Like preludes, prefaces are usually composed last. Putting them in the front of the book is a feeble reflection of what, in the style of mathe matics treatises and textbooks, I usually call thf didactical inversion: to be fit to print, the way to the result should be the inverse of the order in which it was found; in particular the key definitions, which were the finishing touch to the structure, are put at the front. For many years I have contrasted the didactical inversion with the thought-experiment. It is true that you should not communicate your mathematics to other people in the way it...

A title that sounds like poetry, and a subtitle that seems to contradict the title But the subtitle is right, and originally it was just the title. A strange subtitle, isn t it? Preface to a Science of Mathematical Education. All sciences in their prenatal stage have known this kind of literature: only the term used was not Preface, but, for instance, Prolegomena, which * means the same though it sounds less provisional. In fact such works were thicker than the present one, by up to ten times. There is much more that can be said about a science before it comes into being than after; with the...

A title that sounds like poetry, and a subtitle that seems to contradict the title But the subtitle is right, and originally it was just the title. A strange subtitle, isn t it? Preface to a Science of Mathematical Education. All sciences in their prenatal stage have known this kind of literature: only the term used was not Preface, but, for instance, Prolegomena, which * means the same though it sounds less provisional. In fact such works were thicker than the present one, by up to ten times. There is much more that can be said about a science before it comes into being than after; with the...

This book is a product of love and respect. If that sounds rather odd I initially apologise, but let me explain why I use those words. The original manuscript was of course Freudenthal s, but his colleagues have carried the project through to its conclusion with love for the man, and his ideas, and with a respect developed over years of communal effort. Their invitation to me to write this Preface e- bles me to pay my respects to the great man, although I am probably incurring his wrath for writing a Preface for his book without his permission I just hope he understands the feelings of all...