Posted by: Alexandre Borovik | December 28, 2010

Description of mathematics, take 2 bis

I. Mathematics is an exact language for  description, calculation, deduction, modeling, and prediction  — more a systematic way of thinking than a set of rules.

Using a legal analogy, mathematics is a language for writing contracts with Nature that Nature accepts as legally binding.

II. The practical importance of mathematics lies in its ability to describe the real world.

The real world consists of what matters. The word “matter” as a noun is used for what the physical world is made of. But if we ask, “What’s the matter with Anne?” we may be asking about a physical ailment, or we may be asking about an idea that is causing Anne to behave strangely. Ideas matter.

The whole point of mathematical education is to make ideas real for students, ideas that were not real for them before. Ideas like fractions, for example. The fact that 2/3 is smaller than 3/4 matters in the real world.

III. Mathematically educated people are stem cells of a technologically advanced society. Because of the universality of mathematics, mathematicians and well educated users of mathematics  are flexible in applying and inventing tools for work in technological environments which never existed before.

IV. Learning  mathematics involves the profound assimilation of intellectual and aesthetic criteria as well as practically orientated ones. The very difficulty in learning mathematics makes it a personality-enhancing experience.

[With contributions and borrowings from David Corfield, Tony Gardiner, Michael Gromov, Frank Quinn, David Pierce.]


  1. One aspect of mathematics that has been largely overlooked is how children come to understand, use and communicate the abstract symbolic language of mathematics. Early Childhood researchers Worthington and Carruthers have been researching this important aspect for the past two decades.

    For young children’s mathematics, see: ‘Children’s Mathematics: Making Marks, Making Meaning’ by Carruthers and Worthington: Their new book ‘Understanding Children’s Mathematical Graphics: Beginnings in Play’ is due to be published by Open University Press in March 2011.

    Children’s mathematical graphics’ is a term originated by Carruthers and Worthington, whose extensive research is helping teachers understand and support children’s mathematical thinking. This is a semiotic approach developed through play, helping children understand the abstract symbolic language of mathematics through using their own mathematical graphics to make and communicate their mathematical meanings. In England ‘children’s mathematical graphics’ are recommended in official government documents for early childhood teachers. Their work is widely acclaimed and the authors are winners of several awards.

    The international Children’s Mathematics Network welcomes new members and it is free to join. The website has lots of children’s examples and details of research and publications.

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