He was educated at Queen's College Galway, where he won a first-year scholarship in the Science Division of the Faculty of Arts and the Sir Robert Peel Prize in Geometry in 1876.
He then won first place in an open examination for a scholarship to Sidney Sussex College at Cambridge from which he graduated BA (6th wrangler) in 1884.
[2] In 1885, Anderson returned to Queen's College Galway, where he was appointed Professor of Natural Philosophy, a post he held until 1934.
He was appointed President of Queen's College Galway on the resignation of Professor W. J. M. Starkie in 1899.
His daughter, Emily Anderson, was a Professor of German, music historian and noted cryptanalyst.