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 because »

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 »

A lot has happened since my last blog post. I have completed two years of grad school and chosen my area of interest, Geometric Group Theory. »

Now seems like a good time to write about my failed math research. There are several questions I've never been able to answer and today I »

In the last post, Why Ordinal Numbers, I had intuitively guessed that I would be left with a perfect set after enough application of derived sets »

It's about time I write on a non-Euler topic -- the birth of ordinals. I've been reading Georg Cantor's Contributions to the Founding of the Theory »