Skip to main content

Beyond Infinity - Eugenia Cheng ****

Popular maths writers have it much harder than authors of popular science books. Pretty well everyone loves science at junior school, even if they're put off it in their teens, so for science writers, it's just a matter of recapturing that childhood delight in exploring how the world works. But, to be honest, maths is a relatively rare enthusiasm at any age, so the author of a popular maths book has to really work at his or her task - and this is something Eugenia Cheng certainly does, bubbling with enthusiasm and trying hard not to put us off as readers as she explores infinity.

In Cheng's earlier book, Cakes, Custard and Category Theory, food played too heavy a role for me - here that tendency reigned in, though it still rears its head occasionally. We get a quite detailed exploration of infinity, infinitesimals and some additional material such as infinite dimensions and infinite-dimensional categories (we had to get some category theory), plus the usual enjoyment of quantum weirdness. I felt sometimes, because the book doesn't build on a historical basis, we were thrown in at the deep end a little too early with assertions like infinity+1=infinity and infinity x infinity = infinity. The process where Cheng shows us how infinity can't be a real number, or an integer, or a rational fraction etc. also felt a little repetitive and drawn out. There's always a difficulty in letting go a little when you work in a field that requires total precision. But we never lose Cheng's enthusiasm and light touch.

I think this book will particularly appeal to a reader who already has an interest in maths, but not much training, because it is purely focussed on the mathematics itself. For the more general reader, I suspect a book like A Brief History of Infinity, which gives historical context, brings and people and social implications to frame the maths, would work better as an introduction. With the appetite whetted, though, they should be encouraged to go onto Beyond Infinity, which as a wider mathematical context.

I really enjoyed this book, and though the author's desire to include food did still slightly intrude - and I felt it was just a bit too much about her, rather than the maths - it's a great addition to the relatively sparse popular maths shelf.

Paperback (US hardback):  

Using these links earns us commission at no cost to you
Review by Brian Clegg


Popular posts from this blog

On the Fringe - Michael Gordin *****

This little book is a pleasant surprise. That word 'little', by the way, is not intended as an insult, but a compliment. Kudos to OUP for realising that a book doesn't have to be three inches thick to be interesting. It's just 101 pages before you get to the notes - and that's plenty. The topic is fringe science or pseudoscience: it could be heavy going in a condensed form, but in fact Michael Gordin keeps the tone light and readable. In some ways, the most interesting bit is when Gordin plunges into just what pseudoscience actually is. As he points out, there are elements of subjectivity to this. For example, some would say that string theory is pseudoscience, even though many real scientists have dedicated their careers to it. Gordin also points out that, outside of denial (more on this a moment), many supporters of what most of us label pseudoscience do use the scientific method and see themselves as doing actual science. Gordin breaks pseudoscience down into a n

A (Very) Short History of Life on Earth - Henry Gee *****

In writing this book, Henry Gee had a lot to live up to. His earlier title  The Accidental Species was a superbly readable and fascinating description of the evolutionary process leading to Homo sapiens . It seemed hard to beat - but he has succeeded with what is inevitably going to be described as a tour-de-force. As is promised on the cover, we are taken through nearly 4.6 billion years of life on Earth (actually rather more, as I'll cover below). It's a mark of Gee's skill that what could have ended up feeling like an interminable list of different organisms comes across instead as something of a pager turner. This is helped by the structuring - within those promised twelve chapters everything is divided up into handy bite-sized chunks. And although there certainly are very many species mentioned as we pass through the years, rather than feeling overwhelming, Gee's friendly prose and careful timing made the approach come across as natural and organic.  There was a w

Michael D. Gordin - Four Way Interview

Michael D. Gordin is a historian of modern science and a professor at Princeton University, with particular interests in the physical sciences and in science in Russia and the Soviet Union. He is the author of six books, ranging from the periodic table to early nuclear weapons to the history of scientific languages. His most recent book is On the Fringe: Where Science Meets Pseudoscience (Oxford University Press). Why history of science? The history of science grabbed me long before I knew that there were actual historians of science out there. I entered college committed to becoming a physicist, drawn in by the deep intellectual puzzles of entropy, quantum theory, and relativity. When I started taking courses, I came to understand that what really interested me about those puzzles were not so much their solutions — still replete with paradoxes — but rather the rich debates and even the dead-ends that scientists had taken to trying to resolve them. At first, I thought this fell under