Arthur William Conway FRS (October 2 1875–1950) was President of University College Dublin between 1940 and 1947.
Born in Wexford, he received his early education in St Peter's College, Wexford and proceeded to enter old University College, Dublin in 1892. He received his BA degree from the Royal University of Ireland in 1896 with honours in Latin, English, Mathematics and Natural Philosophy. In 1897, he received his MA degree with highest honours in mathematics and proceeded to Corpus Christi College, Oxford, becoming University Scholar there in 1901. Also in 1901, he was appointed to the professorship of Mathematical Physics in the old University College and held the Chair until the creation of the new college in 1909. He also taught for a short time at St. Patrick's College, Maynooth.
He married Agnes Christina Bingham on 19 August 1903; they had three daughters and one son.
One of Conway's students was Éamon de Valera, whom he introduced to quaternions which originated in Ireland. De Valera warmed to the subject and engaged in research of this novelty of abstract algebra. Later, when de Valera became Taoiseach (he was also subsequently President of Ireland), he called upon Conway while forming the Dublin Institute for Advanced Studies.
Conway is remembered for his application of biquaternion algebra to the special theory of relativity. He published an article in 1911, and in 1912 asserted priority over Ludwik Silberstein, who also applied biquaternions to relativity. This claim was backed up by George Temple in his book 100 Years of Mathematics. In 1947 Conway put quaternions to use with rotations in hyperbolic space. The next year he published quantum mechanics applications which were referred to in a PhD thesis by J. Lambek in 1950.