Grieve first matriculated at Edinburgh University in October 1903. During his first year of study he took Latin and Greek at Ordinary level, then in the following session, 1904-05, he studied Mathematics, Natural Philosophy, and Chemistry at Ordinary level. He began his Honours studies in 1905-06 but also took Logic at Ordinary level in that year. Over the next few years he took Honours courses in Mathematics, Dynamics, Thermodynamics, Electrostatics, Constitution of matter, Electricity, and Function Theory. He was awarded an M.A. with First Class Honours in Mathematics and Natural Philosophy from Edinburgh University in April 1908.
Grieve then undertook research in geometry. For example he wrote: A B Grieve, Some Points in the Geometry of Cubic Surfaces, Proc. London Math. Soc. (1913), 315-339. He was awarded a D.Sc. for this research and joined the Edinburgh Mathematical Society in November 1923. In 1924 he became H.M. Inspector of Schools and lived in Orchardhead Road, Liberton, Edinburgh. In 1925 he published a book of 314 pages with title Analytical Geometry of Conic Sections and Elementary Solid Figures. A review of the book, written shortly after its publication, states:-
This book claims to contain the substance of the plane and solid analytical geometry (except straight line and circle) required for Pass and Engineering students at Universities, and for the more advanced pupils of Secondary Schools. It is refreshing to find plane and solid geometry in one volume, but the plan possesses the inherent objection that not very much ground in either can be covered in one book. Furthermore, "any portions of the subject which are difficult or of algebraic interest only" have been avoided. The book therefore consists in the main of what may be called numerical analytical geometry of the conics and conicoids. There are also chapters on the General Conic, Poles and Polars, Confocal Conics and Conicoids, and a final chapter on Curvature; but the great method of abridged notation, which is the very essence of the subject, is only hinted at in one chapter. The book is thus very limited in its outlook, and professes to be so.Barrie Grieve joined the navy during the First World War and fought in the Battle of Jutland. His brother Ian (who was a GP in London and was instrumental in first diagnosing asbestosis) served with the 1/14th London Battalion (London Scottish) and was wounded in the eye, and discharged. His brother David was killed on 9 April 1917 at the Battle of Vimy Ridge in France.
An elementary knowledge of Calculus is assumed; but alternative methods are given, usually in the examples at the end of a chapter. No mention is made, however, of Burnside's beautiful method for writing down secants. Perhaps the author regards this as artificial and "difficult". In any case it might have found a place among the examples, which on the whole are a very good collection. There is a short historical note at the beginning, and an admirable plate showing photographs of models of conicoids. The book is beautifully printed and the diagrams are clear.
Barrie Grieve married Isabella Watson (born 1891) at St George's Church, Dumfries, Scotland on 14 April 1914. Isabella died at 16 Orchardhead Road, Liberton, Edinburgh on 1 December 1930 and Grieve married Eliza McPherson on 16 July 1932 at Duke of Gordon Hotel, Kingussie, Inverness.
Alexander Grieve, Barrie Grieve's father, retired in 1922 and died on 1 April 1933. Barrie Grieve's mother died in 1932. At the time of his father's death A Barrie Grieve was living at Elmbank, Strathpeffer, Ross-shire and was working there as H.M. Inspector of Schools having only shortly moved there from Edinburgh. Barrie Grieve and his brother Ian were pall-bearers at their father's funeral on 4 April 1933.
On 1 July 1933 The Scotsman reported that Barrie Grieve, H.M. Inspector of Schools, and former pupil of Breadalbane Academy, Aberfeldy addressed the pupils while his wife presented the prizes.
Article by: J J O'Connor and E F Robertson