The Great Mathematical Problems

The Great Mathematical Problems – Ian Stewart *****

As a science writer, whose only foray into maths has been to cover infinity – by far the sexiest and most intriguing mathematical topic – I am in awe of those who successfully popularize maths.

By comparison, science is easy. We all know from school that science can be dull, but if you go about it the right way, it is naturally fascinating, because it’s about how the universe we live in works. Admittedly maths has plenty of applications, but an awful lot of mathematics is about a universe we don’t live in. It can seem that many mathematicians spend their time doing the equivalent of arguing about the dietary habits of unicorns. Not really a proper job for a grown human being.

Probably the best of the current crop of popular maths writers is Ian Stewart. Certainly the most prolific – I don’t know how he finds the time for his day job. Stewart is decidedly variable in his books. Some of them are pure unicorn territory. I find myself turning page after page thinking ‘So what? I don’t care!’ But every now and then he gets it just right – and this is such an example.

Okay, there are occasional unicorn moments, where I had to skip through a page or two to avoid dropping off (when, for example, he gets altogether too excited about the prospect of constructing a regular 17 sided polygon using only a ruler and a pair of compasses), but they are rare indeed. Stewart takes on some of the greatest problems to face mathematicians through history – even the names are evocative, like Goldbach’s Conjecture and, of course, the Riemann Hypothesis. They sound like a Sherlock Holmes story. And Stewart makes them interesting. Which is truly wonderful.

In part the readability is because of a good smattering of stuff about the people – historical context is never more important than in popular maths – but he also pitches the mathematics itself at just the right level to keep our interest without going into mind-numbing detail, or being too summary. I am very wary of describing any book as a tour-de-force, but this one certainly comes close.

Even though Stewart does not keep things enthralling throughout – the dullest chapter is the one on Fermat’s Last Theorem, which I suspect is because Stewart focuses more on the maths here and less on the people, so excellently covered by Simon Singh – there is plenty in this book to keep the imagination alive. If you hate maths this is not going to make you a convert. But if, like me, you have a grudging admiration for maths but find a lot of it impenetrable or pointless, you should have a great time in Ian Stewart’s capable hands.

Paperback:

Kindle:

Using these links earns us commission at no cost to you

Review by Brian Clegg

Comments

God: the Science, the Evidence - Michel-Yves Bolloré and Olivier Bonnassies ***

This is, to say the least, an oddity, but a fascinating one. A translation of a French bestseller, it aims to put forward an examination of the scientific evidence for the existence of a deity… and various other things, as this is a very oddly structured book (more on that in a moment). In The God Delusion , Richard Dawkins suggested that we should treat the existence of God as a scientific claim, which is exactly what the authors do reasonably well in the main part of the book. They argue that three pieces of scientific evidence in particular are supportive of the existence of a (generic) creator of the universe. These are that the universe had a beginning, the fine tuning of natural constants and the unlikeliness of life. To support their evidence, Bolloré and Bonnassies give a reasonable introduction to thermodynamics and cosmology. They suggest that the expected heat death of the universe implies a beginning (for good thermodynamic reasons), and rightly give the impression tha...

Humble Pi - Matt Parker ****

Matt Parker had me thoroughly enjoying this collection of situations where maths and numbers go wrong in everyday life. I think the book's title is a little weak - 'Humble Pi' doesn't really convey what it's about, but that subtitle 'a comedy of maths errors' is far more informative. With his delightful conversational style, honed in his stand-up maths shows, it feels as if Parker is a friend down the pub, relating the story of some technical disaster driven by maths and computing, or regaling us with a numerical cock-up. These range from the spectacular - wobbling and collapsing bridges, for example - to the small but beautifully formed, such as Excel's rounding errors. Sometimes it's Parker's little asides that are particularly attractive. I loved his rant on why phone numbers aren't numbers at all (would it be meaningful for someone to ask you what half your phone number is?). We discover the trials and tribulations of getting cal...

Quantum 2.0 - Paul Davies ****

Unlike the general theory of relativity or cosmology, quantum physics is an aspect of physics that has had a huge impact on everyday lives, particularly through the deployment of electronics, but also, for example, where superconductivity has led to practical applications. But when Paul Davies is talking about version 2.0, he is specifically describing quantum information, where quantum particles and systems are used in information technology. This obviously includes quantum computers, but Davies also brings in, for example, the potential for quantum AI technology. Quantum computers have been discussed for decades - algorithms had already been written for them as early as the 1990s - but it's only now that they are starting to become usable devices, not at the personal level but in servers. In his usual approachable style, Davies gives us four chapters bringing us up to speed on quantum basics, but then brings in quantum computing. After this we don't get solid quantum informat...

Search This Blog