Honorary Secretary to the Royal Dublin Society.

[The Imperial Dictionary of Universal Biography, vol. II, p. 801.]

HAMILTON, SIR WILLIAM ROWAN, Royal Astronomer of
Ireland, one of the most distinguished of living men of science,
was born in Dublin on the 4th of August, 1805. There are few
instances on record of more vast development of intellectual
power than he early exhibited. At the age of six he had acquired
the elements of Greek and Latin, and at thirteen he was
acquainted with thirteen languages, including Syriac, Persian,
Arabic, Sanscrit, Hindostanee, and Malay. When the Persian
ambassador, Mirza Abou Hassan Khan, was in Dublin in 1819, young
Hamilton addressed to him a congratulatory letter, of which the
latter observed that he did not think there was a man in these
countries who could write such a composition. At the age of ten
an accident directed his attention to mathematics, in which he
became profoundly interested; and at fifteen he had mastered the
ordinary amount of what was known in every department of science.
In 1822 he presented to Dr. Brinkley, then astronomer-royal, a
paper ``On Contacts between Algebraic Curves and Surfaces,''
which was shortly after followed by one on the same subject,
entitled ``Developments,'' both of which elicited the admiration
and procured him the friendship of that eminent man. ``This
young man I do not say *will* be,'' was his remark, ``but
*is* the first mathematician of his age.'' He entered
college in 1823, obtaining the first place and the first Hebrew
premium; and throughout his course never failed in taking all the
highest honours, and obtained two ``optimes,'' an honour
extremely rare in Dublin college. Meantime he had occupied
himself in the application of algebraic geometry to optics, by
which he had arrived at new and important results. These he
communicated in a paper on caustics to the Royal Irish Academy,
subsequently enlarged under the title of ``Theory of Systems of
Rays,'' published in 1828. But his academical course and honours
were brought to a sudden close, more honourable than their most
successful prosecution could have been. Dr. Brinkley vacated the
chair of astronomy on his elevation to the see of Cloyne in 1827,
and amongst the candidates for the chair was Airy, afterwards
astronomer-royal of England. Hamilton was induced to offer
himself, and was appointed while still an undergraduate, and
before he had attained his twenty-second year. Hamilton now
devoted himself entirely to science. His astronomical lectures
were highly popular and eloquent, and he was ardent and assiduous
as a professor. To mathematics, however, his mind turned with a
peculiar predilection, and he has since devoted himself with
distinguished success to investigations in that department of
science. He has been an eminent member of the British
Association since its formation, contributing on all occasions
valuable papers - at Oxford in 1832 one on his system of optics;
at Cambridge in the following year, on his discovery of conical
refraction. In the year 1834 he contributed to the Philosophical
Transactions his paper on a ``General Method in Dynamics.'' The
originality and power displayed in this memoir would have secured
for the author a place amongst the greatest mathematicians of
Europe, even if it had been his only contribution to mathematical
science. Since that time he has continued to apply himself to
these pursuits with diligence and success. Taking up and
elucidating the celebrated argument of Abel against the
possibility of finding a general and algebraic solution for
equations of the fifth degree, he discussed this question by a
method of his own, and showed that various proposed methods of
reduction and solution involved fallacies. Perhaps his most
remarkable discovery was that of the calculus of quaternions. A
quaternion, as its name imports, consists of four parts, one of
which is real, the three others are imaginary. When interpreted
geometrically, the real part answers to undirected quantity, the
imaginary parts to linear magnitude directed along three
rectangular axes; and the entire quaternion expresses by one
combined symbol, capable of addition, subtraction,
multiplication, and division, the direction as well as the
magnitude of a geometrical quantity, as compared with an unit of
magnitude and a fixed direction. The calculus furnishes rules
and methods for operating upon quantities of this kind, and has
been used by its inventor in the discussion of a variety of
questions both geometrical and analytical. Sir W. Hamilton has
applied it with success in his invention and proof of theorems
relating to surfaces of all kinds, and especially to those of the
second order. He has used it in the theory of rotation, and
expressed in its language several of the leading principles and
results of physical astronomy. Hitherto but few mathematicians
have attempted to use this new instrument of research; but its
power is beginning to be understood, and there is little doubt
that Sir W. Hamilton will be remembered as one of the few who
have furnished new methods for the advancement of mathematical
science. The calculus of quaternions is explained by its
inventor in a separate work on that subject. A popular
explanation of it, from the pen of the disoverer, will be found
in the late Professor Nichol's Cyclopedia of Physical Sciences.
It would be impossible to give in a short compass even the titles
of the papers contributed by Sir W. Hamilton to the scientific
journals of his time. In addition to the subjects already
mentioned, he has written upon the dynamics of light, fluctuating
functions, the calculus of probabilities, definite integrals,
&c. One of his latest inventions is a system of anharmonic
co-ordinates, which he has employed with great elegance and skill
in the discussion of various geometrical problems in space as
well as on the plane. To general literature, also, Sir William
has been a contributor, and his poetical compositions have high
merit for their elegance of diction and depth of thought. Few
philosophers have been more honoured. In 1835, on the occasion
of the meeting of the British Association in Dublin, he
delivered, as its secretary, the annual address, and received the
honour of knighthood; he has obtained the gold medals of the
Royal Society, the Royal Irish Academy, and various other high
institutions. Sir William occupied for several years the
presidential chair of the Royal Irish Academy, which he resigned
in 1846, having been elected in 1837. He is a member of most of
the great scientific societies of Europe and America, and was
enrolled amongst the members of the Imperial Academy of
St. Petersburg for his services in ``the integration of dynamical
equations.''

Links:

- William Rowan Hamilton: Some Nineteenth Century Perspectives
- Sir William Rowan Hamilton (1805-1865)
- History of Mathematics

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School of Mathematics

Trinity College, Dublin