page with 1 upvote within 2 minutes of submission?

That’s how HN works, I had that multiple times over the years with my own submissions. Sometimes it gets picked up quickly, sometimes not. A post can also down rank very, very fast. It depends a lot on the level of engagement and the type of engagement

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

#23

Post by ianm218 »

orphereus wrote: post #11
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 age of humans comprehending things is coming to an end" That's something AI companies would really want you to believe.

> 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 that either you believe there is a fundamental limit that is below peak human mathematician level or there’s not.

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

#24

Post by putlake »

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.

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.

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

#25

Post by seeknotfind »

bewareofscams wrote: post #6

"It's not X, it's Y" hot take AI slop.

100%. Context is big for AI, but it's nothing compared to everything a human can learn. If you efficiently represent everything in context, it may be many papers, but if AI is actively working through proofs, it will quickly fill up. They're no denying AI is making strides, but pinning it to memory is an oversimplification.

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

#26

Post by chongli »

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.

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 don’t mean anything without the interpretative work and the communication necessary to build shared understanding.

[1] https://news.ycombinator.com/item?id=49056620

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

#27

Post by grebc »

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.

Ever heard of string theory.

People go whole lives without being able to make it pan out.

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

#28

Post by tene80i »

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 through the revelation of a deeper truth, or a new framework, a fundamental insight.

AI might help us reach the next level. But that doesn’t mean we won’t understand anything. It could be we have periods of vast intricacy we cannot follow, punctuated by profound elegance we (or at least experts) relatively easily can. And then the scaffolding we needed to get there falls away.

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

#29

Post by a2ff6eeb0 »

mettamage wrote: post #8
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.

But apparently we can teach machines to do it for us

Yeah. We can also teach machines to move hundreds of miles an hour, but we could never do it ourselves.

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

#30

Post by logicchains »

ChaseRensberger wrote: post #17
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 going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers. I agree. > 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. I don't know if I see this being true for quite a while, if ever.

> It's going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers. > I agree.

There's an infinite space of possible statements and proofs. The only thing that makes certain proofs significant is that human mathematicians consider them significant; if AI came up with a proof of some statement that no humans could understand then no humans would bother investing further resources in building upon it, for the same reason we don't waste computational resources iterating over the infinite space of true statements in first-order logic.

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