Following his outstanding success at school it was not surprising that Mitchell should gain the Welsh Mathematics Bursary, the Horslie-Scott Bursary and the Drummond Mathematics Scholarship at the University of Edinburgh. A medallist in mathematics, natural philosophy and Latin, he was also a prizeman in Greek, logic and psychology.
After graduation, with First Class Honours in mathematics and natural philosophy, there was a period of study in Berlin, under Professors Fuchs and Schwarz, where Mitchell dealt principally with the theory of functions of a complex variable. From Germany he went to a number of centres in Europe and the United States for further research and training before finally working at the Royal College of Science in Kensington.
In 1896 Mitchell was appointed as an interim lecturer in mathematics at the University of Edinburgh but after this he decided to follow a scholastic career. His many abilities and intense devotion to thoroughness distinguished each teaching appointment that he held.
It is as Headmaster of Lochgilphead School that Mitchell will be best remembered, and during his twenty-three years at that school he raised the academic standard to an exceptionally high level. He received many letters from his former pupils who owed much to their early training at his hands and who now hold responsible positions throughout the world.
In his long and contented retirement James Mitchell enjoyed tending to the flowers in his Lochgilphead garden, playing a skilful game of chess, and considering the latest in mathematical problems. He was elected a Fellow in 1900, and when he died on September 14, 1959, he was the Society's second most senior member.