August 4 – Happy Birthday, William Rowan Hamilton

Posted on August 4, 2015

To this day, mathematicians pay homage to today's famous birthday, William Rowan Hamilton, by walking from Dunsink Observatory to Broom Bridge, in Dublin, Ireland.

And there they reach the spot where Hamilton was struck by a brilliant thought.

This is where he carved an equation into the side of the bridge with his pen knife. This equation is the most famous of Hamilton's mathematical contributions: an equation for quaternions.

Actually, mathematicians and other tourists cannot see even a remnant of Hamilton's equation carving, but there is a stone plaque under the bridge to commemorate the discovery of quaternions .

You are probably wondering what quaternions are. They are a number system that doesn't work the same way as our more familiar number system. (To give an example of a difference, multiplication isn't commutative. You know how, in our familiar number system, 3 time 6 equals 6 time 3? Well, in quaternions, that kind of turn-around doesn't always work.)

It seems like a theoretical, pure-mathematical number system would have no practical applications, but in actual fact, quaternions are used in 3-D computer graphics, crystal analysis, and other modern scientific applications.

Hamilton, born on this date in 1805, was more than just a mathematician – he was also a physicist and an astronomer. He made important contributions to mechanics, optics, and algebra, and people utilized his work in theories on electromagnetism and quantum physics.

Apparently he showed his talent early. Astronomer Bishop Dr. John Brinkley said of 18-year-old Hamilton, “This young man, I do not say will be, but is, the first mathematician of his age.” 

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