No wonder people think physics and math are so hard. Consider the following from Black Holes and Time Warps by Kip Thorne, a book I’m currently reading:
(pg. 463) Topology is a branch of mathematics that deals with the qualitative ways in which things are connected to each other or to themselves. For example, a coffee cup and a doughnut “have the same topology” because (if they are both made from putty) we can smoothly and continuously deform one into the other without tearing it, that is, without changing any connections.
Thus, we are forced to conclude that doughnuts and coffee cups are made out of putty. Aren’t we?