17 April 2015

Three mathematical stylists

The great masters of modern analysis are Lagrange, Laplace and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace, on the other hand, explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which, while rigorous, shall be a concise and synthetical as possible. (W.W. Rouse Ball, A short account of the history of mathematics, 1908.)

Some time later when the baron Alexander von Humboldt, the famous traveller and amateur of sciences, asked Laplace who was the greatest mathematician in Germany, Laplace replied "Pfaff". "But what about Gauss?" the astonished von Humboldt asked, as he was backing Gauss for the position of director at the Göttingen observatory, "Oh," said Laplace, "Gauss is the greatest mathematician in the world." (James Roy Newman. The world of Mathematics, 1956. Many variants exist of this fanciful anecdote.)