Sir William Rowan Hamilton was an Irish mathematician, Andrews professor of Astronomy at Trinity College Dublin, and Royal Astronomer of Ireland. Hamilton’s work is highly praised, yet his private life has been heavily gossiped about; he is often described as having been an unhappily married alcoholic.
In 2017 I published my first book, or actually a history essay because it is written as a ‘defence’, A Victorian Marriage : Sir William Rowan Hamilton, in which I showed that the unhappy and alcoholic view on Hamilton is flawed, and how this idea emerged, unintentionally, from the enormous biography about Hamilton, written by Robert Perceval Graves and published deep within the Victorian era, vol 1 (1882), vol 2 (1885), vol 3 (1889). Reading the biography in the context of his time, a picture emerged of a man who did not just use his enormous intelligence for his work, but also for his private life. A genius in a happy marriage, with ups and downs as we all have.
The first chapters of A Victorian Marriage are a description of Hamilton’s private life. How in 1824, only nineteen years old, he fell in love with Catherine Disney who after some months of unspoken love married someone else, and how it took him six years to cope with his loss. In 1831 he fell in love with Ellen de Vere, who did not love him back, causing months of very melancholy feelings. Then, in the summer of 1832, Hamilton made a remarkable discovery; he saw that he was wasting his life on passion, and found a way to change his behaviour. His zest for life was restored, and he fell in love with Helen Bayly.
Indeed, instead of what has been suggested, that Hamilton always remained to love only Catherine and hence had an unhappy marriage, it is clear from a letter to a friend that he really had been in love with Ellen de Vere, writing that he had had “another affliction of the same kind and indeed of the same degree” as his love for Catherine had been. And having sent his ante-nuptial poems about Helen Bayly to Coleridge, believing that poems had to come from true feelings and highly admiring Coleridge, may serve as one of the ‘proofs’, if these are needed, that he indeed was very much in love with her. The chapters end with Hamilton’s later years and death.
Chapter 8 is about what happened with his first and lost love Catherine Disney. It is shown here that at the time of her marriage, in 1825, Hamilton had not known that Catherine had been forced to marry someone she did not love. Having been told that she was going to marry he did not see her again; he saw her only in 1830, 1845, and in 1853 shortly before she died. Hamilton had assumed that Catherine had wanted to marry until, in 1830, he visited her, and saw that she was unhappy. About the 1845 visit nothing is known, but in 1848 she told him in a correspondence that her marriage had been unhappy from the start. Only in 1853, some weeks before her death, she could finally tell him that her marriage had been coerced, and that she had wanted to marry him. Each time Hamilton again learned about new details, and about how terribly unhappy Catherine was, he was understandably distressed. Which is entirely different from having loved only her his whole life.
The 9th chapter is a description of the Hamiltons at home, as far as it could be extracted from the biography; although they had their ups and downs, as everyone has, they had a good and happy marriage. It also contains a discussion of their illnesses, Hamilton’s gout and Lady Hamilton’s weak health. Very likely reasons are given for Lady Hamilton’s two nervous breakdowns, which directly had to do with her marriage; being a married woman in Victorian times was indeed extremely difficult. Yet both times the Hamiltons were able to solve their problems.
The 10th chapter is about Hamilton’s alleged alcoholism, and it is shown that Graves never made that claim. In the first part of the 11th and last chapter Hamilton’s use of alcohol is discussed on the basis of the DSM-5, using the information found in Graves’ biography. The conclusion was that Hamilton did not meet the DSM-5 conditions for alcoholism and that, had he lived now, he thus would not be regarded as alcoholic.
Having shown that Hamilton was not an alcoholic, it was considered how much chance there had been that he would have become one. To that aim the data from Graves' biography about when and how much alcohol Hamilton drank is used, in a worst case scenario, to fill in the AUDIT test which can be found on p. 17 of the manual published by the World Health Organization, designed to test what the chances are for someone, in this case Hamilton, to become an alcoholic. The overall conclusion was that in two periods of his life Hamilton had an increasing risk of becoming alcoholic, but that he never reached the higher risk levels of becoming one.
