About a year ago, a San Francisco daily paper published a reader's letter which was signed by a number of distinguished mathematicians on the staff of Stanford University. The main purpose of the letter was to warn the public against the conclusions reached by the Royaumont semi? nar on the teaching of mathematics in secondary schools. The seminar took place already in November December 1959, but the report based on its findings was published only in May 1961.1) The report quickly attracted a good deal of attention and comment, some of it critical. A short time after the publication of the letter from Stanford, and independently of it, there appeared in the Frankfurter Hefte a strong and, one regrets to say, unfair attack against the Royaumont seminar by an otherwise serious scholar.2) We emphasize that both the article and the letter were intended for general consumption, that is to say their authors regarded the matter as one of vital importance not only to their professional colleagues but also to the public at large. How is it that a subject which is traditionally left to the experts and whose experts are usually quite happy to be left to themselves has come to be regarded as a matter of concern to both professionals and laymen ? A partial answer to this question can of course be found in the increasing importance of mathematics for the general development of science and technology in the modern world. However, more details are required in order to understand the special problems that are connected with the teaching of mathematics in secondary schools, as compared with the teaching of the natural sciences such as physics and chemistry. For this purpose it is essential to have a quick look at the development of mathe? matics in modern times.