Three letters, one number, a knife and a stone bridge: how a graffitied equation changed mathematical history

By Robyn Arianrhod, Affiliate, School of Mathematics, Monash University

On October 16 1843, the Irish mathematician William Rowan Hamilton had an epiphany during a walk alongside Dublin’s Royal Canal. He was so excited he took out his penknife and carved his discovery right then and there on Broome Bridge.

It is the most famous graffiti in mathematical history, but it looks rather unassuming:
i ² = j ² = k ² = ijk = –1
Yet Hamilton’s revelation changed the way mathematicians represent information. And this, in turn, made myriad technical applications simpler – from calculating forces when designing a bridge, an MRI machine or a wind turbine,…

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