Professor Stewart's Incredible Numbers

Professor Stewart's Incredible Numbers - Ian Stewart ***

Ian Stewart is the most prolific writer in the field of popular maths, sometimes producing absolute crackers of a book like The Great Mathematical Problems and sometimes turning out ones that don't quite hit the mark. Intriguingly, this seems to manage to be both, in the same way as we discover that zero manages to be the same as minus zero.

The good news is that there's all kind of weird and wonderful mathematical information here. The book is divided into many sections, starting with the small integers, and making it all the way to infinity, via a plethora of different values and climaxing, appropriately enough, with 42.

The bad news is that this format means that the book is mostly a collection of facts with limited context and narrative, the part of a popular maths/science book that makes for a truly engrossing read. There are also heavy duty examples of the classic writer's error of 'If it's interesting to me, it must be to you.' So, at one point we read 'On Christmas day 1640 the brilliant mathematician Pierre de Fermat wrote to the monk Marin Mersenne, and asked an intriguing question. Which numbers can be written as a sum of two perfect squares.'

In fact there are two problems with this particular extract. One is spurious context. Unless there was some relevance to it being Christmas Day, then telling us that makes it sound like we're getting context without actually doing so. But worse is the 'intriguing question' bit - because unless you are a mathematician, there is nothing intriguing about that question.

I think a good general test of whether this book will work for you or not is how you react to magic squares - those grids of numbers that typically add up to the same value along each row, column and diagonal. It's a good example of how the book is organised, by the way, that these turn up in the section for number 9, because the smallest magic square is 3x3. If your reaction to magic squares is a mild interest that the earliest known magic square is called the Lo Shu (no date given), but then you get bored finding out about the properties of all sorts of different magic squares you will find parts of the book hard going. On the other hand, if after four pages on magic squares you think 'I wish there was more on magic squares,' rush out and buy a copy immediately.

If I am honest I am more in the first camp - but it didn't stop me reading the whole book because there are a good few genuinely interesting bits. The ones that work for me are the historically meaty ones, like the origin of zero, negative numbers and complex numbers - my suspicion is that every reader will find some parts to enjoy. So you pays your money (in real numbers) and you makes your choice.

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