Rigorous thinking and the use of instruments

Abstract

The title is a section heading from the lovely biography [1] by Florian Cajori of the English mathematician William Oughtred (15647-1660). Though Cajori was writing history he chose his subject and style to give modern readers (of 1916), and especially teachers of mathematics, something to think about.Oughtred was a fine amateur mathematician and a thoughtful teacher. John Aubrey in his brief lives (quoted in [1p12]) wrote:He was a little man, had black haire, and black eies (with a great deal of spirit). His head was always working. He would drawe lines and diagrams on the dust… did use to lye a bed till eleaven or twelve a clock… Studyed late at night; went not to bed till 11 a clock;… and on top of his bed-staffe, he had his ink-horne fix't. He slept but little. Sometimes he went not to bed in two or three nights.