By Steve Bishop
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Sir William Rowan Hamilton (1805-1865)
Hamilton has been described as ‘one of the most imaginative mathematicians of the nineteenth century’ (Hankins ) and as a ‘mathematical genius’ (Wilkins, 2005). Hamilton was born in 1805 in Dublin, the son of a solicitor. He lived with his clergyman uncle James from the age of three.
He studied at Trinity College Dublin where he excelled. Before going to Trinity he had read many mathematical papers and had even spotted a mistake, which he rectified, in some of Laplace’s work. There he did work on optics. He then became the Royal Astronomer of Ireland. He remained the Royal Astronomer until his death in 1865.
In an obituary De Morgan (1866) had this to say of Hamilton:
In the case of Hamilton there is no occasion to state anything but the simple fact, known to all his intimates, that he was in private profession, as in public, a Christian, a lover of the Bible, an orthodox and attached member of the Established Church, though of the most liberal feelings on all points. He had some disposition towards the life of a clergyman, but preferred to keep himself free to devote all his time to science: he was offered ordination by two bishops.
And Charles Pritchard (1866) in another obituary wrote:
This memoir would be incomplete if we did not add, that our deceased member, together with the character of a scholar, a poet, a metaphysician, and a great analyst, combined with that of a kind-hearted, simple-minded Christian gentleman; we say the latter because Sir William Hamilton was too sincere a man ever to disguise, though too diffident to obtrude, his profound conviction of the truth of revealed religion.
Gene Chase writes of the link between Hamilton’s faith and his mathematics:
In Hamilton’s Calvinistic theology, as in that of his Scottish friend and pupil Clerk Maxwell, God is the creator both of the universe and of the laws governing it. This means that the lawful relations among material objects are as real as the objects themselves. As a Christian, Hamilton was convinced that the stamp of God is on nature everywhere. He expected a Triune God to leave evidence of the Trinity on everything from three-dimensional space in geometry to an algebra involving triples of numbers. This “metaphysical drive,” in the words of Thomas Hankins, his best twentieth-century biographer, “held him to the task” of looking for a generalization of complex numbers to triples.”
It was this search for triples that led him to the discovery of quaternions. This occurred when out walking with his wife, he then carved the formula on the Broome Bridge – there is now a plaque on a bridge marking the spot:
His formula is even celebrated on a Irish stamp:
He was knighted in 1835. Other contributions made by Hamilton include work in optics, dynamics, complex numbers and a board game ‘icosian’ based on his work in graph theory.
He gave his name to the Cayley-Hamilton theorem and to the Hamiltonian.
Chase, Gene B. 1996. ‘Has Christian theology furthered mathematics‘ In Facets of Faith and Science vol 2: The Role of Beliefs in Mathematics and the Natural Sciences: An Augustinian Perspective. Jitse M. van der Meer (ed.) University Press of America/ Pascal Centre for Advanced Studies: Lanham/ Ancaster.
De Morgan, Augustus. 1866 ‘Sir W. R. Hamilton’ Gentleman’s Magazine and Historical Review, vol. I. (new series) : 128-134.
Hankins, Thomas L. 1980. Sir William Rowan Hamilton. John Hopkins University Press.
Pritchard, Charles 1866. William Rowan Hamilton. Monthly Notices of the Royal Astronomical Society 26, 109-118.
Wilkins, David R. 2005. ‘William Rowan Hamilton: mathematical genius’ Physics World (Aug), 33-36.
 It seems Chase may be mistaken in assuming that Hamilton’s faith was Calvinistic. However, his sister certainly was see e.g. E. P. Graves, 1889, Life of Sir William Rowan Hamilton p. 112.
Steve Bishop is the compiler of A Bibliography for a Christian Approach to Mathematics and the author of several articles on the relationship between faith and math. Look for future posts from him in this series on Christian Mathematicians.
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Thanks for a superb article.
John D. Miller