The brilliance of Venn diagrams

In late July 2019, Britain’s Evening Standard newspaper reported on how soon-to-be prime minister Boris Johnson had planned his Cabinet appointments by drawing a Venn diagram. In one circle were “the people who believed in Brexit”. In the other were “the people capable of running the country”. In discussing Johnson’s planning scheme, The Guardian newspaper’s mathematics columnist, Alex Bellos, described Venn diagrams as “a brilliantly simple visual aid to understanding logical relations”, and “one of the few concepts from abstract mathematics that is easily understood, and regularly used, by non-mathematicians”.

The Venn diagram takes its name from British mathematician and logician John Venn, who was born in 1834 in Yorkshire. His father Henry Venn and grandfather John Venn were both Evangelical Anglican priests.

In 1853 he went to Cambridge to study mathematics, receiving a first-class degree in mathematics in 1857.

In 1859 he was ordained as a minister of the church, but in 1862 he returned to Cambridge University as a lecturer in moral science, studying and teaching logic and probability theory.

An article published online by Scotland’s University of St Andrews’ School of Mathematics and Statistics describes how, in 1866, Venn published The Logic of Chance, which the renowned economist John Maynard Keynes called “strikingly original and considerably influenced the development of the theory of statistics”.

The St Andrews article calls it “a ground-breaking book which espoused the frequency theory of probability, offering that probability should be determined by how often something is forecast to occur as opposed to ‘educated’ assumptions”.

Venn’s next book, Symbolic Logic, published in 1881, expanded on work by English mathematician George Boole, who had died in 1864, The Famous Mathematicians website says his “revolutionary advances in maths are fundamental aspects of electronics and computer science. His Boolean Algebra is utilised to design and operate computers as well as other electronic devices.”

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Boris Johnson’s aid for picking a Cabinet.

It was in Symbolic Logic, that Venn expanded upon the overlapping circles used to represent properties of sets and subsets that what would become known as Venn diagrams.

An online educational services provider,, explains that a Venn diagram consists of closed shapes, generally circles, which represents sets. The various operations of sets are represented by partial or complete overlap of these closed figures. Regions of overlap represent elements that are shared by sets.

Apart from his contributions to mathematics and the study of logic, Venn was also something of an inventor, and several sources mention his construction of a machine that could bowl cricket balls.

The machine was believed to be so accurate that it was used in practice sessions by the Australian team when the players visited Cambridge University during their 1909 tour. It was reported that the machine “bowled out a top-ranked team player four times consecutively”, although the player is nowhere named.

A blog titled Lost Cambridge reproduces a newspaper clipping from The Cambridge Independent Press dated 11 June 1909, in which no less a luminary than Australian all-rounder Victor Trumper “expressed an opinion that the new machine will be of special value for schools and for practice generally”.

The article goes to say that the machine “will do away with the drudgery of bowling at the practice nets”.

John Venn died in Cambridge on 4 April 1923.

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