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

Comments

  1. 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

Why Nobody Understands Quantum Physics - Frank Verstraete and Céline Broeckaert **

It's with a heavy heart that I have to say that I could not get on with this book. The structure is all over the place, while the content veers from childish remarks to unexplained jargon. Frank Versraete is a highly regarded physicist and knows what he’s talking about - but unfortunately, physics professors are not always the best people to explain physics to a general audience and, possibly contributed to by this being a translation, I thought this book simply doesn’t work. A small issue is that there are few historical inaccuracies, but that’s often the case when scientists write history of science, and that’s not the main part of the book so I would have overlooked it. As an example, we are told that Newton's apple story originated with Voltaire. Yet Newton himself mentioned the apple story to William Stukeley in 1726. He may have made it up - but he certainly originated it, not Voltaire. We are also told that â€˜Galileo discovered the counterintuitive law behind a swinging o...

Ctrl+Alt+Chaos - Joe Tidy ****

Anyone like me with a background in programming is likely to be fascinated (if horrified) by books that present stories of hacking and other destructive work mostly by young males, some of whom have remarkable abilities with code, but use it for unpleasant purposes. I remember reading Clifford Stoll's 1990 book The Cuckoo's Egg about the first ever network worm (the 1988 ARPANet worm, which accidentally did more damage than was intended) - the book is so engraved in my mind I could still remember who the author was decades later. This is very much in the same vein,  but brings the story into the true internet age. Joe Tidy gives us real insights into the often-teen hacking gangs, many with members from the US and UK, who have caused online chaos and real harm. These attacks seem to have mostly started as pranks, but have moved into financial extortion and attempts to destroy others' lives through doxing, swatting (sending false messages to the police resulting in a SWAT te...

Battle of the Big Bang - Niayesh Afshordi and Phil Harper *****

It's popular science Jim, but not as we know it. There have been plenty of popular science books about the big bang and the origins of the universe (including my own Before the Big Bang ) but this is unique. In part this is because it's bang up to date (so to speak), but more so because rather than present the theories in an approachable fashion, the book dives into the (sometimes extremely heated) disputed debates between theoreticians. It's still popular science as there's no maths, but it gives a real insight into the alternative viewpoints and depth of feeling. We begin with a rapid dash through the history of cosmological ideas, passing rapidly through the steady state/big bang debate (though not covering Hoyle's modified steady state that dealt with the 'early universe' issues), then slow down as we get into the various possibilities that would emerge once inflation arrived on the scene (including, of course, the theories that do away with inflation). ...