During the two periods of increasing risk Hamilton sometimes drank much in public, mainly during parties and dinners, yet he was always temperate at home. The first period started in 1844 when after having discovered the quaternions Hamilton seemed to become overworked, and ended in 1846, with the event at the Geological Society; thereafter Hamilton was warned by Charles Graves, brother of the biographer Graves and fellow mathematician at Trinity College Dublin, that he was ruining his Dublin reputation. Hamilton immediately changed his behaviour and became abstemious for two years. The second period started in the summer of 1848 and ended when, most likely in 1851, but in any case before the end of 1853, Hamilton was again warned by Charles Graves, the gossip was apparently worsening further. This second time Hamilton changed his behaviour less rigorously but lasting; although he did not abstain again, he never drank much any more.
The essay is concluded by discussing briefly where Graves’ information about Hamilton’s private life came from; Graves lived in England during Hamilton’s marriage, and apart from writing letters other means of contact did not exist yet. Also, the biographies written by both Graves in the 1880s, and by Thomas Hankins in 1980, are revalued, showing that all the information the two biographies contain can be placed in a much more positive light by putting Hamilton’s life in the context of his time, and carefully noticing all the nuances Graves gave in his biography.
I started this website when I was writing A Victorian Marriage. It is dedicated to Hamilton’s happy marriage to Helena Maria Bayly, and to how the distorted view on this marriage came about. A second page is filled with photographs of Hamilton’s family, friends and colleagues, to get some notion of how people looked in those days, placing the Hamilton photographs into perspective. A third page is dedicated to the very unhappy life of Hamilton’s first love Catherine Disney; I wrote my second book about her, on the one hand in order to show that it was not at all strange that Hamilton was periodically upset about her fate and that that had nothing to do with his own marriage, but also because her very sad story was in itself worth to be told. Forcing people into marriages they do not want to be in should not be possible anywhere at any time. A fourth page is a miscellany, partly connected to Hamilton, and partly to what I was doing before stumbling on the remarkable stories about the Hamiltons.
This website is ongoing work. I have now planned to write a third book, about Lady Hamilton’s correspondence, and searching for information every now and then I find new details, stories, remarks, which I will give here when I find them. Yet I hope that some day the view on Hamilton’s private life becomes as positive as he deserves, and this work will be finished. While the mathematicians and the physicists carry on the work following from Hamilton’s enormous legacy, of which a glimpse is given below.
This page contains anything not at home in the other pages
From nineteenth century Dublin and Quantum mechanics
to Mars and the Universe.
From subjects belonging to Hamilton’s story,
to my own interests and doings.
Hamilton’s first discovery was a way to describe, at first, optics, and then mechanics. It is now called Hamiltonian mechanics.
In his short article Hamiltonians(1) Terence Tao writes, “At first glance, the many theories and equations of modern physics exhibit a bewildering diversity: compare for instance classical mechanics to quantum mechanics, non-relativistic physics to relativistic physics, or particle physics to statistical mechanics. However, there are strong unifying themes connecting all of these theories. One of these is the remarkable fact that in all of these theories, the evolution of a physical system over time (as well as the steady states of that system) is largely controlled by a single object, the Hamiltonian of that system, which can often be interpreted as describing the total energy of any given state in that system. Roughly speaking, each physical phenomenon (e.g. electromagnetism, atomic bonding, particles in a potential well, etc.) may correspond to a single Hamiltonian H, while each type of mechanics (classical, quantum, statistical, etc.) corresponds to a different way of using that Hamiltonian to describe a physical system. [... In mathematics,] the Hamiltonians play a major role in dynamical systems, differential equations, Lie group theory, and symplectic geometry. [...] Because of their ubiquitious presence in many areas of physics and mathematics, Hamiltonians are useful for building bridges between seemingly unrelated fields, for instance in connecting classical mechanics to quantum mechanics, or between symplectic mechanics and operator algebras.”
