Imagining Numbers (Particularly The Square Root Of Minus Fifteen)

What happens when we imagine something? When we read a line of poetry - "the yellow of the tulip" - we immediately form an image in our mind's eye. But what if we were asked to imagine a number, in particular an impossible number such as the square root of a negative quantity? What mental picture would appear then?

Imaginary numbers first appeared in the sixteenth century, but it was over 300 years later that the amazing geometric formula enabling us to visualise these otherwise unpicturable figures was discovered. This is the story of how the elusive imaginary number was first imagined.

Drawing unexpected parallels between our understanding of ideas in poetry and in mathematics, Mazur looks at some of the earliest Renaissance explorers of these mysterious numbers, such as Rafael Bombelli, and encourages us to share their bafflement and wonder. Then he shows us, step by step, how to begin imagining imaginary numbers by ourselves . . .