Does mathematics have elements?

Abstract

For Empedocles, a little over 2400 years ago, there were four chemical elements, fire, water, earth, and air, and they were continually brought together and torn apart by two opposing forces, harmony and discord. For Aristotle, a hundred years later, two binary classification schemes took the place of one: instead of harmony-discord, he had wet-dry and hot-cold. The serious alchemists of the middle ages found that nature was even more complicated than that; they classified matter by its luster, heaviness, combustilibity, solubility, and so on. Boyle, in the 1600's, offered a definition similar to that of a prime number – an element is a substance from which other substances can be made but which cannot be separated into different substances – and analytical chemistry was off and running. A hundred years later Lavoisier (inspired in part by Newton's insight into the paramount importance of weight) could formulate a modified definition that led for the first time to quantitative tables of chemical elements similar to our modern ones.