Henstock brought the theory to a highly developed stage without ever having encountered Jaroslav Kurzweil's 1957 paper on the subject.
On the Henstock side he was descended from 17th century Flemish immigrants called Hemstok.
Because of his early academic promise it was expected that Henstock would attend the University of Nottingham where his father and uncle had received technical education, but as it turned out he won scholarships which enabled him to study mathematics at St John's College, Cambridge from October 1941 until November 1943, when he was sent for war service to the Ministry of Supply's department of Statistical Method and Quality Control in London.
Henstock wanted to study divergent series but Dienes prevailed upon him to get involved in the theory of integration, thereby setting him on course for his life's work.
in 1944 and began research for the PhD in Birkbeck College, London, under the supervision of Paul Dienes.
In 1947 he returned briefly to Cambridge to complete the undergraduate mathematical studies which had been truncated by his Ministry of Supply work.
Independently, Jaroslav Kurzweil developed a similar Riemann-type integral on the real line.
In the following decades, Henstock developed extensively the distinctive features of his theory, inventing the concepts of division spaces or integration bases to demonstrate in general settings the properties and characteristics of mathematical integration.
Much of Henstock's earliest work was published by the Journal of the London Mathematical Society.
His works, published in Proceedings of the London Mathematical Society, were "Density integration" (53, 1951); "On the measure of sum sets (I) The theorems of Brunn, Minkowski, and Lusternik, (with A.M. McBeath)" ([3] 3, 1953); "Linear functions with domain a real countably infinite dimensional space" ([3] 5, 1955); "Linear and bilinear functions with domain contained in a real countably infinite dimensional space" ([3] 6, 1956); "The use of convergence factors in Ward integration" ([3] 10, 1960); "The equivalence of generalized forms of the Ward, variational, Denjoy-Stieltjes, and Perron-Stieltjes integrals" ([3] 10, 1960); "N-variation and N-variational integrals of set functions" ([3] 11, 1961); "Definitions of Riemann type of the variational integrals" ([3] 11, 1961); "Difference-sets and the Banach–Steinhaus theorem" ([3] 13, 1963); "Generalized integrals of vector-valued functions ([3] 19 1969) Additional publications: The journal Scientiae Mathematicae Japonicae published a special commemorative issue in Henstock’s honor, January 2008.
The above article is copied, with permission, from Real Analysis Exchange and from Scientiae Mathematicae Japonicae.