let's focus on good definitions...” Today, I'll explore a seemingly simple question: what is a rotation? I'm asking for the definition of a rotation, which »

After writing the previous post, I came across several related things that I thought I'd like to share. This serves as an appendix of sorts. The »

Random objects are weird... randomness itself is weird... math in general is weird.— Wire Tapper (@genepeer) February 10, 2017 I've had this thought stuck in »

This is the first of a series of post that I've been working on while I wait to get back to school. It's in the same »

Pierre de Fermat (1607-1665) is my outlier of mathematics: not because math was just a hobby for him — he was a lawyer by profession; nor »

On the last post, I gave a naive idea of where the Jacobian determinant comes from when changing variables: it was the volume of an approximate »

Years ago I used the Jacobian determinant to find the area of an astroid and made a note about finding out where it came from. There »

This is just a collection of my thoughts on debates/discussions and how being a mathematician has shaped them. It's mainly sparked by a group chat »

Suppose $$I = [0,1]$$ and $$f: I \to I$$ is a continuous function. Definition 1. $$f$$ has a period-$$m \ge 1$$ point if there exists »

In the beginning, there was nothing, $$0 = \emptyset$$. Then we realized it was something, $$1 = \{ \emptyset \}$$. Then we wondered, why not have another thing? $$2$$. And »