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 occurred to you, but rather as
it could have occurred to you if you had known then what you know now,
and as it would occur to the student if his learning process is being
guided. This in fact is the gist of the lesson Socrates taught Meno's
slave. The thought-experi- ment tries to find out how a student could
re-invent what he is expected to learn. I said about the preface that it
is a feeble reflection of the didactical inversion. Indeed, it is not a
constituent part of the book. It can even be torn out. Yet it is useful.
Firstly, to the reviewer who then need not read the whole work, and
secondly to the author himself, who like the composer gets an
opportunity to review the Leitmotivs of the book.
