Mathematics isn't art. It doesn't gain its value in human affairs from being interesting to study. I fail to see why we should cater to that.
Mathematics isn't art. It doesn't gain its value in human affairs from being interesting to study. I fail to see why we should cater to that.
I think everyone is conflating a few things:
* (1) Mathematics, the true things known by humans
* Mathematics, the things that are true
* (3) Mathematics, the institution which gets funding and manages resources to expand and maintain 1
AI agents can discover more true things, but that doesn't necessarily expand 1 and it might undermine 3
If someone is worried about 3 and you're talking about 2, then you are talking past each other
Yes, open source isn't art either, yet my point is that the same principle applies to both
There are many ways to stop progress and productivity
What is it, if not an art?
Truth.
What is truth if we are free to pick our axioms?
The universe is either Euclidean or not. If it were, how can theorems on non-Euclidean geometry be true?
You pick your axioms and you see what must be true. With math and logic, we can reason about any possible universe even though we live in only one of them.
A science?
It isn’t even as constrained by material reality as mixing oil paints to get a certain effect is.
Nope. Science demands empirical verification. Math doesn't. No theorem is violated based on experiments and observations.
Importantly, which mathematicians will understand deep useful math? Who will actually care about the knowledge we can generate at will?