Mr Tweedie was born in 1868. He was a member of a Scottish Border family, and was educated in Edinburgh. He became a student of Edinburgh University in the days of Tait and Chrystal. In 1890 he graduated M.A. with First-Class Honours in Mathematics and Natural Philosophy. In the same year he took the degree B.Sc. After this he continued his mathematical studies at the Universities of Göttingen and Berlin. He then returned to Edinburgh University, where he became the Lecturer in Pure Mathematics under Professor Chrystal. He held this appointment for over twenty years.
Mr Tweedie was a man of wide attainments. He was a good linguist, and was well read in the works of the geometers of Britain, France, Italy, and Germany. He wrote a large number of original papers. He contributed a considerable number of articles to the Proceedings of the Edinburgh Mathematical Society. Of this Society he was a Past-President. He was the author of certain papers in the Proc. Roy. Soc. Edinburgh, and he produced many mathematical articles for an encyclopaedia. He was keenly interested in the school teaching of mathematics, and, in conjunction with a friend, wrote a well-known Trigonometry. For a long time he was a University Inspector of Schools under the Scottish Education Department.
Owing to failing health he was obliged to resign his academic duties some years ago, but was able, in the face of overwhelming difficulties, due to illness, to pursue a long-cherished scheme of writing on the Scottish mathematicians particularly Maclaurin and Stirling. Some of these papers appeared in vols. viii., ix. and x. of the Gazette - two have been mentioned already - others were published in the Proceedings of the Royal Society of Edinburgh, and in the Proceedings of the Edinburgh Mathematical Society. In continuation of this line of research he published in 1922 a volume entitled James Stirling, a Sketch of his Life and Works, along with his Scientific Correspondence. His last publication dealt with Gray, the arithmetician, the Scottish Cocker.