# Diversions in Mathematics #2: Hilbert’s Hotel

In this instalment, I introduce the concept of infinity in a simple and (hopefully) entertaining way, which puts into practice the counting concepts introduced in the previous Diversion. In fact, Hilbert‘s infinite hotel was one of the ‘stories’ that got me seriously interested in mathematics in the first place, and so it is a pleasure to share it here. This is a very well-known piece of story-driven mathematics. I hope that experienced mathematicians who happen to come across this blog do not tire of hearing (reading) it again, and that they see the value in telling the story to the general public.

Just before we start: I assume knowledge of the definitions and notations introduced in the previous instalment, namely, the very basics of set theory.

# Composer’s Notebook #5

## Announcement of première performance of Three Concert Pieces for piano

I am very pleased to announce that my Three Concert Pieces for piano will receive its première performance in the Utzon Room at the Sydney Opera House on 9 February at 7 pm. The pianist is a good friend and colleague, Nicholas Young, with whom I collaborated frequently during our time at the Sydney Conservatorium. It is a pleasure to work with him again, but this time as a composer!

For some insight into Nicholas’ project, and the rationale behind such a concert, you may be interested in this interview for CutCommon magazine.

The program notes for the concert are available online now.

# Update Post for the New Year

Dear reader, thank you for visiting the blog, and happy new year! This is an update post, letting you know what I have been up to in the last few months.

# Diversions in Mathematics #1: How to Count like a Pure Mathematician

If you want to know what this is all about, read my introduction to the series.

If you have already read the introduction, then welcome to the first Diversion in Mathematics! I emphasise, as I did in the introduction, that I will write with the general public in mind, so don’t be worried if you don’t consider yourself a “fan” of mathematics, or if you’ve totally suppressed all memories of maths classes from high school. And if you are a keen mathematician, whether recreationally or studying seriously at college/university, hopefully you will also find these blogs to be of some interest.

# Diversions in Mathematics #0

Introduction to the series

I have always been interested in maths, and not only in the subject itself but also the ways in which maths is explained and taught. In general, a crucial part of studying and researching is to be able to communicate one’s findings to other people, who may or may not be knowledgeable in your field. For this reason, I’m all for popular science books and magazines, which (provided that it is done well) serve to explain scientific research in an accessible way, and to promote scientific awareness and appreciation amongst the general public. However, in my opinion, popular science books too often simplify, and even completely skip the mathematics behind the science. There is certainly a cultural aversion to mathematics — at least from my perspective as an Australian, and from my awareness of similar attitudes in the US and UK — which may be part of the reason for the lack of ‘real’ mathematics in popular science writing. Here is an anecdote: apparently Stephen Hawking’s publisher advised the great scientist that every equation he included in his A Brief History of Time would result in reduced sales. (There is one equation though: Einstein’s $E = mc^2$). Of course, this is one of the bestselling science books ever, and sits atop many a coffeetable, but I wonder how many people have seriously read it…

# An update

I know that a non-zero number of people read this blog, and I’m also aware that I haven’t written anything in about two months. Since I intend to keep the blog alive, here is an update for you! Moreover, as I am generally introverted and not talkative, I find it easier and much more natural to express myself in writing anyway.