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Math for English Majors - Ben Orlin *****

Ben Orlin makes the interesting observation that the majority of people give up on understanding maths at some point, from fractions or algebra all the way through to tensors. At that stage they either give up entirely or operate the maths mechanically without understanding what they are doing. In this light-hearted take, Orlin does a great job of taking on mathematical processes a step at a time, in part making parallels with the structure of language.

Many popular maths books shy away from the actual mathematical representations, going instead for verbal approximations. Orlin doesn't do this, but makes use of those linguistic similes and different ways of looking at the processes involved to help understanding. He also includes self-admittedly awful (but entertaining) drawings and stories from his experience as a long-time maths teacher.

To make those parallels, Orlin refers to numbers as nouns, operations as verbs (though he points out that there are some flaws in this simile) and syntax, for example of algebra, as grammar. he then gives us a mathematical 'phrase book' described as 'a local's guide to mathematical vocabulary' to bring in topics such as errors, logic, probability and correlations. This last is my least favourite bit as it's mostly just defining terms and doesn't give us the same dive into the underlying reasoning as occurs in the other sections.

One almost inevitable point when we're talking about mathematics and language is how the word mathematics should be shortened. In once sense Orlin's response to the argument over maths vs math is correct: 'They're interchangeable, and anyone who argues otherwise is a pedant.' But the reality is that to the British ear and eye, 'math' just grates - and I suspect the same is true the other way round in the US. I do wish there had been a British English version of the book.

I'm also sad that when presenting what multiplication is, Orlin doesn't deal with the infamous internet spat when an American student was marked down in a test for representing 5 x 3 as adding three fives, rather than five threes. It would have been perfect fodder for Orlin, as it comes down to how you represent the x symbol in English words. If you (somewhat childishly) replace x with 'lots of' then it is five threes. But if you replace it with 'multiplied by' then it's three fives. Of course, either works - it's commutative - but that didn't prevent plenty of people saying the 'three fives' approach is wrong.

Overall, the book is a delight and though I probably didn't learn much new about mathematics, I very much enjoyed Orlin's storytelling and little facts and different ways of looking at mathematical operations and practices that he introduces.

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