The word 'Mathematics' was later replaced with 'Calculus' in many texts.
This book makes no attempt to give an account of either of these subjects, which
I presume are well-known to the majority of readers. More than thirty years ago,
however, I wrote a book of some 40,000 words on the subject, having been convinced
that no-one had ever attempted to provide a comprehensive account of the subject.
This effort, which has for its chief purpose an exposition of the ideas and
theories of the discipline, must be judged as a failure. Yet it is one of the
few works on the subject of which I have some real pride and which I have not
altered since it was first published in 1956.
My failure to produce a better book was not due to the inadequacy of the subject,
since I had some 50,000 words to say on it; neither was it due to lack of
energy. Instead, I was hampered by the fact that when I commenced the task
only the first 10,000 words had been written, and my main interest was in trying
to determine what else I could do on the subject.
In the course of writing the book I realized that I could not summarize the
subject. The problem is of great interest, but it cannot be solved by a simple
summary. The physical and chemical sciences present similar problems, yet each
is best solved by a system of equations.
I have now written over 30,000 words on the subject and I must still feel dissatisfied.
I find that I am more interested in the developing character of the subject
and that I have become convinced of the need to say much more than the book
The book is organized as follows:
Section 1. The nature of the subject,
Section 2. The development of mathematics
Section 3. The nature of the mathematical universe
Section 4. The evolution of mathematics
Section 5. The origin of mathematical ideas
Section 6. The quantitative sciences and mathematics
Section 7. The nature and extent of the association between mathematics and
the physical sciences
Section 8. Appendices.
Section 1. The Nature of the subject
The subject consists of a great number of mathematical ideas which, it has
been maintained, can best be described as concepts rather than as forms, or
compositions of forms.
If you're a morning person, you probably hate early-risers. (At least, that's how I feel about them.) But now that we've established that I'm not a morning person, you're probably wondering what I do when I get out of bed at the crack of dawn. I don't have an easy answer for you.
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