The Abstract Nature of Mathematics

Excerpts

• The Abstract Nature of Mathematics

  The reason for this failure of the science to live up to its reputation is that its fundamental ideas are not explained to the student disentangled from the technical procedure which has been invented to facilitate their exact presentation in particular instances.

• The Abstract Nature of Mathematics

  Thus we write down as the leading characteristic of mathematics that it deals with properties and ideas which are applicable to things just because they are things, and apart from any particular feelings, or emotions, or sensations, in any way connected with them. This is what is meant by calling mathematics an abstract science.

• The Abstract Nature of Mathematics

  Now, the first noticeable fact about arithmetic is that it applies to everything, to tastes and to sounds, to apples and to angels, to the ideas of the mind and to the bones of the body.

• The Abstract Nature of Mathematics

  The object of the following Chapters is not to teach mathematics, but to enable students from the very beginning of their course to know what the science is about, and why it is necessarily the foundation of exact thought as applied to natural phenomena.

• The Abstract Nature of Mathematics

  But it is equally an error to confine attention to technical processes, excluding consideration of general ideas. Here lies the road to pedantry.

• The Abstract Nature of Mathematics

  In the eye of science, the fall of an apple, the motion of a planet round a sun, and the clinging of the atmosphere to the earth are all seen as examples of the law of gravity.

• The Abstract Nature of Mathematics

  Pythagoras had a glimpse of it when he proclaimed that number was the source of all things.

Equations

Problems

No exercises in this chapter.