At the end of my undergraduate degree, I remember thinking "what better way to mark such an event than to write and record a maths rap?" Well, I did end up recording such a thing, but it was pretty woeful. However, a couple of months ago, I plucked up the zest to do it again. … Continue reading Don’t Mess with the Mathematician →

Integrals can tell us quite a lot. For those of you who are so disgustingly bored that you've found your way onto my blog, you should have a go at evaluating exactly the following integral:$latex \int_0^1 \frac{x^4 (1-x)^4}{1+x^2} dx$It might take some effort, but it's well worth it. Of course, Wolfram Mathematica could do it … Continue reading Late night integration →

I thought it would be a good idea to relay some of the advice given by Sir Michael Francis Atiyah during his talk on Tuesday. Sir Michael Atiyah during his talk at #hlf13 Picture: HLFF @Bernhard Kreutzer Always ask yourself questions. Atiyah says that one of the secrets of his success is to always be curious. … Continue reading Advice to a Young Mathematician →

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 →

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 →

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 →

Another article of mine has just been published by The Conversation. Click here to get on and read it.

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 →

For a quick introduction to the theory of prime numbers, see my earlier post. A mathematician by the name of Yitang Zhang made the news last week, for taking a step towards the twin prime conjecture. This conjecture asserts that there are infinitely many pairs of prime numbers that differ by 2. We call such pairs … Continue reading Almost Twin Primes →