David Kennedy Picken
by T. M. C.
David Kennedy Picken, who died on 17th June 1956, was a member of the Mathematical Association for 51 years and a regular contributor to the Gazette. He was a Scotsman, trained in Glasgow and Cambridge, where in 1902 he was sixth wrangler. After graduation he was successively Lecturer in Mathematics at Glasgow University, and Professor at Victoria College, New Zealand. In 1915 he was called to be Master of Ormond College, residential and ancillary teaching institution affiliated with the University of Melbourne. In that position he had wide administrative duties, and the moral responsibilities attaching to the care of more than 100 undergraduates and a leading lay position in the Presbyterian Church. In a sense therefore he ceased to be a professional mathematician. But the things that interested Picken in mathematics were the fundamental principles -the "elements": their nature, their proper expression, and the proper exposition of the developments stemming from them. On these things he had deep and even passionate convictions, and it seems that these were to some extent linked with his faith regarding the fundamentals of religion and conduct (the comparison of the "infinities" of mathematics and faith would provide such a link); it is understandable therefore that in mathematical thought and teaching he remained active. In the teaching world he had for many years a responsible position on the Board which prescribes "school certificate" syllabuses and recommends courses of study, and he was an influential member of the bodies which deal similarly with studies within the University of Melbourne; but his more intimate care was for the mathematical well-being of the students in his College, and on many of these he had a decisive influence.
To illustrate these generalities: We all know that multiplication is one of the fundamental operations, and that in omitting the sign of multiplication (.) from expressions such as a.b of 2. ft we are departing from our practice concerning the sign + of addition. But for Picken, to omit the multiplication sign was "wrong" notation. This example may be misleading by suggesting that Picken's dominant concern was with what most people would call trivialities, but it does give a fair indication of the flavour of his writing. Examples maybe found in the Gazettes over many years; for one of the last see vol. XXX (1946), p. 200. His published books are The Theory of Elementary Trigonometry (Whitcombe and Tombs, 1910), The Number System of Arithmetic and Algebra (Melbourne Univ. Press, 1923), and (with Miss Winifred Waddell) A First Trigonometry (Melbourne, 1919).
In the field of elementary geometry Picken made a remarkable discovery: the unifying concept of the "complete angle". It is explained, and its utility shown, in the first chapter of Forder's Higher Course Geometry, being there called "the cross". Picken's original paper is in Proc. London Math. Soc. 21, 23 (1925),45-55.
Picken was of course a prominent member of the Mathematical Association of Victoria - which incidentally has this year (1956) celebrated its Jubilee; from 1938 to 1944 he was its President. His addresses to the Association, on topics such as The Number System, Ratio and Proportion, and The Quantities of Physics are substantially embodied in his contributions to the Gazette.
David Kennedy Picken's obituary by T. M. C. appeared in the Mathematical Gazette, Vol. 41, No. 337. (Oct., 1957), pp. xxvi-xxvii.