John Derbyshire’s Unknown Quantity is everything a popular mathematics book should be: gentle, chatty, anecdotal and full of mind-aching equations. It is a history of algebra – the study of number systems, things such as quadratic equations, and of everything that is the bane of schoolchildren’s lives.
Babylonian tax inspectors liked quadratic equations, which are useful for finding areas of things. The more you could determine about the land a man owned – not just its total area but all its little shapes – the more efficiently you could dun him for Sodom-and-Gomorrah era VAT. Derbyshire includes a blissful problem in quadratics (written in cuneiform, but to be chanted in hoodoo) found on a clay tablet from 1800 BC, the time of Hammurabi:
The igibum exceeded the igum by 7
What are the igum and the igibum?
12 is the igibum, 5 the igum.
Algebra is filled with Lewis Carroll-ishness and poetry.
What’s the volume of that minaret? How can we make another even fatter/taller/more thrusting one, without using more stones? For this you need a cubic equation. The Persian poet Omar Khayyam, author of the Rubaiyat, began the first serious investigation of examples of these, but what mathematicians wanted was a