## Update & Forecast

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. »

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 »

Sorry for the long hold up on another post. This new post is a result on my investigations on a proof of \(\zeta(2) = \frac{\pi^ »