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By Nathan Altshiller-Court

''Dr. Court’s publication is a demonstration of his personal credo: arithmetic in earnest will be enjoyable; arithmetic in enjoyable will be earnest.''—American Mathematical Monthly
A world-renowned mathematician takes a lighthearted examine the philosophy, shape, and re-creations of arithmetic during this interesting publication. Nathan A. court docket discusses and illustrates the allure of arithmetic in addition to the science's gigantic sensible application and its very important importance to our cultural historical past. In lucid and witty language, he explains how mathematicians imagine, what they do, and the function of math in daily life.
Dr. courtroom introduces the may possibly and plight of reasoning, the connection among arithmetic and genius, the entice of the limitless, and the allure of natural paintings in arithmetic. He additionally addresses a few remarkable perplexities, together with well-known difficulties in leisure arithmetic (as good as their options) and puzzles that may be solved with no pencil and paper.

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But we could conceivably have nerve ends that would convey to us the sensation of such electromagnetic waves directly. We know that our nerve ends that convey the sensations of high temperatures are different from those that convey sensations of low temperatures. That such an extension of our perceptivity within the domain of electromagnetic waves is not a physiological impossibility is attested by the fact that the visual spectrum of some animals reaches beyond the limits of the visual spectrum of man.

This is a question that cannot be answered by "yes" or "no". 17 44 MATHEMATICS IN FUN AND IN EARNEST In spite of these weaknesses, and many others, we are not likely to give up our mental experimentation for direct action, for various reasons. It is much easier and more convenient to perform operations mentally. The mental process requires no equipment, no apparatus, no installations of any kind. Furthermore, it saves a great deal of time, to say nothing about expense. What is even more important, the "thought experiment" has a much greater degree of generality than any physical experiment can have.

MATHEMATICS AND PHILOSOPHY 51 Let us deal with the latter problem first. The questions of the dependence of our knowledge on our own physical and mental constitution are of rather recent origin. In the mental domain they were first considered by Kant. An adequate discussion of the entire problem would require knowledge of our nervous system that at present is not available. But once we raise these questions, the nature of the answer is beyond doubt. When we look at an object, or at a landscape, and are not quite certain what we see, we turn our heads, or we move closer, or we walk around the object.

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