Background
He was born in Kilbehenny, Limerick, Ireland and educated locally at Mitchelstown, before becoming a teacher under the Board of National Education.
He was born in Kilbehenny, Limerick, Ireland and educated locally at Mitchelstown, before becoming a teacher under the Board of National Education.
He is most famous for Casey"s theorem on a circle that is tangent to four other circles, an extension of the problem of Apollonius. However, he contributed several novel proofs and perspectives on Euclidean geometry. He and Émile Lemoine are considered to be the co-founders of the modern geometry of the circle and the triangle.
He later became headmaster of the Central Model Schools in Kilkenny City.
He subsequently entered Trinity College as a student in 1858, and was awarded the degree of Bachelor in 1862. He was then Mathematics Master at Kingston School (1862-1873), Professor of Higher Mathematics and Mathematical Physics at the newly founded Catholic University of Ireland (1873-1881) and Lecturer in Mathematics at University College, Dublin (1881-1891).
Honours and
Royal Society]
He was elected to the Royal Irish Academy and in 1880 became a member of its council. He was elected a member of the Societe Mathematique de France in 1884 and received the honorary degree of Doctor of Laws from the Royal University of Ireland in 1885.