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The Hamilton Institute at the National University of Ireland, Maynooth The Hamilton Institute is a multi-disciplinary research centre at the National University of Ireland
Hamilton Mathematics Institute The HMI is a mathematics institute in Trinity College, Dublin, the University where Hamilton studied and worked.
The first time he came up with the formula for quaternions, he was crossing the Broome Bridge in Dublin, and scratched the formula in the stone.
To this day it's commemorated by a plaque on the north-west corner under the railing on the bridge. There's an annual commemorative walk over the bridge on October 16.
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In the National University of Ireland in Galway, in the Aras de Brun building, you may find this stone panel: