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Six Maths Essentials - Terence Tao *****

This is a book in the 'compact collection of science/maths essays' category beloved of publishers because they can charge hardback prices for fewer than 80 pages of text - but don't let that put you off, because it's excellent.

Terence Tao introduces six areas of mathematics: numbers, algebra, geometry, probability, analysis and dynamics. Each of these is descriptive rather than practical (there are only a couple of school-level equations in sight), done in a way that gets to the heart of 'what's the point of this subject' with precision and a good level of storytelling.

It's a shame in a way that analysis and dynamics form the final third of the book (apart from a short epilogue), because they don't work as well as the other sections. For the first four, practically everyone will have a vague idea of what they are and what they do - but Tao is then able to open our eyes to their wonders and power. Because Tao has to stay away from any detail of what's going on in the final two sections they feel more vague and woffly. 

My other small moan is that the probability section is weak on Bayes - bearing in mind Tao's focus on what the point of each of these various mathematical disciplines is, he doesn't mention that one of the main benefits of Bayesian probability is being able to translate from what is measured to what we actually want to know.

However, the excellent service this book provides is to give us insights into what mathematics is and why it is so important. Many people struggled with maths at school and can't see the point of anything more than basic arithmetic. Here we take a dive into the mathematical toolkit and, without resorting to the grunt work that many find it difficult to get their head around, makes it clear what gems these mechanisms are to gain an understanding of the world around us - as well as inspiring curiosity.

Hardback:   
Kindle:  
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