He was born on 19 April 1858 in Greenlaw in Berwickshire the third son of Robert Gibson JP (1830–1903).
He attended the free church school in the parish, and showing great promise, went to the University of Glasgow where he graduated with an MA in 1882 and immediately joined the university staff.
[1] In 1895 he became a professor of mathematics at the Glasgow and West of Scotland Technical College.
In 1909 he returned to the University of Glasgow as a professor, replacing his mentor Prof William Jack.
Other lecturers include Charles Coulson and Edward Collingwood.