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):

Kindle:

Using these links earns us commission at no cost to you

Review by Brian Clegg

Comments

Phenomena - Camille Juzeau and the Shelf Studio ****

I am always a bit suspicious of books that are highly illustrated or claim to cover 'almost everything' - and in one sense this is clearly hyperbole. But I enjoyed Phenomena far more than I thought I would. The idea is to cover 125 topics with infographics. On the internet these tend to be long pages with lots of numbers and supposedly interesting factoids. Thankfully, here the term is used in a more eclectic fashion. Each topic gets a large (circa A4) page (a few get two) with a couple of paragraphs of text and a chunky graphic. Sometimes these do consist of many small parts - for example 'the limits of the human body' features nine graphs - three on sporting achievements, three on biometrics (e.g. height by date of birth) and three rather random items (GNP per person, agricultural yields of various crops and consumption of coal). Others have a single illustration, such as a map of the sewers of Paris. (Because, why wouldn't you want to see that?) Just those two s...

The Bright Side - Sumit Paul-Choudhury ***

When I first saw The Bright Side (the subtitle doesn't help), I was worried it was a self-help manual, a format that rarely contains good science. In reality, Sumit Paul-Choudhury does not give us a checklist for becoming an optimist or anything similar - and there is a fair amount of science content. But to be honest, I didn't get on very well with this book. What Paul-Choudhury sets out to do is to both identify what optimism is and to assess its place in a world where we are beset with big problems such as climate change (which he goes into in some detail) that some activists position as an existential threat. This is all done in a friendly, approachable fashion. In that sense it's a classic pop-psychology title. For me, Paul-Choudhury certainly has it right about the lack of logic of extreme doom-mongers, such as Extinction Rebellion and teenage climate protestors, and his assessment of the nature of optimism seems very reasonable, if presented at a fairly overview leve...

Rakhat-Bi Abdyssagin Five Way Interview

Rakhat-Bi Abdyssagin (born in 1999) is a distinguished composer, concert pianist, music theorist and researcher. Three of his piano CDs have been released in Germany. He started his undergraduate degree at the age of 13 in Kazakhstan, and having completed three musical doctorates in prominent Italian music institutions at the age of 20, he has mastered advanced composition techniques. In 2024 he completed a PhD in music at the University of St Andrews / Royal Conservatoire of Scotland (researching timbre-texture co-ordinate in avant- garde music), and was awarded The Silver Medal of The Worshipful Company of Musicians, London. He has held visiting affiliations at the Universities of Oxford, Cambridge and UCL, and has been lecturing and giving talks internationally since the age of 13. His latest book is Quantum Mechanics and Avant Garde Music . What links quantum physics and avant-garde music? The entire book is devoted to this question. To put it briefly, there are many different link...

Search This Blog