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

Cosmology for the Curious - Delia Perlov and Alex Vilenkin ***

In the recently published The Little Book of Black Holes we saw what I thought was pretty much impossible - a good, next level, general audience science title, spanning the gap between a typical popular science book and an introductory textbook, but very much in the style of popular science. Cosmology for the Curious does something similar, but coming from the other direction. This is an introductory textbook, intended for first year physics students, with familiar textbook features like questions to answer at the end of each chapter. Yet by incorporating some history and context, plus taking a more relaxed style in the writing, it's certainly more approachable than a typical textbook.

The first main section, The Big Bang and the Observable Universe not only covers basic big bang cosmology but fills in the basics of special and general relativity, Hubble's law, dark matter, dark energy and more. We then move onto the more speculative (this is cosmology, after all) aspects, brin…

Astrophysics for People in a Hurry – Neil deGrasse Tyson *****

When I reviewed James Binney’s Astrophysics: A Very Short Introduction earlier this year, I observed that the very word ‘astrophysics’ in a book’s title is liable to deter many readers from buying it. As a former astrophysicist myself, I’ve never really understood why it’s considered such a scary word, but that’s the way it is. So I was pleasantly surprised to learn, from Wikipedia, that this new book by Neil deGrasse Tyson ‘topped The New York Times non-fiction bestseller list for four weeks in the middle of 2017’.

Like James Binney, Tyson is a professional astrophysicist with a string of research papers to his name – but he’s also one of America’s top science popularisers, and that’s the hat he’s wearing in this book. While Binney addresses an already-physics-literate audience, Tyson sets his sights on a much wider readership. It’s actually very brave – and honest – of him to give physics such prominent billing; the book could easily have been given a more reader-friendly title such …

Once upon and Algorithm - Martin Erwig ***

I've been itching to start reading this book for some time, as the premise was so intriguing - to inform the reader about computer science and algorithms using stories as analogies to understand the process.

This is exactly what Martin Erwig does, starting (as the cover suggests) with Hansel and Gretel, and then bringing in Sherlock Holmes (and particularly The Hound of the Baskervilles), Indiana Jones, the song 'Over the Rainbow' (more on that in a moment), Groundhog Day, Back to the Future and Harry Potter.

The idea is to show how some aspect of the story - in the case of Hansel and Gretel, laying a trail of stones/breadcrumbs, then attempting to follow them home - can be seen as a kind of algorithm or computation and gradually adding in computing standards, such as searching, queues and lists, loops, recursion and more.

This really would have been a brilliant book if Erwig had got himself a co-author who knew how to write for the public, but sadly the style is mostly heavy…