Leopold Kronecker, a nineteenth-century German mathematician, once said ‘God created the integers; all else is the work of man’.

Although it is not entirely clear how literally one should take his witticism, historically he is far from alone in suggesting a divine origin for mathematics. In ancient Mesopotamia, it was a gift from Nisaba, the patron goddess of scribes. ‘Nisaba, the woman radiant with joy, the true woman, the scribe, the lady who knows everything, guides your fingers on the clay,’ wrote a scribe in the 20th century BC. ‘Nisaba generously bestowed upon you the measuring rod, the surveyor’s gleaming line, the yardstick, and the tablets which confer wisdom.’ On Babylonian mathematical tablets, the solution to a problem was never complete until the solver wrote, ‘Praise Nisaba!’ at the end.

According to the ancient Chinese, the originator of mathematics was Fu Xi, the legendary first emperor of China. He is often depicted holding a carpenter’s square. ‘Fu Xi created the eight trigrams in remote antiquity to communicate the virtues of the gods,’ wrote the third-century mathematician Liu Hui. In addition, he says, Fu Xi ‘invented the nine-nines algorithm to coordinate the variations in the hexagrams.’ The trigrams and hexagrams are the basic units of Chinese calligraphy; thus, in a loose sense, Fu Xi is being credited with the invention of writing, while the ‘nine-nines algorithm’ means the multiplication table. Thus, mathematics was not only divinely inspired, but was invented at the same time as written language.

We can already discern in these accounts three distinct branches of mathematics, which have continued to flow abundantly over the centuries since then. The first branch is arithmetic or algebra, the science of quantity; the second is geometry, the science of shape; and the third is applied mathematics, the science of translating mathematics into solutions to concrete problems of engineering, physics, and economics.

A fourth wellspring is not apparent in the above quotes, and that is the science of the infinite – the analysis of both infinitely large and infinitely small quantities, which are essential to understand any process of continuous motion or change. Mathematicians simply call this branch of mathematics ‘analysis’, even though the rest of the world interprets this word to mean something quite different.

Thus, I consider the four main tributaries of mathematics to be Algebra, Geometry, Applied Mathematics, and Analysis. All four of them mingle together and cooperate in a most wonderful way, and witnessing this interaction is one of the great joys of being a mathematician. Nearly every mathematician finds himself or herself drawn more to one of these tributaries than the others, but the beauty and power of the subject undoubtedly derives from all four.

This is an edited extract from The Universe in Zero Words: The story of mathematics by Dana Mackenzie, published by NewSouth.