 By winning a competitive examination in 1920, Rowe became a Fellow of Trinity College Dublin and retained the fellowship until his death.He spent the academic year 1920–1921 in Paris, where he studied under Hadamard, Lebesgue, and Goursat.From 1923 to 1926 he was the Donegall Lecturer in Mathematics at TCD and, after a probationary period as an acting professor, was appointed in 1926 to the Erasmus Smith's Professor of Mathematics, retaining the position until his death.