# Author Archives: TrueBeautyOfMath

## Your Sixth Sense

It is likely that until this moment in time you’ve been convinced that we have only five senses: seeing, hearing, tasting, touching, and smelling. This is, after all, what we’ve been taught since, well, I don’t know, forever I guess. … Continue reading

## The Three Worlds

I’d be shocked if you’ve ever come to this site and not once wondered what’s going on with that picture across the top of each page. Who is this old scholarly dude and why is he looking at me? What … Continue reading

## Meaningless Truth

In this note we’ll introduce the notion of a “vacuous statement”—a statement that is true, but completely devoid of meaning. In particular, we’ll learn what it means for some statement to be “vacuously true”. Statements that are vacuously true come … Continue reading

## Note on Notation

One reason why people are scared of/hate mathematics is that once people see an expression like they run and hide. Let us step back for a moment and try to see what’s really going on here, so that we can … Continue reading

## Proof by Contradiction

In this post we’ll learn one of the most elegant and beautiful logical weapons that mathematicians can wield. Every mathematician develops a toolbox for proving theorems, and this is one of the most powerful. Its Latin name is reductio ad absurdum, and … Continue reading

## Infinity Primes

Prerequisites: Prime numbers, proof by contradiction Here’s an awesome, easy, super clever, and really beautiful theorem/proof combination (which I cannot take credit for (Euclid can, though)). Once you’ve learned what a prime number is and how to use proof by … Continue reading

## What is abstract thought?

In various posts throughout this site we have discussed the notion of abstract thought. Abstract thought is the primary tool that mathematicians use in practicing their art form. In fact, one could reasonably say that mathematics is the art of pure abstract … Continue reading

## What is a mathematical structure?

In the post “What is math?”, we described mathematics as the art of creating and exploring mathematical structures. It is not unlikely, however, that the reader is slightly unfamiliar with the notion of a mathematical structure. If this is the … Continue reading

## What is mathematics?

Math isn’t what you thought it was. You might think that math goes something like this: Calculate or simplify the following expressions: the derivative of Well, that all sucks. No one wants to do any of that. From this, … Continue reading