One book that comes to mind is On Numbers and Games by John H. Conway. It sort of presents a theory of transfinite numbers, using some sort of game theory. I have only read a little of it and quickly found it a little too difficult to follow without getting out my notebook.
It's somewhat nonstandard, probably not a textbook for any class, and rather abstract as the transfinite numbers are pretty abstract. It's definitely rigorous, though.
You might want to read some original groundbreaking math papers. What they present will be fresh and unique by definition.
I'm also reminded of Category Theory by Saunders Mac Lane, the guy who invented it. It doesn't get any more abstract than category theory.
Happy 2021!
It doesn’t seem to be grounded in philosophy. I would argue Jon Conways writings on games and numbers are a clear influence. https://www.amazon.com/Numbers-Games-John-H-Conway/dp/1568811276