Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

The fall of the theorem economy

davidbessis.substack.com

Post reply on HN
Print view View original

11–20 of 127 posts

Re: The fall of the theorem economy

#11

Post by varjag »

pfortuny wrote: post #6
jdw64 wrote: post #5

Someday, there might be mathematics designed for AI. Mathematics that only a tiny fraction of humans can understand, but a different kind of mathematics might emerge. I wonder if we would still call it mathematics. What would happen if a non-human layer of mathematics emerged on top of human mathematics? In this article, the distinction between Mathlib and Mathslop might be a precursor to that. If models advance enou…

Science is not about results, it is about the transmission of knowledge. So long as those AI-"sciences" are just inside AI, they are "engineering", not science. I am not dismissing engineering (it moves the world we live in), just trying to clarify what science is. Applied fluid dynamics works like that: noone has ever really "verified" that the finite-element method applied to some specific model does converge

Engineering is used fairly loosely these days but I insist engineering ends where you have to prove theorems.

Re: The fall of the theorem economy

#12

Post by bananaflag »

j7ake wrote: post #4

Does the the ⁡(,1) conjecture paper in annnals of Math say 7 years between submission and acceptance? Insane

These stories are common in math, e.g. these recently happened to me, a lowly mathematician:

1) Two and a half years with no reply from a journal (not even to emails I sent that I'd like to retract the paper so I could send it somewhere else). Then suddenly they tell me the paper is accepted.

2) One year with no reply. Then, my "anxious" collaborator sends them countless emails and gets redirected from person to person and finally an editor tells us that they decided almost immediately to reject our paper but they didn't tell us because "they hate giving bad news".

These were not top journals like Annals, but decent, prestigious ones, from whom you'd expect some professionalism.

Re: The fall of the theorem economy

#14

Post by jdw64 »

pfortuny wrote: post #6
jdw64 wrote: post #5

Someday, there might be mathematics designed for AI. Mathematics that only a tiny fraction of humans can understand, but a different kind of mathematics might emerge. I wonder if we would still call it mathematics. What would happen if a non-human layer of mathematics emerged on top of human mathematics? In this article, the distinction between Mathlib and Mathslop might be a precursor to that. If models advance enou…

Science is not about results, it is about the transmission of knowledge. So long as those AI-"sciences" are just inside AI, they are "engineering", not science. I am not dismissing engineering (it moves the world we live in), just trying to clarify what science is. Applied fluid dynamics works like that: noone has ever really "verified" that the finite-element method applied to some specific model does converge

So what I’m most curious about is this: if there are axioms and proofs so enormous that a human could never prove them in a lifetime, but a machine can, does that make it engineering? That’s the point I’m really wondering about.

I mean, what if a human could follow every single step of the process in principle, but the sheer volume is so vast that a human can never see the whole thing—would that be engineering?

But I don’t think of that as engineering. In the future, maybe it will be called an Oracle

Re: The fall of the theorem economy

#15

Post by stackbutterflow »

Tangential but this article got me thinking.

Are we going to see less publicly shared science? With private actors or governments restricting access to AI resources to a few scientists and keeping new knowledge to themselves.

Advancing science in the open was the best strategy when there was real advantage to share the load with every brain on the planet willing to give a try at science, but if a computer can match or surpass the collective output of the entire human scientific community the equation will change.

It's a sad outlook.

Re: The fall of the theorem economy

#16

Post by whack »

The core thesis seems to be that the "real value" is not in producing/proving theorems, but in understanding them. AI might be good at producing and proving theorems, but it fails utterly at getting humans to understand them. Even worse, humans have no interest in working on theorems that have already been proven, so we end up with theorems that will never be understood by humans.

I can understand why this is a major concern for mathematicians. They got into their field because they love the beauty of mathematics, and the intellectual satisfaction of understanding non-obvious insights. But to put it crudely, this sounds like a you problem. As someone who isn't a mathematician, the main value I get out of math is its practical applications in science and technology. And their practical applications in human life. I have zero understanding of the math behind cryptography, but I still deeply appreciate the practical value they have provided humanity.

If AI systems start churning out accurate theorem-proofs, and we are able to use those theorems to build things that improve human quality of life, it doesn't bother me one bit that those theorems have not been understood by humans. If this offends your aesthetics, you are certainly entitled to your opinion and your preferences, but that does not make it a societal problem

Re: The fall of the theorem economy

#17

Post by Staross »

I thought it was very interesting, but maybe also incredibly naive politically ? it's like he's re-discovering alienation under capitalism.

A wood-worker could do the same argument, there's the "official" wood-working word of perfect joinery and beautifully finished tables one can buy, but behind it there's the "secret" messy human element, the art, the craft, the mistakes and hard-ships, the elevation of human skills and imagination, the creation of whole new types of wood-working inventions and techniques, the perpetuation of millenia-old traditions, the teaching, the joy of selling to a happy customer, etc.

But now comes techo-capitalism, division of labor, you cut that piece a that piece over and over, you operate that machine, you won't even see the finished table, fuck your human element, we want that profit !

Re: The fall of the theorem economy

#18

Post by RandomLensman »

whack wrote: post #16

The core thesis seems to be that the "real value" is not in producing/proving theorems, but in understanding them. AI might be good at producing and proving theorems, but it fails utterly at getting humans to understand them. Even worse, humans have no interest in working on theorems that have already been proven, so we end up with theorems that will never be understood by humans. I can understand why this is a major…

Then you have to make sure that the AIs understand the theorems (sort of build a "world" for that - otherwise how'd there be confidence in the use of said theorems?

If cryptography didn't exist but the maths did, how'd you use it?

Re: The fall of the theorem economy

#20

Post by guelo »

When math is so divorced from science and engineering that there's no conceivable way that it will ever be applied in the real world then it is just a complex puzzle game that a tiny group of people play. It doesn't really matter much. If the 200,000 line Mathslop proof has no real world application and it doesn't help the puzzle solvers then it is double useless.
Post reply on HN