The quirky and entertaining aspects of mathematics will be relatively familiar to most SFCrowsnest readers. For example, you would have heard about the way the golden ratio crops up in many aspects of art and architecture or seen prettily coloured diagrams of fractals such as the Mandelbrot set. But the way these topics are handled on television or in popular science books is often rather superficial, glossing over the actual mathematics behind such things and instead focusing on their aesthetic or practical value.
‘Good Math’ is different. Very different! Author Mark C Chu-Carroll is behind one of the best regarded maths blogs on the Internet, ‘Good Math, Bad Math’, http://scientopia.org/blogs/goodmath/. On that blog he’s an excellent writer, but not necessarily a populariser of maths and the distinction between these two skills is important. Chu-Carroll writes his blog for those with serious maths understanding (realistically, some degree of university-level mathematics ability) rather than those who haven’t done maths since high school but still want to know more about how maths works.
That said, ‘Good Math’ isn’t simply a rehash of blog postings and his editor John Osborn (notably, he’s been credited on the front cover) has done a first-rate job of dialling back some of the hardcore maths from the first half of the book. If read from start to finish, ‘Good Math’ is actually much more readable than a random dip into later chapters might suggest. Chu-Carroll and Osborn walk the reader through the less challenging but still very interesting aspects of mathematics such as number theory and imaginary numbers via some historical diversions into Greek logic, Roman numerals and Egyptian fractions. As an aside, it’s a slight annoyance that the more prosaic aspects of editing, such as picking up typos, hasn’t been done perfectly. For example, ‘except’ instead of ‘excerpt’ on page 254.
From about a third of the way in though, the book becomes steadily more challenging, and there’s a definite accent on problems and explanations that can be demonstrated using in formal logic or programming languages. These aren’t necessarily difficult to understand, but those without a maths or computing background will definitely find them unfamiliar. Basically, there’s an assumption that the reader can handle formal logic and the ideas behind programming without handholding.
The later sections of the book cover a mix of mathematical fields including symmetry, set theory, lambda calculus and Turning machines. Parallels and connections between logic and computation are made again and again. If there’s an over-arching theme to all of this, it’s the connection between mathematics and computer programming, in particular how the likes of mathematicians Alan Turning and Alonzo Church laid down the framework around which modern computer science is built. By the end of the book, Chu-Carroll wraps things up with a discussion of the notorious ‘halting problem’, which he describes as whether you can tell if a given computer program will ever end.
To summarise: ‘Good Math’ is hard work to read but definitely rewarding if you’re interested in maths and/or computer science. It’s a rich, deep book tailored very much for a specific audience of maths graduates and computer programmers. It’s definitely not an accessible book though and Chu-Carroll doesn’t make the sorts of concessions necessary to those less mathematically-literate readers who’ve enjoyed books by the likes of Simon Singh and Tim Harford.
(pub: Pragmatic Bookshelf. 262 page paperback. Price: £26.00 (UK), $34.00 (US). ISBN: 978-1-93778-533-8)
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