There are many examples throughout mathematics of abstracting the formal properties of a "familiar" structure, but then having a theorem stating that all models of the abstract axioms embed into one ...
Hopefully Math Overflow is the correct place for this. I had a student approach me ask me what kinds of mathematics goes into the study of wormholes. She specifically asked whether there is any ...
I am wondering what are the prerequisites for being a modern geometer? It seems that the amount you have to know is just huge: differential geometry, differential topology, algebraic topology, ...
Recently I've been reading "Topology" by Klaus Janich. I find this book very entertaining as it contains lots of graphical illustrations that appeal to my "geometrical" imagination. In paragraph 3.6 ...