He was born in London and educated at the City of London School and Trinity College, Cambridge, taking his degree as Second Wrangler and afterwards winning the First Smith's Prize, as Kelvin and Clerk Maxwell had done before him.
After a brief period of teaching at Clifton College, followed by three years as lecturer at Owen's College, Manchester, Steggall was appointed to the Chair of Mathematics and Natural Philosophy in the newly instituted College at Dundee, which later became part of the University of St Andrews. When the growth in the number of students made it a necessity, and the College funds permitted, a separate Chair of Physics was established, and Steggall continued to teach the subjects of Pure and Applied Mathematics. He retired in 1933 after completing fifty years of professorial work.
The generation of British mathematicians to which Steggall belonged delighted in proposing and working out problems whose solution might require the aid of any branch of pure or applied mathematics. A few master strokes would be quickly described putting the whole essence of each question into a nutshell. There was no more to be said. He applied the same devastating treatment to questions outside mathematics; simplicity and frankness dictating a clear answer which would be given fearlessly, and often so quickly that his listeners would be left still wondering what the question implied. Yet he was able to apply himself to such laborious work as the correction of masses of examination scripts, to investigations involving heavy numerical calculation and, again, to the nice construction of geometrical figures or architectural plans. His researches into elementary theory of numbers and on curves described by mechanical linkages, and the fine collection of mathematical models he made for University College, Dundee, testify to this power.
He took an active interest in the work of the Edinburgh Mathematical Society, and contributed a number of papers to the Proceedings. Some of these dealt with applications of mathematics well outside the more formal range and reflected the breadth of his knowledge and the variety of his interests. He was elected President of the Society, not for the first time, during the Session 192930, and his ex officio chairmanship of the St Andrews Colloquium in 1930 contributed greatly to the success of that meeting.
He was a classical and linguistic scholar of wide attainment, and a keen student of architecture, the love of which he inherited from his father, a London physician. He was, in fact, a man of strong artistic tendencies, of high literary instincts, and of wide culture generally.
Besides his professional work, he took a great interest in all matters, especially educational, connected with the welfare of the city of his adoption. He loved Scotland and its countryside, and one of his publications dealt with the scenery of Perthshire. A man of such wide qualifications could not fail to have a great circle of sincere friends, and even today one can hear his students of the earliest years speak gratefully of his power of arousing interests beyond those connected with his own subject.
His hobbies, apart from intellectual, lay in fine carpentry work, in walking, cycling, and latterly in the development of the Youth Hostel scheme.
Those who saw him during the last months of brave quiet waiting for the inevitable end had a great privilege in knowing the true kindness of heart which subsisted beneath and through all the liveliness of life, and can
Greet the unseen with a cheer!His wife, who, with their two daughters, survives him, is a sister of Sir James Frazer. Their only son was killed in the battle of Jutland. Frazer and Steggall were fellow students at Cambridge, and it is interesting to note that the one took second place in the Classical Tripos in the same year as that in which the other was Second Wrangler in the Mathematical Tripos.
Bid him forward, breast and back as either should be,
"Strive and thrive!" cry "Speed,  fight on, fare ever
There as here!"
