Skip to main content

Math Without Numbers - Milo Beckman *****

In some ways, this is the best book about pure mathematics for the general reader that I've ever seen.  At first sight, Milo Beckman's assertion that 'the only numbers in this book are the page numbers' seems like one of those testing limits some authors place on themselves, such as Roberto Trotter's interesting attempt to explain cosmology using only the 1,000 most common words in the English language, The Edge of the Sky. But in practice, Beckman's conceit is truly liberating. Dropping numbers enables him to present maths (I can't help but wince a bit at the 'math' in the title) in a far more comprehensible way. Counting and geometry may have been the historical origin of mathematics, but it has moved on.

The book is divided into three primary sections - topology, analysis and algebra, plus a rather earnest dialogue on foundations of mathematics exploring the implications of Gödel's incompleteness theorems, and a closing section on modelling (including automata and 'science'). What this approach enables Beckman to do brilliantly is to move the image of mathematics away from school maths and onto what professional mathematicians spend their time on. What's more, and perhaps more impressively for a reader who has only ever been interested in applications, it gives the best appreciation I've seen of what the point of pure mathematics is - why some find it so delightful and interesting.

Along the way in those summary headings we come across shapes, manifolds, dimensions, infinity, maps, abstraction, structures and inference. We do eventually meet, for example, sets - though they come surprisingly late when taking a conventional view. Of course not everything can be covered in detail. Groups for example, crop up with brief coverage of both symmetry groups and wallpaper groups - but we are never told what a group is. Of course, most topics have to be handled distinctly briefly. This isn't a long book (I'd say it's just the right length to be enjoyable without being either trivial or getting bogged down), but Beckman fits a lot in.

I do have a couple of small issues. As mentioned, we're told from the start the only numbers in the book are the page numbers. This isn't strictly true - numbers as words crop up reasonably regularly. And though it does provide the freedom I mentioned, in one case - Cantor's diagonal argument for the infinity of the continuum - I found the non-numeric explanation far harder to get your head around than the traditional approach using numbers. It was also, perhaps, a little unfair to include (presumably as a diversion - they aren't given any context) a pair of logic puzzles without providing the solutions: one was straightforward, but the other had some issues. In terms of content, things went ever so slightly astray when Beckman strayed into science, telling us that Newton's gravitational relationship depended on the weights of the two bodies.

No book is perfect, though. The fact remains that Math Without Numbers is a brilliant introduction to pure mathematics and a delight from end to end.

Hardback:

Kindle:  
Using these links earns us commission at no cost to you
Review by Brian Clegg
Labels:

Comments

  1. Ramjet119 January 2024 at 21:59

    In your reiview Re: the hard-level quizz question you struggled with it three doors all identical that you suggest is not solvable I struggled with it as well for days as well and have a Master is Elec Eng hence why I stumbled across your post. My son solved it in in no time. Its how you read into the question what 3 identical doors mean and he realised they weren't'identical (given a different individual is in front of each and they all know each other). It's amusing how we read the question can completely throuh us off. Be nicer if we used longer descriptions to get over these misunderstandings but it's never going happen . In a way a dream for these quizz writers.

    ReplyDelete

Post a Comment

Popular posts from this blog

Roger Highfield - Stephen Hawking: genius at work interview

Roger Highfield OBE is the Science Director of the Science Museum Group. Roger has visiting professorships at the Department of Chemistry, UCL, and at the Dunn School, University of Oxford, is a Fellow of the Academy of Medical Sciences, and a member of the Medical Research Council and Longitude Committee. He has written or co-authored ten popular science books, including two bestsellers. His latest title is Stephen Hawking: genius at work . Why science? There are three answers to this question, depending on context: Apollo; Prime Minister Margaret Thatcher, along with the world’s worst nuclear accident at Chernobyl; and, finally, Nullius in verba . Growing up I enjoyed the sciencey side of TV programmes like Thunderbirds and The Avengers but became completely besotted when, in short trousers, I gazed up at the moon knowing that two astronauts had paid it a visit. As the Apollo programme unfolded, I became utterly obsessed. Today, more than half a century later, the moon landings are
Post a Comment
Read more

Space Oddities - Harry Cliff *****

In this delightfully readable book, Harry Cliff takes us into the anomalies that are starting to make areas of physics seems to be nearing a paradigm shift, just as occurred in the past with relativity and quantum theory. We start with, we are introduced to some past anomalies linked to changes in viewpoint, such as the precession of Mercury (explained by general relativity, though originally blamed on an undiscovered planet near the Sun), and then move on to a few examples of apparent discoveries being wrong: the BICEP2 evidence for inflation (where the result was caused by dust, not the polarisation being studied),  the disappearance of an interesting blip in LHC results, and an apparent mistake in the manipulation of numbers that resulted in alleged discovery of dark matter particles. These are used to explain how statistics plays a part, and the significance of sigmas . We go on to explore a range of anomalies in particle physics and cosmology that may indicate either a breakdown i
Post a Comment
Read more

Splinters of Infinity - Mark Wolverton ****

Many of us who read popular science regularly will be aware of the 'great debate' between American astronomers Harlow Shapley and Heber Curtis in 1920 over whether the universe was a single galaxy or many. Less familiar is the clash in the 1930s between American Nobel Prize winners Robert Millikan and Arthur Compton over the nature of cosmic rays. This not a book about the nature of cosmic rays as we now understand them, but rather explores this confrontation between heavyweight scientists. Millikan was the first in the fray, and often wrongly named in the press as discoverer of cosmic rays. He believed that this high energy radiation from above was made up of photons that ionised atoms in the atmosphere. One of the reasons he was determined that they should be photons was that this fitted with his thesis that the universe was in a constant state of creation: these photons, he thought, were produced in the birth of new atoms. This view seems to have been primarily driven by re
Post a Comment
Read more