Mathematics: A Curious History by Joel Levy (book review).

I like reviewing maths books from time to time, if only to remind me on how much we rely on it in our lives. More so with histories on the subject when it shows how it evolved and maths really does evolve over the centuries. In line with other of publisher Andre Deutsch’s book series, Joel Levy’s ‘Mathematics: A Curious History’ is loaded with pictures and diagrams.

These show the earlier ways our ancestors developed their numerical systems to actually doing calculations which you can try. Levy points out that even if you don’t think that you’re good at maths, all you really need is a little arithmetic and commonsense to try out. On the opening page of his introduction, he shows how when Carl Friedrich Gauss was at school, he calculated the total of the numbers from 1 to 100 by coming up with a quick simple formula and probably did it faster than you could put the numbers in a calculator.

Well, you might want to multiply the two numbers in a calculator but it’s very quicker than putting them in individually. I tried it with other series of numbers and it is effective.

Seeing how the number bases are is pretty standard for any book like this although this time, not only are bases 2 (binary), 10 (decimal) and 8 (hex) covered but also the names of 11 others. You also get the early trigonometry of a circle. Interestingly, such things wasn’t all down to Pythagoras, as his teacher Thales made the first breakthroughs.

What is often the biggest surprise is just how advanced our ancestors were with mathematics than they were with science. Euclid laid down a lot of the formulas we use today. Translations of his books in one volume are still available today.

However, when we come to the section called ‘Medieval Mathematics’, the focus is actually on India and how far advanced they were in maths and astrology, more so as Aryabhata worked out the Earth circled the Sun long before Kepler. I’ve mentioned in other maths book reviews how we use the Hindi-Arabic number symbols but hadn’t realised they concealed in the angles of their numbers the number they represented. Mine you, considering how many of us use curves for many of the numbers that this has become obscured.

The acceptance of a lot of maths was hindered by the gulf between Christianity and Muslims, even that far back but then taken on because it was more practical for doing sums than using the Roman numerals. When you consider that much of maths was used in selling things and accounting, you wanted a ready system that could be used quickly and we owe it to the mathematician Fibonacci who chose the Arabic system in 1202 in his travels.

As you can see from the above, none of this is pure mathematics, that is done for its own sake, but applied. Even calculus has a reason for being there to figure out what was actually happening at an exact moment or dimension. In the section ‘Renaissance And Revolution’, science and maths work together and you see both at the same time and how they are interlinked. Hardly surprising as maths is the tools of the trade in science. I’ll only pick out a few things.

When it comes to who would win on a bet at a set number of times of throwing a coin in the air and was cut short because one of the players was called away, I was left puzzling. If they had time to argue the percentage of dividing the winnings then they might as well have finished the game.

Seeing the Pascaline, an early mechanical gear calculator, reminded me of a gadget pre-electronic calculators, called a ‘magic calculator’ which was made in a more linear pattern and probably a lot more stable by moving columns up and down with a stylus.

Something that becomes apparent as you read is how the various mathematicians work grows over each generation building on each other’s work. Reading this growth puts a lot of things in perspective and an understanding than just being told it was so. Some areas, like with calculus, got Greek letter names and other identification from Euler in the 18th century.

If you thought computers were modern, you need to look at George Boole (1815-1864) because his operation gates are what is used in modern CPU chips. Technology just had to catch up which came with Alan Turing and engineer Thomas Flowers in the last century’s first computer. In comparison, Game Theory is a more modern thing and just shows how important maths is today and that discoveries are still going on.

This book should be useful to any of your spogs who need to understand more of mathematics and its origins and also good for an adult read. There is certainly a lot to digest here and I’m only touching on some things here. As a stepping stone to other maths books this is a good choice to have to give you the right kind of framework to know what you are looking at. Learning some maths along the way is just a bonus.

GF Willmetts

March 2018

(pub: Andre Deutsch/Goodman Books. 191 page illustrated indexed medium hardback. Price: £ 9.99 (UK). ISBN: 978-0-233-00544-7)

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Geoff Willmetts has been editor at SFCrowsnest for some 21 plus years now, showing a versatility and knowledge in not only Science Fiction, but also the sciences and arts, all of which has been displayed here through editorials, reviews, articles and stories. With the latter, he has been running a short story series under the title of ‘Psi-Kicks’ If you want to contribute to SFCrowsnest, read the guidelines and show him what you can do. If it isn’t usable, he spends as much time telling you what the problems is as he would with material he accepts. This is largely how he got called an Uncle, as in Dutch Uncle. He’s not actually Dutch but hails from the west country in the UK.

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