The Irish mathematician and physicist William Rowan Hamilton, who was born 220 years ago last month, is famous for carving some mathematical graffiti into Dublin's Broome Bridge in 1843.

But in his lifetime, Hamilton's reputation rested on work done in the 1820s and early 1830s, when he was still in his twenties. He developed new mathematical tools for studying light rays (or "geometric optics") and the motion of objects ("mechanics").

Intriguingly, Hamilton developed his mechanics using an analogy between the path of a light ray and that of a material particle.

This is not so surprising if light is a material particle, as Isaac Newton had believed, but what if it were a wave? What would it mean for the equations of waves and particles to be analogous in some way?

The answer would co

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