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Mathematics in the age of AI

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Re: Mathematics in the age of AI

#41

Post by a2ff6eeb0 »

TSiege wrote: post #37
a2ff6eeb0 wrote: post #25

I don't know why anyone should care about understanding the results if the AI is better at math than us. It'd be like demanding that human mathematicians are banned from publishing until their cats understand the theorems. If Amazon uses AI math to come up with better routing, the cats can benefit from cheaper delivery fees just as much as humans can. No understanding needed. The human brain is being obsoleted, soon…

I’m not anti AI but thinking the human brain is obsolete and using it will become a hobby is a dystopian view of the future where no one has any agency anymore. By your logic since our brains provide no value why not just shoot ourselves in the head while we’re at?

What's wrong with sitting on the beach with a bottle of wine for eternity, with no need to do anything, knowing that all your needs and desires will be automatically taken care of?

I don't think you can be coherently pro-AI without thinking that the human brain will be obsolete, unless you believe in some inherent magic that the brain is imbued with. The only other option is that you haven't thought through the long term consequences of the innovation.

Re: Mathematics in the age of AI

#42

Post by caglaroktay »

AI also can replace a lot of expert attention too. Why not? What is useful or what is not useful is based on the expert's narrow opinion. An AI system can do much more and deep value comparison. It looks like if our current technological advancement continues, in the space of what is possible (or even impossible), AI can find the optimal solutions better than any human or human organizations. But I think there is only one think will remain for humans to go for these solutions: what we value. that will be the last resort I believe and hopefully ai systems won't start manipulate us too as we are very fragile on manipulation.

Re: Mathematics in the age of AI

#43

Post by piker »

paulpauper wrote: post #20
highfrequency wrote: post #7

Terence Tao's quote about AI's math proofs is relatable outside of pure math: "the writing very often dwells at length on trivialities while passing briefly through — or even actively obscuring — the most interesting and novel portions of the argument."

Similar to Ai writing. Lots of bloat.

Coding, too.

Re: Mathematics in the age of AI

#44

Post by mmoll »

caglaroktay wrote: post #42

AI also can replace a lot of expert attention too. Why not? What is useful or what is not useful is based on the expert's narrow opinion. An AI system can do much more and deep value comparison. It looks like if our current technological advancement continues, in the space of what is possible (or even impossible), AI can find the optimal solutions better than any human or human organizations. But I think there is onl…

But how would „what we value“ still be relevant?

Re: Mathematics in the age of AI

#45

Post by frozenseven »

qsera wrote: post #11

If the title have said in the age of "LLMs", I might have given it a try.

Out-of-hand dismissal of Terence Tao is certainly a take.

And the term "artificial intelligence (AI)" has been the name of the field for 70 years and counting. If anything, "LLM" is a misnomer that's been lingering around since 2018-19. When the term was coined, these systems were relatively small, experimental, and could only produce impractical facsimiles of the English language. This is obviously no longer the case today.

Re: Mathematics in the age of AI

#46

Post by tossandthrow »

sonicrocketman wrote: post #8

Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.

I think any idea that is contingent on a human being in the loop, solely to the property of being a human is most practically doomed to fail, but is inherently anti scientific.

Science,at its core, does not care about the credentials or institutions. It cares about the results and to what extend they can be falsified.

This feel a bit like "we know all about physics, we can only get more precise" - moment

Re: Mathematics in the age of AI

#47

Post by frozenseven »

tocs3 wrote: post #15
rramach wrote: post #10

Terence argues that explanation of results ("understanding") will be the new bottleneck in math research but I am not sure this is the real bottleneck for progress. Understanding was critical for the field to progress when only humans were involved but if humans are not needed to make progress, I wonder if we split into two worlds: an AI math-world where amazing new results continue at a rapid pace bottlenecked only…

In some sense "understanding" (understanding if it is true, if it is important, how to use it) is about the only bottleneck in math. Any theorem that you can write down or imagine is already true, false, not provable already. In some ways we can already start iterating through all the theorems. We will never get to the end (or really get very far down the line) and most all of them be trivial (I think the Busy Beaver…

Chasing these 'trivialities' is a good thing, imo.

The Busy Beaver game has lead to a better understanding of complexity theory and automata. Also, direct "hands on" work on improving proof assistants and related tools.

Btw, for those who are curious, the Busy Beaver Challenge wiki is a treasure trove of rabbit holes and curiosities:

https://wiki.bbchallenge.org/wiki/Main_Page

Re: Mathematics in the age of AI

#48

Post by nilkn »

sonicrocketman wrote: post #8

Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.

I believe this rule of thumb will come to fail. The combination of superhuman mathematical reasoning and synthesis in upcoming AI models plus the rapid build-out of scalable formal verification infrastructure means this exponential in math is going to take off quite explosively, and we've barely seen anything yet. Mathematics is going to decisively move beyond human ability fairly soon (within our lifetimes, if not much more abruptly). It seems abundantly clear to me that much of the work will only be immediately accessible to AI, and rather than trying to explain all of it back to humans we will rather focus on explaining the portions that humans would benefit disproportionately from understanding.

Re: Mathematics in the age of AI

#49

Post by skybrian »

nilkn wrote: post #48
sonicrocketman wrote: post #8

Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.

I believe this rule of thumb will come to fail. The combination of superhuman mathematical reasoning and synthesis in upcoming AI models plus the rapid build-out of scalable formal verification infrastructure means this exponential in math is going to take off quite explosively, and we've barely seen anything yet. Mathematics is going to decisively move beyond human ability fairly soon (within our lifetimes, if not m…

Maybe that will be true when it's math with practical applications, but most theoretical math isn't like that. If it's not practical and it's not for mathematians to understand, what good is it?

Re: Mathematics in the age of AI

#50

Post by GPerson »

kriro wrote: post #35
sonicrocketman wrote: post #8

Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.

The counterpoint to this comes from chess. High level engines "prove" certain lines correct (not in the mathematical sense) but those "engine lines" are really hard to explain to humans, even by GMs. They can sort of explain that something is a good line but not why. Engines crush GMs and are considered ground truth even if noone really understands what is happening. Would it be a nightmare if math was the same, not…

I don’t think it’s pointless to spend time trying to prove a conjecture which is ultimately false if along the way you figure out a bunch of different true variations on the conjecture, which is how mathematics actually works. This is something I’m a bit worried about with LLMs since it gets you to the end too fast.
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