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

The Antigravity Enigma - Andrew May ****

Antigravity - the ability to overcome the pull of gravity - has been a fantasy for thousands of years and subject to more scientific (if impractical) fictional representation since H. G. Wells came up with cavorite in The First Men in the Moon . But is it plausible scientifically? Andrew May does a good job of pulling together three ways of looking at our love affair with antigravity (and the related concept of cancelling inertia) - in science fiction, in physics and in pseudoscience and crankery. As May points out, science fiction is an important starting point as the concept was deployed there well before we had a good enough understanding of gravity to make any sensible scientific stabs at the idea (even though, for instance, Michael Faraday did unsuccessfully experiment with a possible interaction between gravity and electromagnetism). We then get onto the science itself, noting the potential impact on any ideas of antigravity that come from the move from a Newtonian view of a...

The World as We Know It - Peter Dear ***

History professor Peter Dear gives us a detailed and reasoned coverage of the development of science as a concept from its origins as natural philosophy, covering the years from the eighteenth to the twentieth century. inclusive If that sounds a little dry, frankly, it is. But if you don't mind a very academic approach, it is certainly interesting. Obviously a major theme running through is the move from largely gentleman natural philosophers (with both implications of that word 'gentleman') to professional academic scientists. What started with clubs for relatively well off men with an interest, when universities did not stray far beyond what was included in mathematics (astronomy, for instance), would become a very different beast. The main scientific subjects that Dear covers are physics and biology - we get, for instance, a lot on the gradual move away from a purely mechanical views of physics - the reason Newton's 'action at a distance' gravity caused such ...

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...

Search This Blog