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Math

*Most mathematicians have heard the story of how Hamilton
invented the quaternions. In 1835, at the age of 30, he had discovered
how to treat complex numbers as pairs of real numbers. Fascinated by the
relation between C and 2-dimensional geometry, he tried for many years
to invent a bigger algebra that would play a similar role in
3-dimensional geometry. In modern language, it seems he was looking for
a 3-dimensional normed division algebra. His quest built to its climax in
October 1843. He later wrote to his son, “Every morning in the early
part of the above-cited month, on my coming down to the 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 substract them’.”
The problem, of course, was that there exists no 3-dimensional normed
division algebra. He really needed a 4-dimensional algebra.
Finally, on the 16th of October, 1843, while walking with his wife along
the Royal Canal to a meeting of the Royal Irish Academy in Dublin, he
made his momentous discovery, “That is to say, I then and there felt the
galvanic circuit of thought close; and the sparks which fell from it
were the fundamental equations between i, j, k; exactly such as I have
used them ever since.” And in a famous act of mathematical vandalism, he
carved these equations into the stone of the Brougham Bridge:*

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

(source: *The Octonions* by John Baez).

It took eight years for Hamilton to discover Quaternions. Now compare that to the average time it takes you to complete a project.