The day after last week’s budget, I logged onto the BBC News website and clicked on their budget calculator to find out if I was a winner or a loser. The questions are pretty simple: first off, it asks how much you drink, smoke and drive, and then it asks how much you earn, plus a few bits and bobs to cover technicalities. Then, it spits out an answer: did Phil leave you feeling flush, was it more of a hammering at the hands of Hammond? I came away £8 a month better off…and significantly angrier than I expected.

# You're reading: Irregulars

### “Pariah Moonshine” Part II: For Whom the Moon Shines

*This post is part of a series of posts by guest author Joshua Holden.*

I ended Part I with the observation that the Monster group was connected with the symmetries of a group sitting in 196883-dimensional space, whereas the number 196884 appeared as part of a function used in number theory, the study of the properties of whole numbers. In particular, a mathematician named John McKay noticed the number as one of the coefficients of a modular form.

### “Pariah Moonshine” Part I: The Happy Family and the Pariah Groups

Being a mathematician, I often get asked if I’m good at calculating tips. I’m not. In fact, mathematicians study lots of other things besides numbers. As most people know, if they stop to think about it, one of the other things mathematicians study is shapes. Some of us are especially interested in the symmetries of those shapes, and a few of us are interested in both numbers and symmetries.

### Footballs on road signs: an international overview

I’m an old fashioned manager, I write the team down on the back of a fag packet and I play a simple 4-4-2.

- Mike Bassett, England Manager

I’m very much like Mike Bassett: I like standing on the terraces, I like full-backs whose main skill is kicking wingers into the ad hoardings, and – most of all – I like geometrically correct footballs.

### Stirling’s numbers in a nutshell

*This is a guest post by researcher Audace Dossou-Olory of Stellenbosch University, South Africa.*

In assignment problems, one wants to find an optimal and efficient way to assign objects of a given set to objects of another given set. An assignment can be regarded as a bijective map $\pi$ between two finite sets $E$ and $F$ of $n\geq 1$ elements. By identifying the sets $E$ and $F$ with $\{1,2,\ldots, n\}$, we can represent an assignment by a **permutation**.

### A new aspect of mathematics

*This is a guest post written by David Nkansah, a mathematics student at the University of Glasgow.*

Around the fourth century BC, the term ‘Mathematics’ was defined by Aristotle as the “science of quantity”. It’s my own experience as a young mathematician to say this definition, although correct in its own right, poses a problem for those who do not truly know what mathematics is. It fails to highlight the true creativity of the subject.

Human inspiration and imagination are essential ingredients in mathematics. Regarding creativity, one could say, with merit, that in a sense mathematics is an art. Before proceeding to outline similarities between sketching mathematical proofs and painting on a canvas, it is important to know what fundamental premises mathematical proofs are built on.

### Circular reasoning on Catalan numbers

*This is a guest post by researcher Audace Dossou-Olory of Stellenbosch University, South Africa.*

Consider the following question: **How many ways are there to connect $2n$ points on a circle so that each point is connected to exactly one other point?**