Book Reviews

It is some forty years ago since Dieudonn e's Royaumont Seminar address [1] in which he proclaimed \Euclid Must Go" and that it should be replaced by two-dimensional linear algebra. Dieudonn e's quarrel was not with the purpose of geometry, which he considered important, but with the method of teaching geometry. Dieudonn e's reasons were that Euclid as taught was a \Process Fantastically Laborious" as well as having \the a ne and metric properties hopelessly mixed up". While there are many who agreed with the latter reasons, there were many who did not agree with the linear algebra replacement as proposed. Freudenthal [2] in his chapter on \The Case of Geometry" gave a profound critique of Dieudonn e and recommended a piecemeal school geometry program with a strong intuitive spatial content. In his book, The Foundation of Science [3], Poincar e addressed the downgrading of geometry, and I quote: