Sir William Rowan Hamilton
Born: 4 Aug 1805 in Dublin, Ireland
Died: 2 Sept 1865 in Dublin, Ireland
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William Rowan Hamilton discovered the quaternions, the first noncommutative algebra to be studied. He also invented important new methods in Mechanics.By the age of five, William Rowan Hamilton had already learned Latin, Greek, and Hebrew. He was taught these subjects by his uncle, the Rev James Hamilton, who was William's teacher for many years. William soon mastered additional languages but a turning point came in his life at the age of 12 when he met the American Zerah Colburn. Colburn could perform amazing mental arithmetical feats and Hamilton joined in competitions of arithmetical ability with him. It appears that losing to Colburn sparked Hamilton's interest in mathematics.
Hamilton's introduction to mathematics came at the age of 13 when he studied Clairaut's Algebra , a task made somewhat easier as Hamilton was fluent in French by this time.
At age 15 he started studying the works of Newton and Laplace. In 1822 Hamilton found an error in Laplace's Méchanique céleste and, as a result of this, he came to the attention of John Brinkley, the Astronomer Royal of Ireland, who said:
This young man, I do not say will be, but is, the first mathematician of his age.Hamilton entered Trinity College, Dublin at the age of 18 and in his first year he obtained the top mark in classics. He divided his studies equally between classics and mathematics and in his second year he received the top award in mathematical physics. While in his final year as an undergraduate he presented a memoir Theory of Systems of Rays to the Royal Irish Academy.
Hamilton published several further papers on this topic, including one in 1827 in which he predicted theoretically conical refraction in biaxial crystals. This was confirmed experimentally by a colleague two months after his prediction.
In the same year, 1827, Hamilton, although still an undergraduate, was appointed astronomer royal at Dunsink Observatory and professor of astronomy at Trinity College. He succeeded John Brinkley who had become a bishop. Hamilton had not applied for the post, for which there were many excellent candidates including Airy, but was invited to accept it.
Before beginning his duties in this prestigious position, Hamilton toured England and Scotland (from where his family, with the name Hamilton, had originated). He met the poet Wordsworth and they became friends. Wordsworth had to tell Hamilton quite forcibly that his talents were in science rather than poetry.
You send me showers of verses which I receive with much pleasure ... yet have we fears that this employment may seduce you from the path of science. ... Again I do venture to submit to your consideration, whether the poetical parts of your nature would not find a field more favourable to their nature in the regions of prose, not because those regions are humbler, but because they may be gracefully and profitably trod, with footsteps less careful and in measures less elaborate.In 1833 Hamilton published a study of vectors as ordered pairs. He used algebra in treating dynamics in On a General Method in Dynamics in 1834.
On 16 October 1843 (a Monday) Hamilton was walking in along the Royal Canal with his wife to preside at a Council meeting of the Royal Irish Academy. Although his wife talked to him now and again Hamilton hardly heard, for the discovery of the quaternions, the first noncommutative algebra to be studied, was taking shape in his mind.
Hamilton knew the geometrical Argand diagram definition of the complex numbers but he preferred to define complex numbers as pairs (a,b) of real numbers as he had shown in his 1833 paper. He had set himself the task of finding how triples (a,b,c) of real numbers would multiply to give a 3-dimensional analogue. After a number of failed attempts, inspiration struck that day as he walked by the Royal Canal.
And here there dawned on me the notion that we must admit, in some sense, a fourth dimension of space for the purpose of calculating with triples ... An electric circuit seemed to close, and a spark flashed forth.He could not resist the impulse to carve the formulae for the quaternions
iin the stone of Brougham Bridge as he and his wife passed it. Hamilton felt this discovery would revolutionise mathematical physics and he spent the rest of his life working on quaternions.= j
He published Lectures on Quaternions in 1853 but he soon realised that it was not a good book from which to learn the theory of quaternions. Perhaps Hamilton's lack of skill as a teacher showed up in this work.
However he was determined to produce a work of lasting quality and he began to write another book Elements of Quaternions which he estimated would be 400 pages long and take 2 years to write. The title suggests that Hamilton modelled his work on Euclid's Elements and indeed this was the case. The book ended up double its intended length and took seven years to write. In fact the final chapter was incomplete when he died and the book was finally published with a preface by his son William Edwin Hamilton.
Not everyone found Hamilton's quaternions the answer to everything they had been looking for. Thomson wrote:
Quaternions came from Hamilton after his really good work had been done; and though beautifully ingenious, have been an unmixed evil to those who have touched them in any way.Hamilton's later life was unhappy and he became addicted to alcohol. Macfarlane [7] says
... at a dinner of a scientific society in Dublin he lost control of himself, and was so mortified that, on the advice of friends he resolved to abstain totally. This resolution he kept for two years, when ... he was taunted for sticking to water, particularly by Airy ... . He broke his good resolution, and from that time forward the craving for alcoholic stimulants clung to him.Hamilton died from a severe attack of gout shortly after receiving the news that he had been elected the first foreign member of the National Academy of Sciences of the USA.
References elsewhere in this archive:
Tell me about Hamilton's work on the four colour theorem and about his work on abstract linear spaces and on the fundamental theorem of algebra
Tell me about Hamilton's work on orbits and gravitation
Tell me about his work on mathematical games and recreations and about his part in the history of mathematics
You can see a picture of the plaque at Brougham Bridge commemorating where Hamilton discovered the Quaternions.
Show me a picture of Hamilton's Icosian game
References:
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