Professor Stewart's Cabinet of Mathematical Curiosities

Professor Stewart's Cabinet of Mathematical Curiosities - Ian Stewart ****

This is the second review of a trilogy, read in entirely the wrong order (book 3, then 1 here, and 2 to follow), so should you be feeling confused, this book is a predecessor to Professor Stewart's Casebook of Mathematical Mysteries. The format is very similar - a collection of factoids, logical puzzles, mathematical expositions and more to entertain any recreational maths enthusiast. I think it works significantly better in this first book of the series because, to be honest, by volume 3 there is probably a bit of barrel scraping going on. Here the topics are fresh and fun.

There is arguably something for everyone here, which inversely means that there are probably some bits, depending on your mathematical knowledge and interests, that you will either find too trivial or too heavy going. But the format makes it easy to skip through to the next. I personally most enjoy the logic problems (though a small black mark for featuring a near-identical "moving the cups" problem to one in the third book) and, much to my surprise, the geometry, which I suppose took me back to a more innocent time. There were inevitably some entries where there was a strong feeling of 'so what?', leaving the reader suspecting that mathematicians need to get a life. And at least one where I think the answer is wrong, if you apply the same logic as applied in an earlier tricksy question. (It's the one about pigs and umbrellas, if you must know.)

Funnily, what works least well are the bits that are most like a conventional popular maths book, that describe famous mathematical problems and their context, such as the four colour problem and Fermat's last theorem. The entries for these are rather longer than the rest, but obviously much shorter than, say, Simon Singh's brilliant book on Fermat. That means that you get concentrated fact, but none of the interesting detail that makes a popular science or maths book appealing. For me these sections just don't work and I largely skipped them.

But - and that's the joy of the format - it really doesn't matter. Because in a few pages there will be something else, and something else, and something else again to entertain and tickle the brain cells. It's notable that I got not just one (about a strange set of dice) but two blog posts (the other being about an oddity in my review copy) out of this book - because it made me think, reminded me of some old favourite problems and puzzles, introduced plenty of new ones and entertained. What more can you ask from maths.

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 AI Paradox - Virginia Dignum ****

This is a really important book in the way that Virginia Dignum highlights various ways we can misunderstand AI and its abilities using a series of paradoxes. However, I need to say up front that I'm giving it four stars for the ideas: unfortunately the writing is not great. It reads more like a government report than anything vaguely readable - it really should have co-authored with a professional writer to make it accessible. Even so, I'm recommending it: like some government reports it's significant enough to make it necessary to wade through the bureaucrat speak. Why paradoxes? Dignum identifies two ways we can think about paradoxes (oddly I wrote about paradoxes recently , but with three definitions): a logical paradox such as 'this statement is false', or a paradoxical truth such as 'less is more' - the second of which seems a better to fit to the use here. We are then presented with eight paradoxes, each of which gives some insights into aspects of t...

Einstein's Fridge - Paul Sen ****

In Einstein's Fridge (interesting factoid: this is at least the third popular science book to be named after Einstein's not particularly exciting refrigerator), Paul Sen has taken on a scary challenge. As Jim Al-Khalili made clear in his excellent The World According to Physics , our physical understanding of reality rests on three pillars: relativity, quantum theory and thermodynamics. But there is no doubt that the third of these, the topic of Sen's book, is a hard sell. While it's true that these are the three pillars of physics, from the point of view of making interesting popular science, the first two might be considered pillars of gold and platinum, while the third is a pillar of salt. Relativity and quantum theory are very much of the twentieth century. They are exciting and sometimes downright weird and wonderful. Thermodynamics, by contrast, has a very Victorian feel and, well, is uninspiring. Luckily, though, thermodynamics is important enough, lying behind ...

Search This Blog