Tom Whiteside

Who was Tom Whiteside?

Derek Thomas "Tom" Whiteside FBA was a British historian of mathematics. He was the foremost authority on the work of Isaac Newton and editor of the eight volumes of the mathematical papers of Isaac Newton. From 1987 to his retirement in 1999, he was the Professor of History of Mathematics and Exact Sciences at Cambridge University. Anyone interested in this topic should read Whiteside's 19 page nontechnical account, Newton the Mathematician. In this essay he describes Newton's mathematical development starting in secondary school. You learn there, for example, that by far the most important influence on Newton's mathematical development was Book II of René Descartes's La Géométrie. Book II is devoted to a problem that had been considered and partly solved by Pappus of Alexandria and Apollonius of Perga. Descartes completely solved the problem, inventing new mathematics as needed. The problem is this: Given n lines L, with points P on them, find the locus of points Q, such that the lengths of the line segments QP satisfy certain conditions. For example, if n = 4, given lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus had shown that the locus of points Q was a conic section. Descartes considered larger n, allowing some lines to be parallel, and he obtained cubic and higher degree curves. He was able to do this by producing the equation that the points of Q satisfy, using the Cartesian coordinate system. The rest of Book II is occupied with showing that the cubic curves arise naturally in the study of optics from the Snell-Descartes Law. Newton saw this as breaking away from the 2000 year old confinement to conics into modern mathematics. Newton was inspired to undertake the classification of cubic curves, and he identified 72 of the 78 different species.