John Venn

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4 August 1834
Hull, England
4 April 1923
Cambridge, England

John Venn was an English mathematician and logician best known for the Venn diagrams which can be used to visualise the unions and intersections of sets.


John Venn's mother, Martha Sykes, came from Swanland near Hull and died while he was still quite a young boy. His father was the Rev Henry Venn who, at the time of John's birth, was the rector of the parish of Drypool, near Hull. The Rev Henry Venn, himself a fellow of Queen's, was from a family of distinction. His father, John's grandfather, was the Rev John Venn who had been the rector of Clapham in south London. He became the leader of the Clapham Sect, a group of evangelical Christians centred on his church. They successfully campaigned for the abolition of slavery, advocated prison reform and the prevention of cruel sports, and supported missionary work abroad.

It was not only Venn's grandfather who played a prominent role in the evangelical Christian movement, for so did his father the Rev Henry Venn. The Society for Missions in Africa and the East was founded by evangelical clergy of the Church of England in 1799 and in 1812 it was renamed the Church Missionary Society for Africa and the East. The Rev Henry Venn became secretary to this Society in 1841 and in order to carry out his duties moved to Highgate near London. He held this position until his death in 1873.

As might be expected from his family background, John was very strictly brought up, and there was never any thought other than that he would follow the family tradition into the priesthood. He attended first Sir Roger Cholmley's School in Highgate, then the private Islington Preparatory School.

When he entered Gonville and Caius College Cambridge in October 1853 he had:-
... so slight an acquaintance with books of any kind that he may be said to have begun there his knowledge of literature.
Having been awarded a mathematics scholarship in his second year of study, he graduated as sixth Wrangler in the Mathematical Tripos of 1857, meaning that he was ranked in the sixth place out of those students who were awarded a First Class degree in mathematics. He was elected a Fellow of Gonville and Caius College shortly after graduating, and two years later was ordained a priest. In fact the year after his graduation, in 1858, he had been ordained a deacon at Ely, then after his ordination as a priest he had served as a curate first at Cheshunt, Hertfordshire, and then for a year as a curate at Mortlake, Surrey.

In 1862 he returned to Cambridge University as a lecturer in Moral Science, studying and teaching logic and probability theory. He had already become interested logic, philosophy and metaphysics, reading the treatises of De Morgan, Boole, John Austin, and John Stuart Mill. Back at Cambridge he now found interests in common with many academics such as Todhunter. He also played a large role in developing the Moral Sciences Tripos over many years. He lectured and examined the Tripos, developing a friendly atmosphere between the lecturers and the students.

Venn extended Boole's mathematical logic and is best known to mathematicians and logicians for his diagrammatic way of representing sets, and their unions and intersections. He considered three discs R,SR, S, and TT as typical subsets of a set UU. The intersections of these discs and their complements divide UU into 8 non-overlapping regions, the unions of which give 256 different Boolean combinations of the original sets R,S,TR, S, T.

Venn wrote Logic of Chance in 1866 which Keynes described as:-
... strikingly original and considerably influenced the development of the theory of statistics.
In 1867 Venn married Susanna Carnegie Edmonstone, the daughter of the Rev Charles Edmonstone. They had one child, a son John Archibald Venn, who became president of Queen's College, Cambridge, in 1932, and undertook major collaborative research projects with his father that we give more details on below.

Venn published Symbolic Logic in 1881 and The Principles of Empirical Logic in 1889. The second of these is rather less original but the first was described by Keynes as:-
... probably his most enduring work on logic.
In 1883 Venn was elected a Fellow of the Royal Society and in the same year was awarded a Sc.D. by Cambridge. About this time his career changed direction for in the same year that he was elected to the Royal Society, he left the priesthood. His son, John Archibald Venn, wrote his father's obituary in the Dictionary of National Biography and explained the position:-
It had long ceased to be regarded as an anomaly for a clergyman to preach the then circumscribed evangelical creed and at the same time, without the slightest insincerity, to devote himself actively to philosophical studies; yet ... finding himself still less in sympathy with the orthodox clerical outlook, Venn availed himself of the Clerical Disabilities Act. Of a naturally speculative frame of mind, he was want to say later that, owing to subsequent change in accepted opinion regarding the Thirty-nine Articles, he could consistently have retained his orders; he remained, indeed, throughout his life a man of sincere religious conviction.
Venn's interest turned towards history and he signalled this change in direction by donating his large collection of books on logic to the Cambridge University Library in 1888. He wrote a history of his college, publishing The Biographical History of Gonville and Caius College 1349-1897 in 1897, which:-
... involved a vast amount of painstaking and methodical search among university, episcopal, and other records.
The annals of a clerical family (1904) trace the history of his own family back to the seventeenth century and record that he was the eighth generation of his family to have a university education. In 1910 he published a work on historical biography, namely a treatise on John Caius, one of the founders of his College. Three years later he published Early Collegiate Life which collected many of his writings describing what life was like in the early days of Cambridge University. He then undertook the immense task of compiling a history of Cambridge University Alumni Cantabrigienses, the first volume of which was published in 1922. He was assisted by his son John Archibald Venn in this task which was described by another historian in these terms:-
It is difficult for anyone who has not seen the work in its making to realise the immense amount of research involved in this great undertaking.
It was [3]:-
... nothing less than a "biographical list of all known students, graduates, and holders of office at the University of Cambridge from the earliest times to 1900". ... The Venns, father and son, spared no industry in building up these records, which are of extraordinary value to historians and genealogists ...
The first part contained 76,000 names and covered the period up to 1751. At the time of Venn's death the second part, covering the period from 1751 to 1900, existed in manuscript and contained a further 60,000 names.

Venn had other skills and interests too, including a rare skill in building machines. He used his skill to build a machine for bowling cricket balls which was so good that when the Australian Cricket team visited Cambridge in 1909, Venn's machine clean bowled one of its top stars four times.

His son gives this description:-
Of spare build, he was throughout his life a fine walker and mountain climber, a keen botanist, and an excellent talker and linguist.

References (show)

  1. T A A Broadbent, Biography in Dictionary of Scientific Biography (New York 1970-1990). See THIS LINK.
  2. Obituary in The Times
  3. A D D Craik, Mr Hopkins' Men: Cambridge Reform and British Mathematics in the 19th Century (Cambridge 2007)
  4. M Ferriani, L'induzione in John Venn, Quaderni di Storia e Critica della Scienza, Nuova Serie 3, Domus Galilaeana (Pisa, 1973).
  5. John Venn zum 150. Geburtstag, Praxis Math. 26 (11) (1984), 343-345.
  6. Obituary of John Venn, Proc. Roy. Soc. London A 110 (1926), x - xi.
  7. W C Salmon, John Venn's Logic of chance, Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science II (Dordrecht- Boston, Mass., 1981),125-138.
  8. J A Venn, John Venn, Dictionary of National Biography 1922-1930, 869-870. See THIS LINK.

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Written by J J O'Connor and E F Robertson
Last Update October 2003