Lying in the bath this morning – relaxing into the Christmas holiday (despite the raging epidemic of omicron-variant Covid that is currently rampaging through London in an increasingly frightening manner), I had thoughts about several blog posts to write over the break, and this is the first…

It’s a book recommendation: Ian Stewart‘s Concepts of Modern Mathematics. It’s around 50 years since its first edition (and even this Dover edition is 26 years old) but – part from the disconcerting habit of assuming all humans are male – it doesn’t feel like a dated work at all.

In one other way, though, it is a product of its times – the controversy over “new mathematics” – the teaching methods adopted widely across the west in the 60s and 70s in an effort to improve mathematical understanding of students and move beyond rote-teaching. Interestingly, as the wikipedia article demonstrates, its adoption was driven, in part, by the post-Sputnik panic in US science and engineering.

It’s adoption was certainly controversial as Tom Lehrer makes clear here…

Now, having been educated in both Ireland (primary and secondary) and England (secondary) I have actually seen both approaches in operation at first hand – and its certainly the case that the traditional methods gave me a solid (algorithmic in the sense of using a simple and repetitive method) grounding in such things as long division which I think were missing in England, but it’s also not difficult to see why discussions of things like sets, modular arithmetic and matrices are pretty essential for anyone thinking of a career in science and technology.

That said the UK’s School Mathematics Project seems to have avoided what appears to be the excesses of “new math” in the US. I cannot produce any evidence for it but I am tempted to wonder if the UK’s 1980s (and continuing) software boom was in part driven by its innovation in maths teaching (read Francis Spufford’s excellent Backroom Boys for more on that).

Indeed these things are so fundamental to software development that it’s hard to imagine a case for not teaching them – but 50 years ago they were clearly seen as in some way esoteric or even fetishistic.

Professor Stewart’s book concentrates on understanding of the concepts and not rigorous proofs – which makes the book readable and digestible in settings like my bath. I am not going to say it could be mastered by anyone regardless of their current understanding of maths, but its not a traditional textbook and I would suggest it would be a good backgrounder if you had basic (O level/GCSE) maths qualifications and were interested in working as a software developer.

One of the points the author makes in his preface is that the UK has seen its science and technology bases erode as more and more graduates look for careers in law and financial services. I hope that will become the subject of another blog here shortly.