Mathematical genius

County Meath was central to the life of Ireland’s greatest ever scientist, a man whose mathematical breakthroughs more than 150 years ago have been utilised by space-age video-game and movie software in the 21st century.

Hamilton spent his formative years in Trim, enjoying the bliss of precocious early learning under the shadow of the castle, where his character of an academic of historic proportions was moulded.
But the county was central to the lowest points in his life too, for he never fully recovered from a broken heart after his lover, whom he met at Langford Estate in Summerhill in his late teens, was married off to a clergyman, a rebuke that would drag him into the depths of alcoholism in later years.
A programme of events scheduled to celebrate the 200th anniversary of the mathematician’s birth, Hamilton 2005, saw more than 50 events take place nationwide over the past 12 months, while the Government added to 2005 the unwieldy but no doubt well-meaning moniker “Hamilton Year: Celebrating Irish Science”.

In addition to his standing as a ground-breaking scientist, Hamilton was appointed to the Andrews’ Professorship of Astronomy – and with it Astronomer Royal of Ireland – before he had even graduated from Trinity College, was knighted by the British monarchy by the age of 30 and numbered the famed English poet William Wordsworth among his friends.

Indeed, seemingly not wholly satisfied or preoccupied with his work in science, he also saw himself as a bit of a sonneteer – and found few equals among his Irish contemporaries, earning the prestigious Vice-Chancellor's Prize for English verse during his time at the University of Dublin, an accolade also claimed by such luminaries of the literary game as John Todhunter and Oliver St John Gogarty in later years.

He sent some samples of his verse to Wordsworth but was effectively told by his friend to stick to the day-job, with the poet fearful that Hamilton’s legacy in the field of science would be diluted if he concentrated on lyrical ballads rather than complex theorems.

It is his discovery of quaternions, while out for a walk in 1843 – Ireland’s very own Eureka! moment – that is regarded as his greatest gift to future generations of scientists, mathematicians ... and Playstation-gamers.

Hamilton’s stroll took him from his home at Dunsink Observatory – he was by now Royal Astronomer, a post he would hold for the rest of his life – along the Royal Canal. In a moment of mental clarity, he devised the formula for quaternions, a radical theory relating to complex numbers and three-dimensional space, and scratched the immortal equation, i2 = j2 = k2 = ijk = -1, into the stone of Broome Bridge. (His discovery is celebrated on October 16th each year by the NUI Maynooth’s Hamilton Walk, from Dunsink Observatoty to Broome Bridge, and was attended in 2002 by Murray Gell-Mann, the American winner of the Nobel Prize for Physics in 1969.)

While the equation was regarded for many years as inapplicable outside of applied mathematics, it has found its way, invidiously, into the quotidian lives of people worldwide through its use as a rotational tool in software behind computer games such as the multi-million-selling Lara Croft: Tomb Raider and smash hit movies like The Matrix.

Hamilton’s promise was spotted early, and he was sent from his home in north Dublin to live with his uncle, the Reverend James Hamilton, curate of Trim.

He lived for that time at Talbot Castle, an old manor house and formerly St Mary’s Abbey directly across the river from Trim Castle which was rebuilt from ruins by Sir John Talbot in the 15th century and was later acquired in the 18th century by Jonathan Swift, the author of the satirical masterpiece Gullivers Travels and former Dean of Trinity College.

In the peaceful surrounds of the old manor house, William’s budding genius was given the nourishment from which a stupendous mind would burst forth.

A true child prodigy, he is held to have mastered Latin, Greek and Hebrew by the age of five, and another few years saw him fluent in 13 languages, ancient and modern, European and Asian. Two anecdotes display his exceptional expertise in linguistics: at the age of seven he passed an examination in Hebrew conducted by a doctor of Trinity College, and later, at the age of 14, he is said to have composed a letter in the Persian tongue to Mirza Khan, the Ambassador of Persia, during the dignitary’s visit to Ireland in 1819.

While his uncle guided him in the art of languages, Hamilton hungrily immersed himself in all strands of mathematical teaching and theory from the age of 10, scorching his way through the usual courses of applied and pure mathematics over the next five years.

His status was growing – an American mathematical prodigy, Zerah Colburn, visiting Dublin to exhibit his astonishing powers of calculation, was introduced to his contemporary, and the pair engaged in battles of wits the like of which must have confounded their small-minded elders.

The wonder is that Hamilton managed to avoid burning himself out through the myriad achievements of his boyhood, but such a mind was certain to make its mark in greater circles.

Having worked his way through the theses of Euclid and Newton, his arrival as a mathematician of staggering standing was assured when he submitted a paper to Dr Brinkley, then Bishop of Cloyne and Astronomer Royal of Ireland, elucidating an error spotted in the work of Pierre-Simon Laplace, the renowned French scientist and mathematician.

The graph of Hamilton’s achievements continued on its starkly upward journey through his time at Trinity College, and he was appointed Professor of Astronomy Astronomer Royal of Ireland at the age of 21 – before he had even graduated – while a knighthood followed on the recommendation of the Lord Viceroy of Ireland, Lord Normanby, in 1835. By then he had taken up residence at Dunsink, from where he embarked on his famous walk in 1843, and where he would live until his death, at the age of 60, in 1865.

Yet for all the highlights of an astonishing career, Hamilton’s life-story would not be complete without reference to his periods of melancholy, of a lost love that pushed him to the brink of suicide, and of an introspection that led to alcoholism in his later years.

For Hamilton, though married to Helen Bayly, had never forgotten his first love, Catherine Disney, whom he met at Langford Estate in Summerhill in 1824.

Besotted with the girl, he was tied to his studies and was unable to broach the subject of marriage, and Catherine was soon married off to a clergyman 15 years her senior, a development which broke Hamilton’s heart.

He outlined his love for Catherine in several mournful poems, his own loveless marriage turning unhappy, while the passing of his friend Wordsworth, beloved sister Eliza, two uncles and Trinity fellow James MacCullagh, also had a detrimental impact on his mental state.

His melancholia saw him turn to alcohol as a means of escape, a situation which grew steadily worse after correspondence with Catherine Disney was recommenced. The pair met once more, two weeks before her death, and Hamilton was consumed by grief.

While still suffering from a severe addiction to grape and grain, he threw himself into his work, spending seven years composing his final work, Elements on Quaternions, which was published incomplete and posthumously after his death from a severe case of gout.

His life of achievement extended right until his dying days, for he was informed only a short time before his death that he had been elected to the American National Academy of Sciences, the first non-American to achieve that distinction.

His influence still being felt to this day, his legacy built to last, Hamilton is considered without peer among Irish scientists. And County Meath can lay claim to at least some of his heritage.