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^ » Descartes' Circle Theorem is a very remarkable and simple statement and, to prove it, I had to use three other surprising theorems of the triangle, including » Last post was a proof for the Inclusion-Exclusion Principle and now this post is a couple of examples using it. The first example will revisit derangements » The Inclusion-Exclusion principle is one of those things I understood quickly and intuitively; in fact, it seemed obvious to me. It was not until I tried » Today, I'll translate the proof for a theorem by André Schinzel that gives a circle with \(n$$ integer coordinates (also known as Lattice Points) on »