A Brief History of Mathematical Thought

A Brief History of Mathematical Thought - Luke Heaton ***

I had great hopes at the start of this book that we'd get a meaty but approachable history of the development of mathematics. When describing the origins of number, arithmetic and mathematical processes the opening section is pitched well, but things go downhill when we get to detailed mathematical exposition.

The problem may be that Luke Heaton is a plant scientist, which may have prepared him better for using maths than for explaining it. If we take, for instance, his explanation of the demonstration that the square root of two is irrational, I was lost after about two lines. As soon as Heaton gets into mathematical detail, his fluency and readability are lost.

There's a central chunk of the book where the mathematical content seems too heavy for the way the contextual text is written. We then get back onto more effective ground when dealing with logic and Turing's work, before diving back into rather more impenetrable territory.

One slight concern is that, in talking about Turing, Heaton presents the largely discredited idea that Turing committed suicide by eating a poisoned apple, laying the blame for this on his arrest and 'treatment' for homosexuality, a narrative that doesn't stand up (it's a shame the author didn't have a chance to read The Turing Guide). I suspect this is a one-off and much of the mathematical history is fine.

I didn't realise until I'd finished it that it has an interesting publishing history. It was initially part of the same Robinson published series as my A Brief History of Infinity, but this is a US hardback edition, just brought out by OUP. This was, then, a curate's egg book for me. I really enjoyed it when it was dealing with history and philosophy of maths, but found the technical explanations, even of mathematics I understand perfectly well, hard to follow.

Paperback (US hardback):

Kindle:

Using these links earns us commission at no cost to you

Review by Brian Clegg

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