Died: 14 September 1959 in Lochgilphead, Argyll, Scotland

James Mitchell's father was James Mitchell (born in Edinburgh about 1839) who was a school board officer. His mother was Thomasina A Mitchell (born in England about 1839).

James Mitchell studied at George Watson's College, Edinburgh, where he had a highly successful career winning many prizes in a range of subjects. He entered the University of Edinburgh where he held the Welsh Mathematics Bursary, the Horslie-Scott Bursary and the Drummond Mathematics Scholarship. He won medals or prizes in a wide range of subjects: mathematics, natural philosophy, Latin, Greek, logic, and psychology.

Mitchell graduated with an M.A. with First Class Honours in Mathematics and Natural Philosophy in 1893, then continued his studies, being awarded a B.Sc. in 1895. He undertook postgraduate studies in Berlin under Lazarus Fuchs and Hermann Schwarz. After travels in Europe and the United States he was appointed to the University of Edinburgh, but quickly decided to make a career in school teaching. He taught at Waid Academy, Anstruther, Fife, from 1896; The Academy, Nairn, from 1900; The Academy, Kilmarnock, from 1905; and Lochgilphead School, Argyll, from 1912 where he was Headmaster.

In March 1894, after obtaining his first degree, Mitchell joined the Edinburgh Mathematical Society. He remained in the Society throughout his career. He was elected to the Royal Society of Edinburgh on 2 July 1900, his proposers being A Crum Brown, Cargill Gilston Knott, Peter Guthrie Tait, Alexander Buchan.

Mitchell married Margaret J Mitchell (born in Port of Menteith, Perthshire about 1874). By the 1901 census they had one daughter Margaret A Mitchell. At this time he was living at 7a Bath Street, Nairn and was a mathematics teacher at Nairn Academy.