Numbers: a very short introduction – Peter M. Higgins ***

Part of the massive ‘a very short introduction’ range of pocket books, this book sets you straight immediately if you thought it was going to be about mathematics – no, it’s about number, which is quite a different thing. This is both true and not true, which really sets the pattern for the whole little book. Number is a quite distinct concept from maths, yet in discussing number, Peter Higgins inevitably brings in quite a lot of mathematics.

The mixed feel continues with the presentation. The writing style is light and accessible for what can be quite an indigestible topic, but bits of the book are better than other in this respect. I wanted to keep reading, but I found myself feeling a strong urge to skip bits that seemed to be getting bogged down.

After an introduction to what numbers are we’re plunged into prime numbers in some detail. From here we go on to the various labels mathematicians have for numbers, from perfect to deficient – this is faintly interesting, but it does generate an urge to ask ‘Yes, but why does it matter?’ We go on to the likes of cryptography and the use of large primes to perform encryption/decryption, the various fractions, infinity and more. (Yes, you can have more than infinity, and you know what I mean anyway).

There seemed a couple of strange omissions. I think we could have done with significantly more on the philosophy of number – just what numbers are, why human beings use them, whether they have a real existence outside of mathematics etc. I was also surprised by the near-absence of set theory – it comes into the infinity chapter, but there is none of the use of set theory to establish the basics of number and operations, which seemed odd. I’d have expected it up front.

In the end it’s a book that falls between two stools. It isn’t consistently readable enough to be good popular science, but it isn’t detailed enough to be a textbook. I’m not really sure what it’s for. But it’s certainly not a bad addition to the series – and ‘number’ certainly deserves its place there.

Paperback:

Kindle:

Using these links earns us commission at no cost to you

Review by Jo Reed

Comments

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...

Should we question science?

I was surprised recently by something Simon Singh put on X about Sabine Hossenfelder. I have huge admiration for Simon, but I also have a lot of respect for Sabine. She has written two excellent books and has been helpful to me with a number of physics queries - she also had a really interesting blog, and has now become particularly successful with her science videos. This is where I'm afraid she lost me as audience, as I find video a very unsatisfactory medium to take in information - but I know it has mass appeal. This meant I was concerned by Simon's tweet (or whatever we are supposed to call posts on X) saying 'The Problem With Sabine Hossenfelder: if you are a fan of SH... then this is worth watching.' He was referencing a video from 'Professor Dave Explains' - I'm not familiar with Professor Dave (aka Dave Farina, who apparently isn't a professor, which is perhaps a bit unfortunate for someone calling out fakes), but his videos are popular and he...

Everything is Predictable - Tom Chivers *****

There's a stereotype of computer users: Mac users are creative and cool, while PC users are businesslike and unimaginative. Less well-known is that the world of statistics has an equivalent division. Bayesians are the Mac users of the stats world, where frequentists are the PC people. This book sets out to show why Bayesians are not just cool, but also mostly right. Tom Chivers does an excellent job of giving us some historical background, then dives into two key aspects of the use of statistics. These are in science, where the standard approach is frequentist and Bayes only creeps into a few specific applications, such as the accuracy of medical tests, and in decision theory where Bayes is dominant. If this all sounds very dry and unexciting, it's quite the reverse. I admit, I love probability and statistics, and I am something of a closet Bayesian*), but Chivers' light and entertaining style means that what could have been the mathematical equivalent of debating angels on...

Search This Blog