# The Birthday Problem

Yesterday, I had another article published for The Conversation. I wrote about the Birthday Problem, which (I think!) is well known to most mathematicians, but certainly not to the general public. Anyways, it was very well received. I guess it's a bit sad that there's a ton of crazy maths facts like this that we … Continue reading The Birthday Problem

# A sledgehammer proof of irrationality

Mathematical proofs are a bit like people. You can choose which ones to love and which ones to spit at. The loveable proofs are undoubtably the most important, especially as a pick-me-up on those cold lonely days. I'd like to share with you all a little proof that the $latex n$th root of 2 is … Continue reading A sledgehammer proof of irrationality

# Merten’s Function

I thought that today I might write about my most favourite arithmetic function. The Moebius function $latex \mu:\mathbb{N} \rightarrow \{-1,0,1\}$ is defined as follows: $latex \mu(1)=1$, $latex \mu(n)=0$ if $latex n$ is divisible by $latex m^2$ for $latex m>1$, and $latex \mu(n)=(-1)^k$ if $latex n$ is a product of $latex k$ distinct prime numbers.  So … Continue reading Merten’s Function

# The Monty Hall Problem

Here's a cute little problem.Can every number of the form $latex 4/n$ (where $latex n$ is an integer) be written as the sum of three unit fractions? (A unit fraction is a fraction of the form $latex 1/a$ where $latex a$ is an integer.)For example, if $latex n = 5$ we have\$latex \frac{4}{5} = \frac{1}{2} … Continue reading The Erdős-Straus Conjecture