John Burkill went from St Paul's school winning a scholarship to Trinity College, Cambridge in 1918. After spending a short time in the Royal Engineers he entered Cambridge in 1919. After taking his first degree he remained at Cambridge as a research student then became a fellow.
In 1924 he accepted the chair of pure mathematics at Liverpool. In 1929 he returned to Cambridge taking up a lectureship at Peterhouse. He remained in this post for the rest of his life.
Burkill is equally well known for his research in analysis and the excellent teaching books which he wrote. He research is introduced in  by saying:-
Burkill's work is all in the theory of functions of a real variable with its main emphasis on theories of differentiation and integration. This was a particularly active area of research in the early decades of this century after the pioneering work of Lebesgue, Borel and their contemporaries in establishing the concepts of measure and the Lebesgue integral associated with it.Burkill introduced what is now called the 'Burkill integral' and applied it to extend W H Young's work on the definition of the area of a curved surface. He introduced the notion of approximate differentiation extending and simplifying work of Besicovitch.
Among his books are The Lebesgue integral (1951), A first course in mathematical analysis (1962) and A second course in mathematical analysis (1970). These are described in  as follows:-
These all display, as we might expect, not only his mastery of the field but a lucidity and elegance that encourages his readers to appreciate the profound aesthetic quality of good mathematics.After retirement Burkill served as Master of Peterhouse College from 1968 until 1973. He then served as editor of the Mathematical Proceedings of the Cambridge Philosophical Society. Burkill received many honours including election to the Royal Society in 1953 and the Adams prize in 1949.
In  he is described as having a
... fastidious concern for accuracy and economy in the use of words. In respect of the spoken word, this economy became something of a legend. Taciturn is not a sufficiently friendly word to describe his conversational style, because it contained no hint of malice or lack of concern but only an unerring judgement about what was important, and the clearest way of saying it. What is even more important is that his distaste for excessive display of feeling concealed, at first, a truly generous and hospitable nature.Reference (One book/article)
References elsewhere in this archive:
John C Burkill was elected to the Royal Society of London in 1953. You can see a history of the Royal Society and a list of the members among the mathematicians in our archive.
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