David Middleton Greig was brought up in Dundee where his father and his grandfather had practised medicine. He was educated at St Andrews and Edinburgh University. After graduating, he was resident medical officer at Perth Asylum before becoming a surgeon with the Army medical staff for three years from 1886 to 1889. His father had also been in the army, in the Crimea, where he had been looked after by Patrick Heron Watson, a former fellow student, when he was ill.
After he left the army Greig became demonstrator in anatomy and lecturer in clinical surgery at University College, Dundee and assistant surgeon to Dundee Royal Infirmary. The outbreak of the South African War found him an officer in the Forfar Volunteer Artillery. He served as a major in the RAMC throughout the Boer War. On his return to civil life he became full surgeon to Dundee Royal Infirmary and acted as examiner in surgery at the University of St Andrews. His special interest as a surgeon was in paediatrics.
Throughout his life, he was a keen collector of pathological specimens, especially of bone pathology and he donated his large collection to the College. He published a monograph ‘Clinical Observations on the Surgical Pathology of Bone’.
He was Conservator of the College Museum for fifteen years from 1921. During this time he rearranged and catalogued all the exhibits with their clinical and post-mortem findings. In 1925 he assumed the additional duties of Librarian of the College.