William Rowan Hamilton

An Irish mathematician who, after years of trying to extend the complex numbers from a plane to a space, had the answer suddenly come to him while walking along the Royal Canal in Dublin on 16 October 1843. He scratched the formula $i^2=j^2=k^2=ijk=-1$ into the stonework of Brougham Bridge. Those were the quaternions, and from his work the modern vector calculus eventually emerged: the mathematics that today describes everything from satellite orientation to the rotation of a tablet screen.