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 Laws of Thought - Tom Griffiths *****

In giving us a history of attempts to explain our thinking abilities, Tom Griffiths demonstrates an excellent ability to pitch information just right for the informed general reader. We begin with Aristotelian logic and the way Boole and others transformed it into a kind of arithmetic before a first introduction of computing and theories of language. Griffiths covers a surprising amount of ground - we don't just get, for instance, the obvious figures of Turing, von Neumann and Shannon, but the interaction between the computing pioneers and those concerned with trying to understand the way we think - for example in the work of Jerome Bruner, of whom I confess I'd never heard. This would prove to be the case with a whole host of people who have made interesting contributions to the understanding of human thought processes. Sometimes their theories were contradictory - this isn't an easy field to successfully observe - but always they were interesting. But for me, at least, ...

The Infinity Machine - Sebastian Mallaby ****

It's very quickly clear that Sebastian Mallaby is a huge Demis Hassabis fan - writing about the only child prodigy and teen genius ever who was also a nice, rounded personality. After a few chapters, though, things settle down (I'm reminded of Douglas Adams' description of the Hitchhiker's Guide to the Galaxy ) and we get a good, solid trip through the journey that gave us DeepMind, their AlphaGo and AlphaFold programs, the sudden explosion of competition on the AI front and thoughts on artificial general intelligence. Although Mallaby does occasionally still go into fan mode - reading this you would think that AlphaFold had successfully perfectly predicted the structure of every protein, where it is usually not sufficiently accurate for its results to have direct practical application - we get a real feel for the way this relatively unusual company was swiftly and successfully developed away from Silicon Valley. It's readable and gives an important understanding of...

Nanotechnology - Rahul Rao ****

There was a time when nanotechnology was both going to transform the world and wipe us out - a similar position to our view of AI today. On the positive transformation side there was K. Eric Drexler's visions in the 1986 Engines of Creation. Arguably as much science fiction as engineering possibilities, it predicted the ability to use vast armies of assemblers to put objects together from individual atoms. On the negative side was the vision of grey goo, out of control nanotechnology consuming all in its path as it made more and more copies of itself. In 2003, for instance, the then Prince Charles made the headlines when newspapers reported ‘The prince has raised the spectre of the “grey goo” catastrophe in which sub-microscopic machines designed to share intelligence and replicate themselves take over and devour the planet.’ These days the expectations have been eased down a notch or two. Where nanotechnology has succeeded, it has been with the likes of atom-thick mat...

Search This Blog