The Royal Irish Academy/Acadamh Ríoga na hÉireann champions research. We identify and recognise Ireland’s world class researchers. We support scholarship and promote awareness of how science and the humanities enrich our lives and benefit society. We believe that good research needs to be promoted, sustained and communicated. The Academy is run by a Council of its members. Membership is by election and considered the highest Academic honour in Ireland.

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Hamilton Day

Hamilton Day

Hamilton Day commemorates a groundbreaking discovery by Ireland’s most famous scientist. On 16 October 1843, William Rowan Hamilton discovered quaternion algebra, while walking along the Royal Canal from Dunsink Observatory to the Royal Irish Academy (RIA). This was one of those very rare Eureka moments in the history of science. So excited was he by his discovery that he scratched his equation on the wall of Broome Bridge, Cabra. 

 Sir William Rowan Hamilton

Who is Hamilton?

William Rowan Hamilton was born in 1805 and is universally recognised as the greatest mathematician, and arguably the greatest scientist, that Ireland has produced to date.

He came to early fame for his work on optics, including his remarkable prediction of the phenomenon of conical refraction, but his lasting fame is for his work on the fundamentals of mechanics. Hamilton’s canonical form of the equations of motion, and his emphasis on the importance of variational principles, remain at the heart of theoretical physics and were essential bridges from the world of classical physics to the modern quantum mechanics.

Hamilton’s discovery of quaternions, famously in a moment of inspiration at Broom Bridge, was important in the development of modern abstract algebra and the quaternions remain useful in calculating rotations of solid bodies and are thus important in satellite navigation and video game programming. He died in 1865 in Dunsink Observatory and is buried in Mount Jerome cemetery.

On October 16th 1843 Hamilton was walking with his wife from Dunsink Observatory along the Royal Canal into Dublin to attend a meeting of the Council of the Royal Irish Academy in Dawson Street. For several years he had been trying to generalise the algebra of complex numbers, which Hamilton interpreted as a set of rules for multiplying pairs of real numbers, to three dimensions with rules for multiplying and dividing triples of real numbers, but without success (it is in fact impossible). He records in a letter to his son that as they arrived at Broom Bridge his wife was talking to him, but he was paying no attention when suddenly he had a spark of inspiration and realised that the key was to go to four dimensions where it is possible to define a sensible division algebra, the quaternions. He states that he pulled out his penknife and scratched on the stone of the bridge the fundamental defining relations for the quaternion algebra.

The episode is famous as a classic example of how an idea can suddenly drift up out of the unconscious when the brain is relaxed and receptive - in this case the walk and his wife’s idle chit-chat - after years of hard mental concentration. It is annually commemorated by the mathematical community who re-enact the walk and celebrate this flash of creative inspiration at Broom Bridge every 16th October, now called Hamilton day.

Hamilton Day - A celebration

Each year the RIA celebrates Hamilton’s life and contribution to mathematics by holding Hamilton Day to coincide with the anniversary of Hamilton’s discovery in October 1843. The day includes an award ceremony to recognise the most gifted third level mathematics students in Ireland; a masterclass for early-career researchers; a public discussion on a topical issue and the day concludes with the Hamilton lecture which is given by an international renowned speaker.

2018 Hamilton Day Celebrations

With support from Arup and the Irish Times, the next Hamilton Day will take place on Tuesday 16 October 2018.  

Professor Martin Hairer, Imperial College London, will give the Hamilton lecture in the Mac Neill Lecture Theatre, Trinity College Dublin on 16 October 2018. Booking for the lecture is essential, details to follow in due course.

Martin Hairer is an Austrian mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Professor of Mathematics at Imperial College London, having previously held a position at the University of Warwick and the Courant Institute of New York University.

Martin Hairer has advanced the field of stochastic partial differential equations (SPDEs) by providing a toolkit for addressing these previously thought inaccessible problems. Martin’s work is also furthering the more general areas of stochastic analysis — a part of mathematics concerned with random processes — and stochastic dynamics. In August 2014 he was awarded the Fields Medal for his outstanding contributions to the theory of stochastic partial differential equations, and in particular for the creation of a theory of regularity structures for such equations.

Past Hamilton Day speakers

Past Hamilton Day speakers have included Roger Penrose, Robert Merton, Cédric Villani, Lisa Randall and Frank Wilczek. View a complete list of all Hamilton Day speakers.

In 2015, Professor Daniel Spielman, Henry Ford II Professor of Computer Science, Mathematics, and Applied Mathematics at Yale University gave the Hamilton lecture.

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