On the 16th October 1843 the Irish mathematician William Hamilton was taking a walk with his wife, alongside the Royal Canal in Dublin, when the answer to a problem that he had been puzzling over came to him, and he was so excited by this discovery that he carved the equation:

**I**^{2} = **j**^{2} = **k**^{2} = **ijk** = -1

on a stone of the nearest bridge.

History does not record the reaction of his wife to this act, but judging by his recollection of his conversation with his sons:

*Every morning in the early part of the above-cited month, on my coming down to breakfast, your (then) little brother William Edwin, and yourself, used to ask me: “Well, Papa, can you multiply triplets?” Whereto I was always obliged to reply, with a sad shake of the head: `No, I can only add and subtract them”.*

I suspect that she was not unduly surprised.

The graffiti was soon worn away, but the event was later recorded more permenantly with a commemerative stone with the words:

Here as he walked by

on the 16th of October 1843

Sir William Rowan Hamilton

in a flash of genius discovered

the fundamental formula for

quaternion multiplication

i^{2} = j^{2} = k^{2} = ijk = -1

& cut it on a stone of this bridge

For more information look here: http://math.ucr.edu/home/baez/dublin/ for an account of a trip to the bridge by mathematician John Baez and friends, including some nice photographs of the structure itself.

Another site with more on the mathematical significance of the quaternion, and a quote from Hamilton himself: http://adaptivecomplexity.blogspot.com/2007/06/science-in-against-day-vectors-and.html

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