Aug 042016


Today is the birthday (1834) of John Venn, English mathematician and logician, primarily remembered for his use of diagrams, which we now call Venn diagrams, to help explain concepts in set theory. Venn was not exactly a giant in his field, but I’d settle for having something reasonably commonplace named after me. Venn diagrams have served me very well in my own work.

Venn was born in Hull, and educated at private schools in London before studying mathematics at Cambridge University, at Gonville and Caius College where he subsequently became a fellow and then head of the college.

Venn’s father was an Anglican clergyman and Venn followed suit in the late 1850s, as was normal for fellows at Cambridge at the time. In fact, after receiving his degree in 1857 he did parish work for a few years before devoting himself full time to mathematics. Even after he left the clergy in the 1880s he continued being involved in the church, although he found strict Anglicanism incompatible with logic and mathematics.


Venn’s first major publication was The Logic of Chance (1866), a significant accounting of the laws of probability. He then turned to George Boole’s work in logic and produced Symbolic Logic in 1881. It was in this work that he introduced Venn diagrams which he had been using as a teaching device for several years:

I began at once somewhat more steady work on the subjects and books which I should have to lecture on. I now first hit upon the diagrammatical device of representing propositions by inclusive and exclusive circles. Of course the device was not new then, but it was so obviously representative of the way in which any one, who approached the subject from the mathematical side, would attempt to visualise propositions, that it was forced upon me almost at once.

As Venn notes, other mathematicians, notably Gottfried Leibniz and Leonhard Euler, had used similar diagrams earlier, but Venn popularized them as well as extending their application to a wide variety of fields outside of mathematics and logic, and making their application more rigorous than previous attempts.

Venn diagrams don’t actually serve a technical function in mathematics or logic, but they do make certain concepts easier to grasp by displaying them visually. Here’s a simple example showing the Greek, Russian, and Roman alphabets each contained within circles which are drawn to overlap. Symbols in common between two of the alphabets are shown at the intersections of their circles, and symbols common to all three are shown in the central intersection.


Venn diagrams also have the possibility of excluding items from any of the circles, such as in the example below of a diagram concerning “people I know” and the use of social media. Harry uses neither Facebook nor Twitter so fits inside the rectangle representing people I know but outside the circles representing social media.


Venn was elected to the Royal Society in 1883 and continued to publish other works, including The Principles of Empirical or Inductive Logic (1889) and volumes on the history of Cambridge and a list of its alumni, compiled with the aid of his son, John Archibald Venn.

Venn died on April 4, 1923, in Cambridge at the age of 88. He is memorialized by a stained glass window at his old college.


When dealing with mathematical subjects before I’ve focused on mathematical objects. The Venn diagram is not a mathematical object per se, but it does lend itself to cooking ideas. This site gives an idea for a Venn diagram pie.  It was created for Pi Day (3/14 in countries that use month/day format), so it is more about being a pie than being an accurate Venn diagram. But you can take the original and modify it.


The site shows you how to cut two disposable pie pans to make the Venn diagram shape, and the crust conforms to the general idea of sets – no crust and full crust intersect to make a lattice crust. The recipe fails with the fillings. It just suggests using three different ones. It shouldn’t be too difficult to come up with categories such as fruit and dairy, so that one side is fruit, no dairy, the other is dairy, no fruit, and the middle is fruit and dairy. I’ll leave it to you.

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