He was educated at Manchester Grammar School, entering at the age of eleven, and at first he concentrated on classics but as he progressed through the school he was happy to specialise in mathematics. From there he went up to Trinity College, Cambridge in 1892 where he held a scholarship. He was taught as an undergraduate by, among others, G H Darwin and A R Forsyth. His interests at this time were on the applied side of mathematics which is certainly illustrated by the fact that, in 1894, he was awarded the Sheepshanks Exhibition in Astronomy. Whittaker graduated as Second Wrangler in the examination of 1895, and was awarded the Tyson Medal. He was beaten into second place in the Mathematical Tripos examinations by Bromwich. Whittaker was elected as a fellow of Trinity College in 1896 and became first Smith's prizeman in 1897 for a work on pure mathematics, namely on uniform functions.
After Whittaker became a Fellow of Trinity College he began to teach and give lecture courses and, among his first pupils were G H Hardy and J H Jeans. Whittaker made revolutionary changes to the topics taught at Cambridge. He taught a course based on his famous book A Course of Modern Analysis (1902). This work is important in the study of functions of a complex variable. It also develops the theory of special functions and their related differential equations. Other courses Whittaker taught at Cambridge included astronomy, geometrical optics, and electricity and magnetism. Hardy and Jeans were not the only famous mathematicians which Whitttaker taught at Cambridge. His pupils included Bateman, Eddington, Littlewood, Turnbull, and Watson.
The Rev Thomas Boyd lived in Cambridge and was the Scottish Secretary of the Religious Tract Society. Whittaker married his daughter, Mary Ferguson McNaghten Boyd, in 1901. They had three sons and two daughters. The middle son from the three was John Whittaker who went on to become a famous mathematician and also has a biography in this archive. The eldest of their two daughters was Beatrice Mary Whittaker, who later married Copson.
Whittaker's interest in astronomy is illustrated by the courses he taught, but he also joined the Royal Astronomical Society serving as its secretary from 1901 to 1906. He became the Royal Astronomer of Ireland in 1906 and moved to Dunsink Observatory where Hamilton had worked. He was at the same time appointed as Professor of Astronomy at the University of Dublin. The Observatory was not well equipped and his appointment as Royal Astronomer was more to teach mathematical physics at the University than to undertake observational astronomy.
George Chrystal, the professor at Edinburgh, died in November 1911 and in the following year Whittaker took up the chair in Edinburgh where he remained for the rest of his career. In fact he reached retirement age in 1943 but due to World War II he agreed to carry on for a further three years. Soon after he arrived in Edinburgh, Whittaker set up the Edinburgh Mathematical Laboratory to give a practical side to his interest in numerical analysis. His many lecture courses on this topic were collected into a book which he published in 1924 The Calculus of Observations: a treatise on numerical mathematics.
Whittaker's best known work is in analysis, in particular numerical analysis, but he also worked on celestial mechanics and the history of applied mathematics and physics. He wrote papers on algebraic functions and automorphic functions. He found expressions for the Bessel functions as integrals involving Legendre functions. He studied these special functions as arising from the solution of differential equations derived from the hypergeometric equation.
His results in partial differential equations (described as 'most sensational' by Watson) included a general solution of the Laplace equation in three dimensions in a particular form and the solution of the wave equation. This work was of fundamental importance for it united various strands of potential theory making it into a unified topic. The unification came in the form of bringing together different special functions, as mentioned above, and exhibiting them all as special cases of what became known as a 'Whittaker integral'.
On the applied side of mathematics he was interested in relativity theory for many years, publishing at least five articles on the topic. He also worked on electromagnetic theory giving a general solution of Maxwell's equation, and it was through this topic that his interest in relativity arose. Another application which interested him came through his association with actuaries in Edinburgh who were dealing with life assurance. This motivated him to study the mathematics lying behind somewhat ad hoc methods that the actuaries were using and Whittaker proved some important results on interpolation as a consequence.
One of his most important historical studies was A History of the Theories of Aether and Electricity, from the Age of Descartes to the Close of the Nineteenth Century (1910). In 1953 he produced a revised version including the work of the first quarter of the 20th Century.
In  McCrea describes Whittaker's research lectures which he gave twice a week throughout the whole academic year while he was professor in Edinburgh:-
Either he discussed his own current work or he gave his own development of topics of current interest in mathematics. One marvels at the mathematical power that enabled him always, year after year, to have material for these lectures - he never repeated the same ones - just as though he had nothing else to think about, when actually he was inundated with other duties.Whittaker received many honours. He was a member of the London Mathematical Society, being President in 1928-29. He won the De Morgan Medal of the Society in 1935. He was elected a Fellow of the Royal Society in 1905, served on its Council for two periods, 1911-12 and 1933-35, and he was vice-president during part of this second period on the council from 1934-35. He was awarded the Society's Sylvester Medal in 1931 and the Copley Medal in 1954:-
... for his distinguished contributions to both pure and applied mathematics and to theoretical physics.He was knighted in 1945. He was a Fellow of the Royal Society of Edinburgh, awarded the Society's Gunning Prize in 1929, and served the Society as President for most of the years of World War II. He was also President of the Mathematical Association (1920-21), and of the Mathematics and Physics section of the British Association in 1927. He served as secretary to the Royal Astronomical Society from 1901 to 1907.
Whittaker was a committed Christian and joined the Roman Catholic Church in 1930. In this capacity he was awarded the cross Pro Ecclesia et Pontifice in 1935, was appointed to the Pontifical Academy of Sciences in the following year (the year of foundation of the Academy by Pope Pius XI), and was president of the Newman Association from 1943 to 1945. He gave lectures on science and theology such as the Riddell Memorial Lecture on The beginning and end of the world in Dublin in 1942, and the Donnellan Lectures on Space and spirit also in Dublin four years later.
As to Whittaker's character McCrea writes in :-
He grasped new ideas with unbelievable rapidity and he had an infallible memory for everything he read. ... He was the most unselfish of men with a delicate sense of what would give help or pleasure to others. Always he seemed to have his vast number of friends at the tip of his mind so that he never missed an opportunity to do or say something on behalf of any one of them. He had a quick wit and an ever-present sense of humour and liked telling harmlessly mischievous stories about people he had known.In  Whittaker is described in these terms:-
... he was a brilliant teacher, a master of his subject, with a great love of his fellow men. His warmth and his interest in his friends and students made him the most agreeable of companions. Scholars from abroad who knew him seldom failed to visit him and enjoy his conversation, and the friendships thus founded he kept up by correspondence to all parts of the world.
Article by: J J O'Connor and E F Robertson