Skip to Content

Hamilton Walk

Photo of William Rowan Hamilton

William Rowan Hamilton

(1805 - 1865)

This is an annual walk held on the 16th of October, formerly known as the Quaternion Walk. Places on the walk should be booked with Dr. Fiacre Ó Cairbre (Tel: 01 708 3763 or Email: Fiacre.OCairbre@nuim.ie ).

Press Release - Hamilton Walk, 16th October, 2014

Twenty Years of the Hamilton Walk

Recently it has been graced by famous guests: the Fields Medallists, Timothy Gowers (2004), Efim Zelmanov (2009), the Nobel Prize winners: Murray Gell-Mann (2002), Steven Weinberg (2005), Frank Wilczek (2007) and Andrew Wiles of Fermat's Last Theorem fame (2003) and Roger Penrose (2013).

The discovery of the quaternions


In 1843, on a bright October day, William Rowan Hamilton, the greatest Irish Mathematician of all time, discovered the numbers called Quaternions.

For many years he had been trying to find a satisfactory way to multiply points in three dimensions, in such a way as to allow division. The idea of using four dimensions instead, and the way to do it, came to him in a flash, as he walked with his wife by the Royal Canal. Since it is one of the few major mathematical discoveries which is precisely located in time and circumstances, the event is very well-known in the international mathematical community, and people from all over the world know about "Hamilton's Bridge". When he made the discovery, Hamilton paused under Brougham (or Broom) Bridge, took out his penknife, and scratched the fundamental formula:


i2 = j2=k2=ijk=-1

into the stone.

Photo of Hamilton Walk, Broombridge, 2005

Professor O'Farrell giving the speech at Broom Bridge, Hamilton Walk 2005

The day was the 16th of October, 1843. No trace of this can be found today, but in 1958 a plaque was erected on the site, commemorating the discovery and displaying the formula.

Hamilton lived and worked at Dunsink Observatory, and was on his way into Dublin to attend a meeting at the Royal Irish Academy.

Of other such incidents, the outstanding ones are perhaps Archimedes' discovery while bathing, and Poincare's while stepping off a bus. The relative durability of the Royal Canal and its stonework makes the scene of Hamilton's discovery unique, and has led a steady trickle of mathematicians to make the pilgrimage to Broom Bridge.

In 1990, we (the Department of Mathematics at NUI Maynooth) initiated the annual commemoration on the anniversary of the discovery, in the form of a walk from Dunsink observatory to Broom Bridge. Since then, a growing number of people have been participating. In 1993, the sesquicentenary, the first New Yorker appeared. He had flown across just for the day.

What happened in 2014:

About 350 people participated in the walk. There were students and staff from Maynooth University, St. Patrick's College, Drumcondra, WIT, UCG, Kilbeggan Mercy school, Coláiste Mhuire, Cabra, Mount Temple Comprehensive, Gaelcholáiste Reachrann, Donaghmede, Our Lady's Templeogue, Kildare Town Community school and a great diversity of people from the general public. There were also groups from the Cabra Community Council, Royal Canal Amenity Group and the Castleknock Tennis Club. Fiacre Ó Cairbre and Eoin Gill spoke at Dunsink Observatory and Tony O'Farrell spoke at Broombridge.

What happened in 2013:

About 120 people came on the walk. There were students and staff from NUI, Maynooth, St. Patrick's College, Drumcondra, WIT, TCD, DIT, Maynooth Post Primary, St. Colman's College of Claremorris, Co. Mayo and a wide variety of people from the general public. There were also groups from the Cabra Community Council and the Royal Canal Amenity Group. Roger Penrose, Fiacre Ó Cairbre and Eoin Gill spoke at Dunsink Observatory and Tony O'Farrell spoke at Broombridge.

What happened in 2012:

About 150 people participated in the walk. There were students and staff from NUI, Maynooth, St. Patrick's College, Drumcondra, DIT, WIT, TCD, Coolmine Community School, Maynooth Post Primary and a great diversity of people from the general public. There were also groups from the Cabra Community Council, the Royal Canal Amenity Group and the Castleknock Tennis Club. Fiacre Ó Cairbre, Eoin Gill and Luke Drury spoke at Dunsink Observatory and Maurice O'Reilly spoke at Broombridge.

What happened in 2011:

A large group of about 140 people came on the walk. There were students and staff from NUI, Maynooth, St. Patrick's College, Drumcondra, UCD, DIT, WIT, TCD and a great diversity of individuals from the general public. There were also groups from the Fingal Heritage Society, Cabra Community Council and the Royal Canal Amenity Group. Fiacre Ó Cairbre and Eoin Gill spoke at Dunsink Observatory. Later, Anthony G. O'Farrell gave a speech at Broombridge. Mary Mulvihill made some recordings on the walk for a radio podcast and Zoe Comyns interviewed various people on the walk for a radio documentary.

What happened in 2010:

Photo at Hamilton Walk, Dunsink Observatory, 2010

Professor O'Farrell, Eoin Gill, Joan Burton T.D and Dr. Fiacre Ó Cairbre on the Hamilton Walk, 2010.

About 120 people participated in the walk. Fiacre Ó Cairbre, Joan Burton T.D. and Eoin Gill of Calmast spoke at Dunsink Observatory at the start of the walk. Later, Anthony G. O'Farrell gave a speech at Broombridge. There was a great diversity of people on the walk including staff and students from NUI, Maynooth, St. Patrick's College, Drumcondra, UCD, Waterford IT, TCD, DCU, St. Fintina's Post Primary, Longwood, members of the Cabra Community Council, the Royal Canal Amenity Group and the South Fingal Heritage Society. Many other individuals, who had read/heard about the walk in the media, also joined us on the day. The walk was also featured on local radio Phoenix FM.

