I haven't been around very much lately. I've been a graduate student in mathematics the whole time you all have known me, but now I have an adviser, and when you have an adviser, your adviser gives you a ton of shit to do, and that really cramps the whole making-jokes-on-the-internet scene. It's like he's never thought even once that I might want to try to make a bunch of anonymous porn addicts laugh with a three-paragraph joke about Nerlens Noel's haircut.

Is it good for anything? Probably not. Who cares?

â€”-

What I want to do right now, and hopefully on a regular basis, is describe the stuff I'm working on in plain English. I want to do this for three reasons: 1) Explaining mathematics to others, especially without specialized notation, is kind of hard and something I want to get better at; 2) explaining mathematics to others, especially without specialized notation, forces me to think about it in ways I might not have previously, and thus makes me a better mathematician; and 3) I truly believe that the stuff I'll be talking about is very interesting and cool and awesome, and I want to see if anyone here agrees, because you guys are my e-friends and e-friends tell each other about interesting and cool and awesome things. I'm very excited to make this one post and then not make another one ever again once I receive absolutely no feedback whatsoever, and also because I'm lazy.

Let's begin!

There's a very special set of numbers called the natural numbers, sometimes called the counting numbers, because you count with them. The natural numbers consist of 1, 2, 3, ... off to infinity, and they might include 0 depending on who you ask, and whether or not 0 is a natural number is one of those silly things some mathematicians like to argue about, usually loudly and in public, because they think it makes them look weird and quirky, and for some reason that is desirable to them. I am not friends with such mathematicians.

Contained within the natural numbers are the prime numbers. A number is prime if, among the natural numbers, it is divisible only by itself and 1. By convention, 1 is not prime. But 2 is! 2 is divisible by itself, and 1, and there are no other natural numbers that could possibly divide it. A moment's consideration leads you to the fact that 2 is the only even prime number; indeed, any other even number is, obviously, divisible by 2, and thus not prime. 3 is also prime, as is 5, 7, 11, 13, 17, ... off to...

infinity?

"Surely," you say to yourself, "there are infinitely many primes. After all, every natural number is just some collection of primes multiplied together, and since there are natural numbers as big as I want, if there were a biggest prime number, well, it just doesn't seem likely that I could obtain every number bigger than that by multiplying some subset of the finitely-many prime numbers together, even with repetitions, without missing a few."