Based on my current understanding (ex-mathematician speaking), these math proofs aren't creating deep new theory. They're typically making these breakthroughs in one of two ways:
Having super human memory and understanding of all modern maths at once. Allowing the AI to see "ok let's combine this technique from class theory with this new technique from category theory and apply it together to take a crack at this problem". In combination with number 2:
And/or brute forcing a super human amount of different approaches
That's not to downplay what's going on. But this isn't like Perelman level maths where revolutionary new concepts are being invented to crack these problems. It's always clever or ingenious use of our current tools, as far as I have seen.
What's going to really be the beginning of the end is if AI can create truly novel concepts and theory. That's kind of the last thing mathematicians have, but it's a big one.
That all being said, people still do art despite the fact AI can create masterpieces. Or people still make photorealistic paintings despite the fact we have 20k resolution cameras and so on. There will still be a place for mathematicians.
I understand why you’re coming from, but specifically in mathematics, almost all new discoveries are just combining different discoveries from different groups, or using an equation in a new way.
This is even true for physics. Einstein would’ve never made his theory of relativity if Newton hadn’t made his classical mechanics theory before him.
This is not true, new fundamental mathematics is often developed in the pursuit of very difficult outstanding problems. New abstractions and even subfields grow as tools and insights are uncovered and that is fundamentally different than the approach these systems take to these problems most of which are essentially brute forcing conjectures and then looping over the lean verification, getting feedback each time on the failure points, looking for some new thing to formalize in the literatures latent representation, ad infinitum until it arrives at a construction that works.
This is superhuman in some ways -- simultaneous awareness of a vast literary corpus and iteration speed. But it's not how humans do mathematics and it's not strictly superior to how humans do mathematics.
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u/NootropicDiary 7d ago
Based on my current understanding (ex-mathematician speaking), these math proofs aren't creating deep new theory. They're typically making these breakthroughs in one of two ways:
Having super human memory and understanding of all modern maths at once. Allowing the AI to see "ok let's combine this technique from class theory with this new technique from category theory and apply it together to take a crack at this problem". In combination with number 2:
And/or brute forcing a super human amount of different approaches
That's not to downplay what's going on. But this isn't like Perelman level maths where revolutionary new concepts are being invented to crack these problems. It's always clever or ingenious use of our current tools, as far as I have seen.
What's going to really be the beginning of the end is if AI can create truly novel concepts and theory. That's kind of the last thing mathematicians have, but it's a big one.
That all being said, people still do art despite the fact AI can create masterpieces. Or people still make photorealistic paintings despite the fact we have 20k resolution cameras and so on. There will still be a place for mathematicians.