Numbers & Arithmetic: An Introduction

The arithmetic of numbers is foundational to all of mathematical thought. Virtually every civilization, both ancient and modern, has evolved unique ways of representing numbers and operating upon them. The counting numbers were the natural beginnings of such endeavours. The number 0 was first introduced as a blank and then later gained status among the other numbers by being granted a special symbol. The symbols for 0 varied according to the particular culture which chose them. Negative numbers were known and used as early as the first century B.C. by the Chinese. They utilized different coloured rods to distinguish between positive and negative numbers in their arithmetical calculations, much the same way as we do now in some of our accounting systems with the well known phrases 'in the black' and 'in the red'. What is interesting is that the ancient Chinese used red rods to denote positive numbers and  black rods for negative numbers – just the reverse. However, apart from the rather ubiquitous understanding of credit and debt as being positive and negative, it took a long time for most cultures to recognize the importance of the notion of the negative in mathematics. The minus sign was actually a rather late starter in the world of arithmetic.

Today, our collective understanding of number systems has expanded to include not only the counting numbers, but the whole numbers, the fractions, the decimals, the complex numbers (represented as points in the Cartesian Plane) and even the quaternions (a nineteenth century invention of Sir William Rowan Hamilton, an Irish mathematician). The quaternions are even more 'complex' than the complex numbers because they are represented by points in 4-dimensional real space.

There appears to be a ubiquitous presence of the ethereal workings of numbers within natural phenomena, our own physical beings and other species on planet Earth. Professor Marcus Du Satory of Oxford University, in association with the BBC, presents an argument illustrating how the abstract world of mathematical thought permeates our sensorial realities and even our biology.

Watch The Story of Maths 1. The Language of the Universe (2008) (courtesy of Roger Beaver)

Last Updated by SAS October 07, 2026, 16:00:50