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A Case For Mathematics: To Begin At The Beginning

by Dexter Booth 12th March 2019

In the first of an eight-part blog series 'The Invention of Numbers', Dexter Booth explains why the number system was constructed

The White Rabbit put on his spectacles. ‘Where shall I begin, please your Majesty?’ he asked.
‘Begin at the beginning,’ the King said gravely, ‘and go on till you come to the end: then stop.’
- Lewis Carrol, Alice's Adventures in Wonderland
Within these blogs is a tale of how the number system can be constructed, starting from the bean-counting whole numbers and ending with the complex numbers that measure the innermost workings of an atom. It is not a primer in arithmetic, more a treatise on the dynamic interaction between human need and human invention. The development described is not historic; as with a lot of human endeavour, the actual, historic development was a haphazard, hit-and-miss affair. No, the development here is a pragmatic one that moves back and forth between needs that identify problems and their resolution via invention; a pragmatic engine that culminates in one of the most remarkable of achievements of the human mind.

Why numbers? Because they are the alpha and the omega of mathematics; the seed corn from which springs our entire ability to understand the workings of the universe around us. From the tick-tock of a simple pendulum to the formation of the stars in the firmament, without numbers we would comprehend nothing!

We are taught about whole numbers from an early age; we count in the cradle. As infants we progress into fractions and then into negative numbers as we move through our school years. We even meet the odd irrational number like pi or Euler's number or the square root of 2 if we are lucky but no-one ever tells us where these numbers come from. Oh yes, we are told about Pythagoras, the area of a circle and, possibly, natural logarithms but no-one ever talks about the numbers themselves. We then move on into College and people talk about imaginary numbers, the word itself giving the impression that they do not really exist – regardless of whether we understand what the existence of a number really means anyway. Then we dash into complex numbers and immediately confuse the word complex with complicated with the result that little is really understood about what is basically quite straightforward. Straightforward yet very important, standing as it does at the gates of mathematics through which all our understanding of the world around us is found. Like it or not, mathematics is at the root of all of our intellectual endeavours; it has taken us from the cave mouth to where we are today – walking on the moon and beyond and the aim of this blog is to expose you to the power of the inventive human mind as the very foundations of mathematics unfold before you.

This blog is the first of Dexter Booth's 'The Invention of Numbers' series. The rest can be found below:

  1. A Case for Mathematics (the one you're reading now)
  2. Inventing The Idea Of Numbers
  3. Numerals and Numbers
  4. Whole Numbers, Natural Numbers And Integers
  5. Coming soon!
  6. Coming soon!
  7. Coming soon!
  8. Coming soon!
Featured image: 'LH 95 star forming region of the Large Magellanic Cloud' by European Space Agency. Available on Wikimedia Commons via CC BY 4.0