A lot of claims are being made about how electronic media and new platforms will revolutionize education. I confess that until now I’ve been a bit skeptical. For instance, there’s been a lot of discussion about whether MOOCs (Massive Open Online Courses) open up higher education to the less privileged, or whether in practice they are only used by people who already have an extensive education.
However, I’m now convinced that devices like the iPad not only open up new routes to education: they go beyond it. They provide a new way to engage the public with math and science — and philosophy, music, and literature, for that matter. What convinced me is when Touch Press managed to turn a fairly dry stack of text and diagrams that I sent them into an app. It’s now out: Incredible Numbers. The reviews currently give it five stars, and it’s gone down really well with users. It’s easy and fun to use, and it makes important mathematical ideas intuitive and accessible to anyone.
It all started a couple of years ago, when my book publisher Profile wanted to start producing apps, possibly linked to books, and wondered if I’d be interested in working on a math app. It sounded an intriguing idea. I’ve always preferred breaking new ground to doing the same thing over and over again, though I do that too when the mood takes me. So I put together a big pile of material, loosely related to special numbers like 17 and pi. Along with short biographies of the mathematicians who’d discovered interesting features of those numbers, and some puzzles.
Profile got together with Touch Press, who make apps. Touch Press had access to Wolfram Research’s developer tools, including Mathematica, which provides a powerful way to do remarkable things quickly and accurately. I use it myself all the time for research. The material got edited and reorganised until it began to look like an app. By the time I got to play with an alpha version, it had progressed well beyond anything I’d originally expected.
When you launch the app, it offers you a choice of eight main topics: prime numbers, pi, nature, polygons, and so on. One of them is music. I’ll describe just one of the interactive topics that appears. It’s a way to break a sound wave up into very simple wave forms—pure notes, represented by sine curves. Mathematicians call this process Fourier analysis, and it’s pretty advanced. You don’t do it at school. It’s important: engineers use it all the time, it tells us about earthquakes, it makes digital cameras work.
On the app, you don’t even need to know what a sine curve is (though it does tell you if you want, and you’ll end up knowing even if you don’t want). You can create your own waveform just by tracing your finger across the screen. No formulas: any shape you want. And then you flick the lower part of the screen upwards, and the app starts to work out successive terms of the Fourier series. As it does so, it draws the sine waves, and it shows you how well those sine waves, when added together, approximate your designer wave. You can actually see how adding more and more terms gives an increasingly accurate description of your own personal wave. You can listen to what it sounds like, too.
You can also search for your birthday in the first million digits of pi, see how to make a regular 17-sided polygon, explore the paradoxes of Hilbert’s infinite hotel, and see how the wartime enigma code machine worked. Plus a lot more.
Everyone I’ve shown the app to is blown away by how easy it is to use. It’s not remotely like school lessons. Everything is done in a friendly, non-technical way, and it’s interactive. Even when a formula turns up (and some do, we didn’t shy away from them, but we do keep them under control) you can flick across it, change the symbols to numbers, and see what the formula really means. Touch some mathematician’s name, and up comes their biography. Touch a technical term and you get the definition.
When I was learning math, it was all pencil and paper and blackboards and chalk. This way is far more fun. Even mathophobes enjoy using it. Is it education? If it is, it’s education as never before. But what it really is, and what I personally prefer to promote, is motivation. I don’t want to teach people math: there are plenty of professionals doing that. I want to persuade people to engage with it, enjoy it, and appreciate what it’s for. If you can do that, the learning process becomes so much more pleasurable.
As a mathematician, I believe that my subject is of vital importance to humanity, and I’ve written plenty of books to argue the case. But I don’t think it’s enough to convince people that math is important. I want to change how they feel about the subject. I want them to experience how interesting it really is, once you get past the dry symbols and sums. I want converts, not just unengaged approval.
I’m beginning to believe that platforms like the iPad, used with imagination and intelligence, can help achieve that. And even if they don’t, it’s a lot of fun. We all gain from that.