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William Fowan Hamilton, by all odds Ireland's gratest caaim to fame in the
field of mathematics, was born in Dublin in 1805 and, except for short visits
elsewhere, spent his whole life there. He was early orphaned, but even before
that. When only a year old, his upbringing was entrusted to an uncle who gave
the boy a strenuous but lopsided education with a strong emphasis on languages.
He was fluently acquainted with as many foreige hanguages as he was
years old. He developed a fondness for the classics and,
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with no real succcess,
indulged in what was to become a lifelong desire-the writing of poetry.
He
became an intimate friend and mutual admirer of the great poet William
Wordsworth.
It was not until Hamilton was fifteen that his interests changed and he
became excited about mathematics. The change was brought about by his
meeting Zerah Colburm, the American lightning calculator, who, though only a
youngster himself, gave a demonstraltion of his powers at an exhibition in
Dublin. Shortly after, Hamilton chanced upon a copy of Newton's Arithmetica
universalis. This he avidly read and then mastered analytic geometry and calculus.
Next he read the four volumes of the Principia and proceeded to the great
mathematical works of the continent. Reading Laplace's Mecanique celeste, he
uncovered a mathematical error and in 1823 wrote a paper on it that attracted
considerable attention. The following year, he entered Trinity College, Dublin.
Hamilton's career at the university was unique. For in 1828, when he was
only twinty-two year old and still and undergraduate, the electors unanimously
appointed him Royal Astronomer of lreland, Directorof the Dunsink Observatory,
and Professor of Astronomy at the University. Shortly after on mathematical
theory alone, he predicted conical refraction in biaxial crystals, which
was then dramatically confirmed experimentally by physicists. In 1833, he
presented to the lrish Academy his significant paper in which the algebra of
complex numbers appears as an algebra of ordered pairs of real numbers (see
Section 13-10). He was knighted in 1835.
Following his 1833 paper. Hamilton thought off and on for a long peroid of
years on albebras of ordered triples and quadruples of real numbers, but was
always stymied on the matter of how to define multiplication so as to preserve
the familiar laws of that operation while at the same time making the operation
fit his physical investigations. Finally, in a flash of intuition in 1843 (as described
in Section 13-10), it occurred to Hamilton that he was demanding too
much and that he had to sacrifice the commutative law, and the algebra of
quaternions, the first noncommutative algebre, was suddenly born.
Hamilton's name is encountered by stydents of physics in the so-called
Hamiltonian function and in the Hamilton-Jacobi differential equations of dynamics.
In matrix theory there is the Hamilton-Cayley theorem, equation, and
polynomial; in mathematical recreations, one encounters the Hamiltonian
game played on a regular dodecahedron (see Problem Study 13.24)
It is perhaps pleasing to Americans to recall that in the sad final years of
Hamilton's illness and marital strife, the newly founded National Academy of
Sciences of the United states elected him as its first foreign associate. Another
rare honor and compliment accored Hamilton occurred when, in 1845. He
attended the second cambridge meeting of the British Association; he was
lodged for a week in the sacred rooms of Trinity College in which tradition
asserts that Isaac Newton composed his Principia.
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