This year, a hero of mine passed away. You can find an obituary here:
I encountered W.W. Sawyer when I was a young teenager, through one of his books on mathematics. I have since collected as many books by him as I could find (many are out of print), and I love them all. There is something both about the content and the tone that has stayed with me all through my life and that infuses my own writing about math.
Sawyer’s tone is a beautiful mixture of playfulness and seriousness about his subject. There is nothing stuffy or traditional about his approach; he thinks you and everybody can appreciate math, and he is very much aware of what has killed math appreciation for so many people for so long. And he’s doing real math, not just regaling some impressionable audience with mathematical sleight of hand or legerdemain.
The way Sawyer rearranges the stuff of math, the content, is a work of art. He digs himself and us out from underneath a big pile of rubbish under which the traditional presentation of material has buried the original excitement of a discovery. After a while, you pick up the desire to do some of that digging yourself. Many mathematical discoveries (at all levels) make sense once you appreciate what people were grappling with, what they were trying to figure out, when the discovery was made. The problem context, the historical context, the environment in which both the problem and the discovery made sense – this part is often completely lacking. In traditional presentations of the material, all the scaffolding has been proudly removed from the edifice, and the edifice now looks smooth, forbidding and impenetrable. Mathematicians like Gauss were explicitly proud of their work removing all traces of scaffolding. Sawyer brings the opposite sensibility to mathematics. I specifically remember a short piece Sawyer wrote on the origin of Napier’s logarithms that, in the face of the astounding amount of computation that it called for, at last made it completely obvious why Napier would be interested in high powers of (1 + 1/n), let alone why he was interested in making n big. Take n=10,000, for example. If you think of a table of powers of 1.0001, calculated in 8 decimal places, till the power reaches 10, you’ve just invented yourself a very long slide rule. (This is worth a later blog post.)
I take my inspiration from W.W. Sawyer, and want to see his work extended to the mathematics of the elementary school curriculum (more precisely, K-8). I dedicate this blog to his work.