Hamilton’s second discovery was the extension of the imaginary numbers to what he called Quaternions. He developed them as pure mathematics, but at the same time he aimed, and succeeded, to use them to solve engineering and astronomical problems.(3)
The quaternions had a difficult start, for instance because they live in four dimensions and therefore are hardly visualizable. About twenty years after Hamilton’s death vector analysis was directly derived from the quaternions,(4) and because contrary to quaternions vector analysis was very visual, intuitive and easy to work with, in physics the quaternions disappeared for a long time. Although it can easily be claimed that in the form of vector analysis they are at the heart of physics, just as Hamilton had expected. But with the coming of computers, in the late 1950s the quaternions themselves emerged again because computers appeared to work with quaternions more easily than with vector analysis.(5) The quaternions mainly reappeared in applied physics; after being used in the Space Shuttle program, they found their way into games and films, and they are now widely used for smoothly changing orientations in for instance robotics, gaming and spacecraft, from your phone up to the rovers on Mars.
Yet for mathematics the history of quaternions is quite different; there they never disappeared from sight. In his upcoming book Quaternion algebras,(2) John Voight writes, “Quaternion algebras have threaded mathematical history through to the present day, weaving together advances in [many branches of mathematics, and they ...] continue to arise in unexpected ways. [...] Quaternion algebras sit prominently at the intersection of many mathematical subjects. They capture essential features of noncommutative ring theory, number theory, K-theory, group theory, geometric topology, Lie theory, functions of a complex variable, spectral theory of Riemannian manifolds, arithmetic geometry, representation theory, the Langlands program – and the list goes on. Quaternion algebras are especially fruitful to study because they often reflect some of the general aspects of these subjects, while at the same time they remain amenable to concrete argumentation. Moreover, quaternions often encapsulate unique features that are absent from the general theory (even as they provide motivation for it). [...] The enduring role of quaternion algebras as a catalyst for a vast range of mathematical research promises rewards for many years to come.”
(1) Terence Tao (2008), Hamiltonians.
(2) John Voight (2020), Quaternion algebras, a work in progress.
(3) Physics as we know it now did not exist yet, see below for the state of science in Hamilton’s days.
(4) Michael J. Crowe (1967), A History of Vector Analysis: The Evolution of the Idea of a Vectorial System.
(5) Alfred C. Robinsons (1958), On the Use of Quaternions in Simulation of Rigid-body Motion. In his Foreword Robinsons writes, “The general subject of quaternions as applied to coordinate conversions has been under investigation for approximately two years, though the bulk of the work reported here was accomplished during the last six months of 1957.” His abstract reads, “The theory of the four-parameter method is developed with specific application to coordinate conversion in aircraft simulations. This method is compared with the direction cosine method both in a theoretical error analysis and in an example simulation on an analog computer. It is shown that the quaternion method is no more sensitive to multiplier errors than is the direction cosine method, and it requires nearly 30 per cent less computing equipment. In addition, the multiplier bandpass requirement in the four-parameter method is only half as severe as for direction cosines. By every important criterion, the quaternion method is no worse than, and in most cases, better than the direction cosine method.”
The Dublin and Kingstown Railway was Ireland's first railway,
the locomotive depicted here was built in 1834.
Copied from the Dublin Penny Journal of September 1834.
This engraving, of the steam locomotive Hibernia, shows the state of science a year after Hamilton’s marriage, two years after the publication of the Third Supplement to an Essay on the Theory of Systems of Rays(6) which would lead to Hamiltonian mechanics, and nine years before Hamilton found the quaternions.
Thus having made his discoveries in a time in which there were no telephones and radios yet, people travelled by horse, carriage, steam train and steamship, Hamilton’s son reported that “Sir W.” was indifferent to contemporary fame, “arising from his conviction that his belonged to a future age entirely.” He was right, yet little could he know that large parts of his work had to wait until quantum mechancis and the dawn of computers before they would start to blossom.
(6) For short descriptions of the original essay and the three supplements see David Wilkins’ Theory of Systems of Rays.