Apart from their technical statement and proof, a usual presentation of theorems is by leading up to them with a definite motivation or intuition, for example putting the results in the wider context ...
"Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions." Felix Klein What notions are used but not ...
There are many concepts in mathematics that begin with the German word "eigen": eigenvector, eigenvalue, eigenspace, eigenstate, eigenfunction, eigensystem etc. (to name just the most important (?) ...
I thought it might be fun to ask this question as a way of celebrating Pi Day. One way in which people popularize pi is that they say that even though it's defined in terms of properties of a circle, ...
I would like to ask about examples where experimentation by computers have led to major mathematical advances. Motivation I am aware about a few such cases and I think it will be useful to gather ...
Here is a topic in the vein of Describe a topic in one sentence and Fundamental examples : imagine that you are trying to explain and justify a mathematical theory T to a skeptical mathematician ...
It is not unusual that a single example or a very few shape an entire mathematical discipline. Can you give examples for such examples? (One example, or few, per post, please) I'd love to learn about ...
This post is community wiki. A comment on another question reminded me of this old post of Terence Tao's about toy models. I really like the idea of using toy models of a difficult object to ...
This question is inspired by a lecture Bjorn Poonen gave at MIT last year. I have ideas of my own, but I'm interested in what other people have to say, so I'll make this community wiki and post my ...
Or more specifically, why do people get so excited about them? And what's your favorite easy example of one, which illustrates why I should care (and is not a group)?