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John Venn

Explore connections in mathematics and history with this article on John Venn.
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Updated on: June 8, 2001

John Venn

John Venn was a mathematician remembered best for his contributions to the study of mathematical logic and probability. Venn was born in England in 1834, and studied at Cambridge University until 1857. He was ordained as a priest in 1859, and served as a curate for a year before returning to Cambridge to lecture on Moral Science.

While at Cambridge, Venn spent his time both teaching and studying probability theory and logic. There he developed a method of using diagrams to illustrate set theory, called Venn Diagrams. Typical Venn diagrams use overlapping circles to represent groups of items or ideas that share common properties. Each circle represents one property, and shared properties are represented by the overlapping areas of the circles. For example, suppose you use three overlapping circles (A, B, and C) to represent four-legged animals, domesticated animals, and predatory animals, respectively. From this diagram, you could start to see how the overlapping categories create different sets. A cat, for example, would fall in the set represented by the overlap of A, B, and C. A horse, however, would fall in the set shown by the overlap between A and B only, not C. Although they have many applications, Venn diagrams also aid in the study of Boolean logic, another type of logic named after the 19th-century mathematician, George Boole.

In 1866, Venn wrote Logic of Chance, a work that was considered highly original and influential on the development of the theory of statistics. He also wrote Symbolic Logic, in 1881, and Principles of Empirical Logic in 1889. In 1883, he was elected a member of the Royal Society for his work in math and logic.

Later in his life, however, Venn turned to interests outside of mathematics. He began compiling a history of Cambridge University, of which he completed three volumes. He also had a talent for building machines, and invented one that automatically bowled cricket balls. Venn lived until 1923.

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