1 What is mathematics?
1 Aims
The aims of this section are to:

help you clarify your own ideas of what mathematics is;

give you experience of reading different types of written mathematics;

give you an initial feel of how a mathematician views the world.
You have chosen to study a course entitled ‘Mathematics everywhere’, but what exactly is mathematics? It sounds a simple enough question but, in fact, mathematics is not easy to define.
The Concise Oxford Dictionary defines mathematics like this:
mathematics n. pl. (also treated as sing.) (pure) ∼, abstract science of space, number, and quantity; (applied) ∼, this applied to branches of physics, astronomy, etc.; (as pl.) use of mathematics in calculation etc.; so mathemati’cian n.
While Pears Cyclopaedia describes it like this:
Mathematics is a body of knowledge expressed in a language of symbols. Pure mathematics studies the propositions that can be deduced in this language by applying definite rules of reasoning to sets of axioms. In Applied mathematics, the mathematical language is used, often with great effect to discuss problems of the real world, such as mechanics, statistics and science generally. In range, subtlety, complexity and depth mathematics is unsurpassed among the intellectual disciplines and its study has attracted some of the most brilliant men (sic) in history.
One of these ‘brilliant’ individuals, Jacob Bronowski, under the heading The Music of the Spheres wrote:
Mathematics is in many ways the most elaborated and sophisticated of the sciences—or so it seems to me, as a mathematician. So I find both a special pleasure and constraint in describing the progress of mathematics, because it has been part of so much human speculation: a ladder for mystical as well as rational thought in the intellectual ascent of man.
However, not all scientists share the same enthusiasm for the subject. Carl Jung, the eminent Swiss psychiatrist, described his ‘downright fear of the mathematics class’ and went on:
All my life it remained a puzzle to me why it was that I never managed to get my bearings in mathematics when there was no doubt that I could calculate properly.