Category: Books

Finding Moonshine

I registered for M208 this week, and I’m really looking forward to the delivery of my course materials next month, so I can carry on with the Group Theory A block. In the meantime, I’ve been reading another Marcus du Sautoy book, Finding Moonshine, which is a very apt choice to pass the time with, since it’s about group theory and symmetry.

Finding Moonshine is split into twelve chapters, one for each month of one year of du Sautoy’s life, and each chapter combines the history of group theory with more personal anecdotes about the author’s own career. I was a bit ambivalent about this approach at first, but over the course of the book I really warmed to it. I enjoyed getting a glimpse of what it’s like to be a professional mathematician; particularly the little details of du Satuoy’s working style, like the yellow legal pads he prefers to write on, and stories about the overseas trips he makes over the course of the year.

Actually, aside from the wonders of group theory, the main thing I got out of reading Finding Moonshine was an increased urge to travel! I particularly enjoyed the passages about the Alhambra, and I’m now determined to take a trip there myself, most likely in 2012 when I’ll hopefully be taking M336: Groups and geometry. I also really want to visit the glass pyramid at the Louvre, too. I can only imagine how awe-inspiring it must be to see it in person.

The glass pyramid at the Louvre
Louvre Pyramid, Paris by batigolix

As for the mathematical content of the book, I think it’s more enjoyable in that respect than The Music of the Primes; I’ve certainly come away from Finding Moonshine with group theory fever, and I can’t wait to get back to studying it formally. I do think that the book might have been a bit over my head if I hadn’t already met the concept of symmetries as transformations in MS221, though, so perhaps this wouldn’t be a great choice for someone completely new to the subject. The next book on my reading list is Ian Stewart’s Why Beauty Is Truth: The History of Symmetry, so it’ll be interesting to see if it turns out to be a gentler introduction to the awesome world of group theory.

The Music of the Primes

I must admit, I haven’t done very much studying at all over the last couple of weeks. I can’t seem to gather up the motivation to finish Unit AA1, knowing that I’ll probably have to go through the entire unit again next year once the Analysis Block A assignment(s) is/are actually due. Instead I’ve been reading Marcus du Sautoy’s The Music of the Primes, and falling in love with prime numbers!

A couple of years ago I attempted to read a different book about the Riemann Hypothesis – I think it was Prime Obsession – and I just couldn’t get into it, so I was half-expecting to find myself bored by The Music of the Primes. Thankfully it was much a more compelling read than I anticipated! Or perhaps I’m just better equipped to understand the appeal of the primes these days.

The Music of the Primes is a really enjoyable book, and the only criticism I’ve got is that some of the material was quite familiar to me – the bit about cicadas and their prime-numbered breeding cycles, for instance – so perhaps if you’re a seasoned reader of popular maths books then you might find The Music of the Primes a bit boring. But otherwise, I’d recommend it to anyone interested in primes and their mysteries.

For me, the main attraction of prime numbers is that they are fundamental, and at the same time infinite; it seems odd that there are an infinite number of the building blocks out of which the integers are made. Imagine if there were an infinite number of chemical elements! One of my favourite daydreams is imagining the primes stretching out across the far reaches of the real number line, getting bigger and bigger, but more and more sparsely dotted around the line – on and on forever!

The other thing I like about primes is the fact that they’re so important in cryptography – it amuses me that the study of prime numbers has such big practical applications, and I suppose it goes to show that seemingly abstract and academic topics can yield unexpected concrete benefits. Although of course, not everything humans have used prime numbers for could be described as beneficial.

I wonder what the practical applications of group theory are? The next book on my reading list is Finding Moonshine, also by Marcus du Sautoy, so hopefully I’ll find out soon enough!