William Milne was educated at Peterhead Academy and Aberdeen Grammar School before going up to Aberdeen University. He took all the available prizes in mathematics and natural philosophy and a Ferguson Scholarship (that year all five scholarships, open to students in all the ancient Scottish universities, went to Aberdeen) allowed him to continue his studies at Cambridge where he also too first-class honours.
He married Mary Deas Burnett in 1910. She was born in Echt, Aberdeenshire about 1883.
He taught mathematics at Clifton College from 1907 to 1919, when he was appointed to the Chair of Mathematics at Leeds University. He held this appointment until 1946. During his tenure of the chair he was appointed Pro Vice Chancellor. Aberdeen honoured him was an honorary Doctorate of Laws on 4 May 1946 and Leeds University honoured him in the same way in 1955.
Almost ten years after he retired, Milne published Eppie Elrick, described at the time as a new doric classic. It is a full-scale historical romance in the dialect he sought to foster as an enthusiastic member of the Buchan Field Club. He was president of this Club in 1947 when the Club renewed its activities after a period of abeyance during World War II. The first field day of the revived Club took place in August 1948.
Milne's life is described in the extract from  which is given at THIS LINK
Here we mention a few of Milne's research papers such as the following which were published in the Proceedings or the Journal of the London Mathematical Society: The construction of co-apolar triads on a cubic curve (1916); Determinantal Systems of Co-Apolar Triads on a Cubic Curve (1920); The Significance of Apolar Triangles In Elliptic Function Theory (1920); The Harmonic and the Equianharmonic Envelopes of a Cubic Surface (1926); and 7-Tangent Quadrics of the Same System of the C57.
However, Milne was also interested in mathematical education and published a series of papers and mathematical notes in the Mathematical Gazette. These included: The geometrical meaning of the triad of points (1910); A property of the complete quadrangle (1911); The teaching of limits and convergence to scholarship candidates (1911); The teaching of limits and convergence to scholarship candidates (1912); The teaching of limits and convergence to scholarship candidates (1913); Another proof and generalisation of the theorem given in note 339 (1913); The teaching of modern analysis in secondary schools (1915); The graphical treatment of power series (1918); The uses and functions of a school mathematical library (1918); Mathematics and the pivotal industries (1919); The training of the mathematical teacher (1920); and Noether's canonical curves (1920).
Milne joined the Edinburgh Mathematical Society in December 1910. Even before he was formally through the procedure of membership, his papers were being read to the Society; Triangles Triply in Perspective by Charles McLeod and William P Milne, was communicated to the meeting on Friday 10 June 1910 by A D Russell. At the meeting at which his membership was confirmed, on Friday 9 December 1910, Milne read the paper A harmonic property of cubic curves. Further papers read by Milne to the Society include: The Focal Circles of Circular Cubics on 10 February 1911; The system of cubic curves circumscribing two triangles and a polar to them (communicated by Neil McArthur to the meeting of 10 November 1911); An easy geometrical representation of the Sextic Covariant of a Binary Quartic (communicated by Neil McArthur to the meeting of 10 November 1911); Investigations on Circular Cubics and Bi-circular Quartics on 10 May 1912; Nonagons nonuply in perspective (communicated by N McArthur on 9 May 1913); Easy Proof of von Staudt's Theorem (communicated by P Comrie on 15 January 1915); The apolar locus of two tetrads of points (communicated by P Ramsay on 12 January 1917); and The co-apolars of a cubic curve (communicated by Archibald Milne on 9 February 1917).
Article by: J J O'Connor and E F Robertson