Skip to main content

Mathematics for the Million - Lancelot Hogben ***

This is one of the strangest maths books you are ever likely to encounter. Written in the 1930s and reissued in 2017, it's an attempt to provide mathematical instruction up to around A-level standard (though obviously the curriculum has changed a lot) for someone who, perhaps, doesn't respond well to the classroom and works better from self-teaching.

It's telling of the way popular science was considered in the period that apparently the author delayed publication as he was up for election to Fellowship of the Royal Society, which back then was dead against science popularisation. 

Hogben, in a distinctive, mellifluous (if sometimes prolix) style, starts with the basics of arithmetic and leads us all the way through to calculus. Unlike his contemporaries, who were all for working through hundreds of geometry proofs for completeness, Hogben fills in the parts at each stage of mathematical development needed to reach the next stage and gives us no more. 

The narrative here is very much centred on the application of mathematics through history. We see how geometry might have been used by Egyptian architects, and how trigonometry benefits those who need to navigate by the stars. The only problem with this learning-through-history approach is it can sometimes be hard to then relate what has been learned to uses in the present day.

Lancelot Hogben never intended this to be a fun read to pootle through just for the sake of it. The book is peppered with many exercises. It seems to be devised as a self-teach textbook of the future (as seen from the 1930s), throwing away the strictures of the rigid teaching approach of that period for something that is more approachable.

It's hard to say how well it delivers from the modern viewpoint of someone who has gone through all this stuff at school in a fairly traditional way. Clearly a lot of people decided it was a good approach back then: the book might not have made the 'million' in the title but certainly sold many copies. 

To the modern eye, there is a danger of the book falling between two stools. It's not approachable enough to read purely for fun, but Hogben's distinctive, quirky style, combined with what is sometimes a rather tedious approach to the maths, means that it's not the best way for a modern reader, with no mathematical training, to learn about the subject. It stands best as a unique and fascinating oddity in the history of mathematical books for the general public - and as such is worth taking a look at.

Paperback:  



Review by Brian Clegg

Comments

Popular posts from this blog

The Demon in the Machine - Paul Davies *****

Physicists have a habit of dabbling in biology and, perhaps surprisingly, biologists tend to be quite tolerant of it. (I find it hard to believe the reverse would be true if biologists tried to do physics.) Perhaps one reason for that tolerance is Schrödinger’s lecture series and book What is Life?, which had a huge impact on molecular biology and with a reference to which, not surprisingly, Paul Davies begins his fascinating book. 

At the heart of the The Demon in the Machine (we'll come back to that demon in a moment) is the relationship between life and information. In essence, Davies points out that if we try to reduce life to its simple physical components it is like trying to work with a computer that has no software. The equivalent of software here is information, not just in the best publicised aspect of the information stored in the DNA, but on a far broader scale, operating in networks across the organism.
This information and its processing gives life its emergent compl…

The Cosmic Mystery Tour – Nicholas Mee ****

This is another book, like last year’s Enjoy Our Universe by Alvaro de Rújula, that sets out to provide a light-hearted introduction to physics and astrophysics for the general reader. It’s from the same publisher (OUP) and packaged in the same way: as a high quality small-format hardback with 200 glossy pages, the majority of them adorned with colour pictures. But that’s where the resemblance ends. Unlike its predecessor, this new book by Nicholas Mee delivers exactly what it promises.

It’s not that de Rújula’s book was a bad one, but he just wasn’t able to think his way into the reader’s mind. He kept saying ‘physics is fun’, but he was talking about the fun a professional physicist gets out of doing it – which is a very arcane, often highly mathematical, type of fun. The result, for a non-specialist reader, was actually quite alienating. Mee, on the other hand, understands exactly how his readers think, what they find interesting, and the details that – no matter how important they …

Professor Maxwell's Duplicitous Demon - Brian Clegg ****

‘It’s not uncommon when trying to give Maxwell his rightful place in the pantheon of physics to bracket him with Newton and Einstein’, Brian Clegg says towards the end of this book. In one sense that’s perfectly true. Dip into any physics textbook and you’ll see Maxwell’s name at least as often as the other two. His greatest achievement – Maxwell’s equations – did for electromagnetism what Newton had done for gravity, while laying the essential theoretical groundwork for everything Einstein was to do.

There’s a big difference, though. A few years ago, when I was offered the chance to write short biographies of Newton and Einstein, I jumped at it – because they addressed mysteries of the universe that anyone can relate to, and their lives outside physics were, if anything, even more fascinating. At the risk of sounding downright rude, you can’t say either of those things about James Clerk Maxwell. In spite of that, Brian Clegg has done a wonderful job here of recounting just what Maxwel…