April 8, 2013


A Guided Tour of Mathematics, From One To Infinity
by Steven Strogatz
316 pages, Atlantic Books

Review by Pat Black

Numbers, as my bank bot will tell you, are not my strong point.  

I can remember being awarded a big round of applause for being the first kid in class to recite the five times table. I thought I was cock of the walk. But after that, something happened. I grew bored of sums, fractions and division. Stories, art and history are just so much more interesting than the plod-plod-plod of hundreds, tens and units. There was a horrible teacher lurking in there, too – a supply case, some sort of refugee from the 1950s system of torture/repetition/humiliation, barking out sums each morning. How to make learning difficult in one easy sitting. How to instil fear and unease in your charges, and then something worse: indifference. I learned something in those couple of months, alright. I was educated. “Black! What’s 253 minus 177? Come on, not fast enough!” Moron. Hot indeed is the room in hell reserved for sadistic teachers.

I had a brief fling with algebra and geometry once I went to secondary school – enough to get me through the first tranche of exams – but I had something of an academic Waterloo with calculus a bit later.

Now, while I still sweat slightly when asked to be the banker at Monopoly, or to man the scoreboard at darts, I have come to appreciate numbers and mathematics. Maths is everything. And it can be flawlessly beautiful. It enhances our appreciation of art; think of poetry and music without rhythm, logical beats and illogical ones. It exists in fine art, in paintings. Look at the brush strokes; how many of those are sine waves? Plotting, too – there’s an equation out there that matches the storyline of your book, no matter how complicated. If you multiply your tiredness after work by your natural inclination to laziness, and divide it by your motivation, that’s your writer’s block rating. It even exists in chaos, bad luck, misfortune, the random as well as the ordered.  

And even better, maths is the whole universe. It’s every solid object. It’s every element, every atom. It’s sound, colour and taste. It’s everything natural and man-made. It’s the future and the past. It’s time travel and warp speed. Eventually, it’s god, or whatever kicked the whole thing off with a great big bang. It even stretches out forever, further than we can see or calculate. That’s the sort of stuff they should try to tell seven and eight year old kids. Start off spacey, then dial it down. Fire the imagination – don’t make them stand to attention and spew joyless, mechanical rote learning, liberally oiled with contempt.

In his collected columns for the New York Times, Steven Strogatz takes us through the whole universe of mathematics from basic counting to infinity. We start with the reason we use units of ten – use your fingers if you can’t work it out – but also look at why some ancient societies used to count in blocks of sixty, the better to tally with the passage of time. We make our way through multiplication and division, Pythagoras and trigonometry, and then onto the harder stuff.

A bit like my formal education, my head began to swim a little when we got to calculus, but Strogatz didn’t become a professor of applied mathematics at Cornell for nothing. When he talks about how water bends light, and how we map out this change through numbers and symbols, we realise that the world of nature understands calculus, even if you don’t.

Similarly, he uses popular figures to help round off our understanding of complex theories and proofs. Compound probability might have led the jury to a different conclusion in the murder trial of OJ Simpson, for example. The defence argued that there was a very low percentage of people who beat their partners who went on to actually murder them. Strogatz points out that if this figure was worked out for the number of people who were beaten by their partners who then ended up murdered, the percentage would be far higher.  

A more pleasant character, Ernie from Sesame Street, also pops up to help us understand why we assign values to numbers in the first place, how it helps apply logic, avoid confusion. Meanwhile, parabolic curves can allow you to whisper sweet nothings to your honey at Grand Central Station in New York, and you can start to build a very basic idea of infinity using a tin can and a piece of string.

It’s a grand journey, with an excellent guide. Strogatz understands that people have a basic curiosity that outstrips any system of learning that formalised education can impose. Witness the public’s ravening thirst for Sir David Attenborough’s nature documentaries, or more recently Professor Brian Cox’s introduction to physics and the wonders of the universe. This is the kind of intellectual need that Strogatz satisfies. There’s a little bit of Alain de Botton, here, in the philosophical wanderings, and a touch of Johnny Ball, too, in the use of good humour and whimsy - but never at the expense of his subject. There’s an extensive notes section at the back of The Joy of X, for people who enjoy their sums. But if you don’t, that’s alright too. You don’t have to show your working or write reams of notes - just appreciate the lesson.

Hail to the good teachers: the kind ones, the inspirational ones. Society would be a complete joke without them.


  1. OK, I've read umpteen books on Maths because I know it's a beautiful, mysterious subject which permits wordless thinking but they've all defeated me. This one sounds promising so I'll try again.

  2. Hi Bill - heartily recommended, lovely book.