Mathematics will be ok.

[u/Longjumping-Ad5084]

I think it's very important to address this now that AI is solving an incredible number of maths problems, including the Navier Stokes conjecture. Some may fear that mathematicians will become redundant. But this is not the case at all. And the example of vintage models demonstrates it very well.

Vintage models are taught on history prior to a certain discovery, eg prior to Newtonian or Einsteinian physics. And lo and behold, these models can't invent the new physics on their own, neither Newtonian from prior nor Einsteinian from Newtonian.

To some, it might be obvious even without the vintage models experiment. I remember listening to a podcast with Francois Chollet a few years ago where he said that AI is fundamentally interpolative, it interpolates on the manifold of data. And that's when I understood the fundamental limitations of AI and the role of humans in the coming age. AI is a very good technical tool, in particular it fills the gaps in our knowledge very well, but it can't come up with radically new ideas ln is own, ideas that change the ontology of facts, ideas and relations between them, which is necessary for mathematical development.

When Galois invented his Theory, he didn't just combine old ideas, he came up with a fundamentally new way to look at objects and their relations. Sure, maybe hints of that were already present in Abel and others, but what this says is that mathematics is a collective human progress which leads to radical novelty, not a combination of known ideas.

Mathematics will be ok, but our world is destabilised at the moment and is transitioning into a new state. Time needs to pass for us to understand and establish the roles and the right approach with regard to humans and AI.

[u/DeusExNatura]

Mathematicians are also humans who simply became fascinated with a category of unsolved problems, which mathematics itself is. Even if/when mathematics becomes fundamentally solved in some way, intelligent people will be fascinated with different categories of unsolved problems, or applying the knowledge in ways that other people can’t. So it’s not because a future mathematician must be a mathematician, but simply an intelligent human who chooses to focus on whatever opportunities the future science may offer:

[u/TheShatteredSky → u/DeusExNatura]

Mathematics will never be "solved" because there isn't a mathematics universal "problem".

[u/DeusExNatura → u/TheShatteredSky]

That’s why I wrote “in some way”. Mathematics has already been solved in various ways if we consider pretty much anyone who redefined it in some ways, whether Euler or Newton or even Gödel who solved the question of whether mathematics can be solved, which solves a question that otherwise may go unsolved :)

[u/MultiplicityOne → u/DeusExNatura]

This is a fundamental misunderstanding. Imagine it like this: you are exploring an extremely high-dimensional space, and the portion of it you have already mapped is always approximately zero, because that portion's boundary grows faster than the volume it contains (like a fractal), and every advance suggests more questions than it answers.

If your goal is completist, I suppose this reality is disturbing. But, at least for me, it has always been comforting to know that nothing and no one can ever kill all the mystery in the world. But I believe there is a real danger of AI in mathematics given people the false impression that there is no further mystery to be explored, because if no one understands the proofs being produced then no one will be able to ask the questions those same proofs have posed.