As I write this article, the mathematics education community is being asked to consider proposals for 'functional mathematics'. In this context, I am not the first, nor shall I be the last, to ask the question 'What is mathematics?', but is my 2006 perspective different to others?
Mathematics has its roots in practical requirements. Around 1500 years after Babylonian algebraic texts, the Greeks took the subject to a new level and Euclid, amongst others, laid down the foundations for mathematics as a deductive science.
Buxton, debating the nature and purpose of mathematics in 1984, identified varieties of maths in terms of purpose: mathematics for survival; useful mathematics; direct applications of mathematics; mathematics as a language and a tool; mathematics for its own sake and mathematics for personal development.
Perhaps my favourite exposition on the topic of what is mathematics comes from Davis and Hersch (1980), who concluded that:
'The definition of mathematics changes. Each generation and each thoughtful mathematician Jbrmulates a definition according to his lights.'
This gives mathematicians the freedom to define their field in any way they want. It enables the primary teacher who is encouraging the use of mathematics as a language, the secondary teacher who is asking fifteen-year-olds to be creative and pose their own questions, the university lecturer encouraging proofs to be rigorous and the would-be Andrew Wiles extending the subject to solve hitherto unsolvable problems, all to be united under the banner of mathematics. In fact, isn't that why the subject is so important? There are far more people using mathematics in this world than there are using the English language.
So, when I am asked to consider …