On the other hand, taking notes with a lot of equations is cumbersome with a computer, and straightforward with paper and pen. I also can't do any serious maths without paper, e.g. playing with equations. It flows naturally with pen and paper, it is just horrible with a computer, unless you actually defer the equation solving to the computer using dedicated symbolic math software which is very useful, but that's not always what you want to do.

I am not sure about this. I talk basis on my personal experience, but typing is write things you listen. Handwriting implies listen, summarise and write (you are slower than conversation so you need make a just in time summary). Also handwriting is not only write text, I usually add non textual information like draw schemas, symbols, complex formulas, link with lines... implies a mental work that typing hasn't it