Math History: The Secret Lives of Numbers (Kitagawa & Revell)

Kate Kitagawa & Timothy Revell. The Secret Lives of Numbers (2003) A history of mathematics taking all currently known mathematical texts into account. The Eurocentric view of mathematical development is shown to be egregiously wrong-headed. Miscellaneous theorems (and some proofs) were discovered or invented in many different places at many different times well before Euclid’s demonstration of the logical coherence of all mathematics. Algorithms for solving trade and other complicated problems ditto. The notation that freed European mathematicians to discover number theory was invented in India, and brought to Europe by Arabs. The need to plan planting and seed-time prompted the study of astronomy, which was perhaps the first science to be mathematised. Either it, or geometry, needed for land surveys. Formal mathematics is at least as old as writing.
     The history of mathematics is not even a winding road; it’s a maze of paths leading in all directions with surprising shortcuts, connections in unexpected places, and backtracking. What’s constant is that whenever possible mathematicians exchanged ideas and knowledge. Powerful rulers recognised the value of mathematics and other knowledge, and sponsored the collection of texts, and their study and collation by the best minds they could attract. And ever and again, barbarians with limited insight into anything beyond their immediate goals of getting treasure and women destroyed those collections. We owe a great debt to the scholars who preserved what knowledge they could and taught their students to do likewise.
     I think that Kitagawa and Revell deprecate Euclid’s achievement. True, pretty well every theorem he proved in his books, and many of the proofs themselves, were known before him. Compilations of all known mathematics were made centuries before him. But he seems to have been the first one to organise all known mathematics into a logical system, in which rules of inference applied to a handful of axioms, carefully defined, would connect all theorems. It is the critique and emulation of his methods that has led to new mathematics.
     I also think that Kitagawa and Revell don’t examine the source of mathematics in ordinary language. As far as I know, it’s possible to express distance, time, size, weight, quantity, similarity and difference, direction, etc, in all human languages. The only variation seems to be in emphasis and detail. Mathematics is the more or less systematic formalisation of these concepts when people found it necessary to do so for some practical purposes involving trade and taxes. (Aside: Where I grew up, distance was expressed as time. A certain relative lived one hour away, for example. That’s an hour’s walk. This may be one reason why I find it easy to accept Einstein’s proposal of a space-time continuum, even though I can’t do the relevant math.)
     A keeper, worth an occasional reread. Breezy style, often cliched, which makes it seem easier to understand the math than it really is. The title is a teaser, possibly intended to attract the unnerdy.***