What happened in 2009:

About 200 people participated in the walk. Fields Medallist, Professor Efim Zelmanov, gave a talk at Dunsink Observatory. Later, Fiacre Ó Cairbre unveiled the restored Hamilton plaque at Broombridge and Professor Anthony G. O'Farrell gave a speech at the bridge. There was a wide variety of people on the walk including staff and students from NUI Maynooth, St. Patrick's College, Drumcondra, Waterford IT, St. Colman's , Claremorris, St. Declan's, Navan Rd, Castleknock College, members of Cabra Community Council and the Royal Canal Amenity Group. Many other individuals, who had read about the walk in the media, joined us for the event. The walk was one of the main events for Maths Week Ireland which aims to promote the understanding, appreciation and awareness of mathematics among schoolchildren and the general public. The walk was featured on the Morning Ireland programme on RTÉ radio.

Photo of Hamilton Walk, Dunsink Observatory, 2009

Professor O'Farrell, Professor Efim Zelmanov (Fields Medallist) and Dr. Fiacre Ó Cairbre on the Hamilton Walk, 2009.

What happened in 2008:

Photo of Hamilton Walk, Dunsink Observatory, 2008

Setting off from Dunsink Observatory,
Hamilton Walk 2008

A large group participated in the walk. Harvard Professor, Lisa Randall, gave a talk at the start of the walk in Dunsink. Later, Professor Anthony G. O'Farrell gave a speech at Broombridge. There was a diverse group of people on the walk including students and staff from NUI, Maynooth, Trinity College, Waterford IT, Maynooth Post-Primary School, Royal Canal Amenity Group and Cabra Community Council. Many other individuals, who had read about the walk in the media, also joined us on the day.
The walk was one of the main events for Maths Week Ireland which aims to promote the understanding, awareness and appreciation of mathematics in schools and the general public.

What happened in 2007:

About 200 people participated in the walk. Nobel Prize winner, Professor Frank Wilczek, gave a talk in Dunsink Observatory at the start of the walk. Later, Professor Anthony G. O'Farrell gave a speech at Broombridge. There was a great variety of people on the walk including staff and students from NUI Maynooth, St. Patrick's College, Drumcondra, Maynooth Post-Primary School, Lucan Community College and Longwood College. Many other individuals, who had read about the walk in the media, also joined us on the day. The walk was one of the main events for Maths Week Ireland which aims to promote the understanding, awareness and appreciation of mathematics in schools and the general public.

What happened in 2006:

About 250 people participated in the walk. Professor Ingrid Daubechies from Princeton gave a talk in Dunsink Observatory at the start of the walk.
Later, Dr. Maurice O'Reilly gave a speech at Broombridge. The walk was one
of the events for the inaugural Maths Week Ireland. There was a great variety of people on the walk including staff and students from NUI Maynooth, St. Patrick's College, Drumcondra, Waterford IT, Maynooth Post-Primary School, Lucan Community College, Maryfield College, Colaiste Bride, St. Columba's College and St. Patrick's Cathedral Grammar School. Many other individuals, who had read about the walk in the media, also joined us on the day. A Radio crew covered the walk and it appeared on RTÉ Radio 1 later in the week.

What happened in 2005:

About 150 people participated in the walk.  Nobel Prize Winner,  Professor Steven Weinberg gave a talk in Dunsink Observatory at the start of the walk.  

Later, Professor A.G. O'Farrell gave a speech at Broombridge. There was a diverse group of people including staff and students from NUI Maynooth, St. Patrick's College Drumcondra, DCU and St. Columba's College. A wide variety of individuals, who had read about the walk in the media, also joined us on the day. A television crew covered the walk and it appeared as part of an RTÉ documentary on Hamilton (7.30 p.m., Nov 14th - Léargas).

What happened in 2003:

About 150 people participated in the walk. This was the greatest number of participants ever. Professor Andrew Wiles gave a talk in Dunsink Observatory at the start of the walk.  Also, the Minister of State, Brian Lenihan, addressed the group at the Observatory. Later, Professor A.G. O'Farrell gave a speech at Broom Bridge. There was a diverse group of people including staff and students from NUI Maynooth, St. Patrick's College Drumcondra, DIT Kevin St, UCD, Maynooth Post-Primary and St. Andrew's, Booterstown. There were also members of the Royal Canal Amenity Group. A variety of individuals, who had read about the walk in the media, also joined us on the day. A group of people walked on into town and ended up in the Royal Irish Academy where they were welcomed with refreshments. A television crew covered the walk and it appeared on the national six o'clock news.

What happened in 1999:

We did something extra this year. First, a bus brought us from Maynooth to Dunsink. After the walk, the bus brought us from the bridge to Trim, Co. Meath.

On arrival in Trim we visited the house where Hamilton lived and received his early education. This house, now called St. Mary's Abbey, is beautifully situated on the banks of the Boyne across from the spectacular ruins of Trim Castle. From there we proceeded to a local establishment for dinner and an evening of entertainment, including a talk on Hamilton by Dr. Ó Cairbre, musical interludes and a table quiz. Finally the bus brought us back to Maynooth. In all, there were about forty-five people, mostly staff and students.



page | by Dr. Radut