What's the next step in mathematics research after imaginary, complex, numbers?

Surreal numbers

I believe a lot of the bleeding edge stuff with math is being done around knots and complex planar geometries, but that could just be my naive impression based on my interests and how the recommendation algorithms pop up as that stuff sometimes is tangentially related to topics on Youtube I watch sometimes.

I think a lot of this stuff has very useful applications as well. Remember that the James Web Telescope had a lot of folding parts and there’s a lot of research being done into engineering origami-like folding structures.

I don’t know if I have an answer to your actual question, but if you haven’t read Flatland by Abbott, you should give that a read. It will stretch your mind a bit about the dimension question and it’s a lot of fun!

Quaternions I needed to use them in my Master’s thesis.