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There's a fundamental difference between the goal of code and math. The goal of code is to produce software that does something useful. As long as the code does

There's a fundamental difference between the goal of code and math. The goal of code is to produce software that does something useful. As long as the code does what it's supposed to do, arguably, it's good to ship. (As you imply, we want the code to be good enough to also be reasonably certain there are not too many bugs, that it is maintainable and can be extended etc. This is what early models failed at but now seems broadly fine.) But for math: what is the point of a proof if no one will read it and no one uses its result? To quote the article, "AI systems will [...] result in the production of an abundance of PDFs. The contents of some of those PDFs may even have important applications." But if there's no one reading the PDFs, what's the point - no matter how good your AI model. The point of math is understanding. So mathematicians should feel free to use AI as much as you want, but in the end, they should've gained some understanding on what happened.

ComplexSystems 12d ago
> But for math: what is the point of a proof if no one will read it and no one uses its result? What is the point of writing software if nobody will run it? > So mathematicians should feel free to use AI as much as you want, but in the end, they should've gained some understanding on what happened. So they ask the AI to explain the proof.
kenjackson 12d ago
If the point of math is understanding then maybe our incentive structure is wrong. Maybe it should be teaching the concepts to as many people as possible rather than just continuing to write papers that 10 people in the world understand, which is the current state of a lot of math.
cman1444 12d ago
I keep seeing people repeat that the goal of math is "understanding". I do think that is one goal of math but I don't think it's the only one. I think an additional goal is simply "truth", which can be found without understanding as we've seen with these human-incomprehensible proofs. Yet another is practical applications. While there's less of these in pure mathematics than in most domains, they do still exist.
- curt15 12d ago
  The primary goal of all basic sciences is human understanding. "Truth" is no more a goal for mathematicians than the physical laws are a goal to physicists; they simply exist in nature. The goal is rather to develop useful language and conceptual frameworks for reasoning and communicating. That understanding underpins all practical applications.
  - bonoboTP 11d ago
    Sciences don't have goals, people have goals and they differ. Some are fans of pure math as a kind of religious or almost erotic activity in elegance and beauty, others are application minded. Some are in it for the community and outreach and conferences, some are in it to just sit in an office alone and be left alone to do it in a zen like flow state all day and night. Some treat it as a 9-5 to pay the bills with a skill they happen to be fit for but aren't especially passionate about.
bonoboTP 11d ago
I won't understand it, but can benefit from it in better data structures with proven invariants, faster algorithms, convergence guarantees for some iterative computations, better practical linear algebra and matrix factorizations, deriving things in statistical hypothesis testing, tightening upper and lower bounds etc. I don't care if some mathematician somewhere who isn't me "understands" it or not. It has practical use. I know that practical is dirty peasant word for many ivory tower mathematicians but that's their problem and I don't interact with them much, except when they throw a hissy fit like this and try to ban restrict matchmaking to their guild and ban the plebs from getting math from anywhere but them on their terms.

ComplexSystems 12d ago

> But for math: what is the point of a proof if no one will read it and no one uses its result? What is the point of writing software if nobody will run it? > So mathematicians should feel free to use AI as much as you want, but in the end, they should've gained some understanding on what happened. So they ask the AI to explain the proof.

kenjackson 12d ago

If the point of math is understanding then maybe our incentive structure is wrong. Maybe it should be teaching the concepts to as many people as possible rather than just continuing to write papers that 10 people in the world understand, which is the current state of a lot of math.

cman1444 12d ago

I keep seeing people repeat that the goal of math is "understanding". I do think that is one goal of math but I don't think it's the only one. I think an additional goal is simply "truth", which can be found without understanding as we've seen with these human-incomprehensible proofs. Yet another is practical applications. While there's less of these in pure mathematics than in most domains, they do still exist.

curt15 12d ago
The primary goal of all basic sciences is human understanding. "Truth" is no more a goal for mathematicians than the physical laws are a goal to physicists; they simply exist in nature. The goal is rather to develop useful language and conceptual frameworks for reasoning and communicating. That understanding underpins all practical applications.
- bonoboTP 11d ago
  Sciences don't have goals, people have goals and they differ. Some are fans of pure math as a kind of religious or almost erotic activity in elegance and beauty, others are application minded. Some are in it for the community and outreach and conferences, some are in it to just sit in an office alone and be left alone to do it in a zen like flow state all day and night. Some treat it as a 9-5 to pay the bills with a skill they happen to be fit for but aren't especially passionate about.

bonoboTP 11d ago

I won't understand it, but can benefit from it in better data structures with proven invariants, faster algorithms, convergence guarantees for some iterative computations, better practical linear algebra and matrix factorizations, deriving things in statistical hypothesis testing, tightening upper and lower bounds etc. I don't care if some mathematician somewhere who isn't me "understands" it or not. It has practical use. I know that practical is dirty peasant word for many ivory tower mathematicians but that's their problem and I don't interact with them much, except when they throw a hissy fit like this and try to ban restrict matchmaking to their guild and ban the plebs from getting math from anywhere but them on their terms.