David Acheson's Reading List

"I came across this book when I was about 12. I liked the deductive aspects of geometry, and especially the way that simple assumptions could lead quickly to surprising results. The second part of Abbott’s book, in particular, offered a very concise exposition of the main theorems and proofs, making it possible to get something of a ‘big picture’. On top of all this, I found the actual layout of Abbott’s book, such as the thickness of line in the diagrams, visually appealing, and some 60 years later this had a major influence on the whole design of The Wonder Book of Geometry ."

"This book was recommended to me by my inspirational maths teacher at senior school, Mr Bellis, soon after I met calculus for the first time. And I still remember very well the moving dedication at the front of the book: ‘To my brother, Dr Nicolas Politzer, who perished at Colditz in Saxony, 1945’. The author, Rozsa Peter, was a distinguished Hungarian pure mathematician, and she included some fairly advanced ideas, including, for instance, the way in which imaginary numbers can help us understand infinite series. Nonetheless, she was writing for the general public. In this way, then, I was introduced quite early to the whole idea of how serious mathematics – as opposed to ‘numeracy’ – might, in principle, be brought successfully to a wide readership."

"At university, my interests turned sharply towards applied mathematics, and, in particular, fluid mechanics. And it was while doing research in that subject that I eventually came across this immensely scholarly book by Clifford Truesdell, which immediately got me interested in the history of maths, and the notion of returning – where possible – to original sources. It made me realise, in particular, how classical mechanics owes as much to Euler and the Bernoulli family as it does to Galileo and Newton . And I found Truesdell’s essay “Whence the Law of Moment of Momentum?” particularly striking for the light that it shed on the unsatisfactory and almost bizarre way in which the angular momentum principle for a rigid body is introduced in virtually every mechanics textbook of the 20th century. Truesdell himself seems to have been something of a character, not least because one of his published research papers in the 1960s was in Latin."

"I should perhaps say that I know Rob Eastaway quite well, through his Maths Inspiration shows for teenagers, which are held in major city-centre theatres all over the UK. And I greatly value being a member of that team, not least because it is the only opportunity I get to play the electric guitar in public! But I wanted to include a fairly modern and wide-ranging popular maths book, and this one is, I believe, exceptional in the amusing and cartoon-illustrated way in which it relates mathematics to everyday life, with topics like ‘How fast should you run in the rain?’, ‘Which snooker shot is hardest?’ and even ‘Why do clever people get things wrong?’."

"For my final choice I must return to geometry, and this kaleidoscopic and superbly illustrated collection by David Wells. There are about 250 short items, and for me, at least, it is the more oddball ones that really leap off the page. It was here, for instance, that I first came across Malfatti’s problem. This is a conjecture dating from 1803 about the densest way to pack three non-overlapping circles into a triangle, and it took over 100 years for someone to realise that the conjecture itself was completely and utterly wrong. Above all, perhaps, David Wells’s book is great for dipping into, almost at random, with a nice cup of cocoa on a cold winter’s night."