We publish as the first text in this series a short but illuminating study by one of the most versatile mathematicians of our time of what can be understood by modern mathematics. The author is an outstanding example of a thinker who has made a distinguished contribution to mathematics and who does not consider the problems of teaching mathematics unworthy of his most careful attention. President since 1952 of the International Commission for the Study and Improvement of the Teaching of Mathematics, he has given generously of his time and his substance to a number of groups involved in this field.
Quite convinced that mathematicians have a great deal to give to teachers of mathematics at all levels, he has been largely instrumental in the organization of courses for secondary school teachers. These courses have been in existence for some years now and have been warmly welcomed by his colleagues. The material for the courses was reprinted in the Bulletin de l'Association des Professeurs de Mathematiques and later in the form of books for the benefit of secondary school mathematics teachers in France and elsewhere who could not attend the courses. We hope that some of these books will appear in English in this series.