John Venn's 100th Death Anniversary: How Do His Famous Diagrams Continue To Help the World Today?

John Venn, a mathematician and philosopher, is known primarily for inventing the widely used diagrams that now bear his name. Venn diagrams are utilized in a variety of fields, such as set theory, problem solving, and assessing the validity of syllogisms in logic. The diagrams are composed of intersecting circles that depict the relationships between two or three groups of items.

This month, April 2023, marks Venn's 100th death anniversary. Get to know the Venn behind the diagram, which most people likely have encountered either in their studies or professional life, and learn how his model was created.

Origins of the Venn Diagram

Venn diagrams are a method of summarizing and presenting information, and they have the potential to generate new insights. John Venn, the inventor of these diagrams, first introduced them in 1880 in an article published in the Philosophical Magazine.

As per the Institute of Mathematics, the process of creating a Venn diagram involves two steps: (1) create a primary diagram that represents the combinations between the terms involved in a proposition or argument and (2) add syntactic signs, such as shading, to indicate the state of sub-classes.

The origins of Venn diagrams are somewhat mysterious because there is no mention of them in Venn's writings or correspondence before 1880. In his autobiography, Venn simply states that he "first hit upon" Euler diagrams in 1862 and that his diagrams "did not occur to [him] till much later."

Venn's description of how he came up with the idea is brief and not particularly informative: he tried to use Euler diagrams to represent the complicated propositions of Boolean logic but found them inadequate and came up with his plan.

While its origins can be traced to the development of Venn diagrams from post-Eulerian diagrammatic representation and Boolean logic, it remains unknown when or why Venn invented them. The only information available is that Venn's diagrams emerged from his attempt to adapt Euler diagrams to Boolean logic.

Venn Diagram: Visualizing Logical and Mathematical Area

Venn diagrams are used as one visualization tool in a mathematical area known as set theory, which is a branch of mathematics used to describe collections of objects, Phys.org reported.

For example, a set of cars could be divided into subsets, like electric cars, petrol cars, and diesel cars. These subsets can be manipulated by applying a discount to the electric car set. Set theory is used in databases and various areas of science.

Moreover, Venn also worked on probability theory and symbolic logic. He used diagrams to prove categorical syllogisms, which are used to model reasoning. For instance, "All computers need power. All AI systems are computers." This can be used to show that "all AI systems need power."

Today, Venn diagrams are commonly used to illustrate relationships between different sets. For example, the SmartArt tool in Microsoft products lets you create Venn diagrams to show the relationships between different sets. In our earlier example of cars, we could create a diagram showing electric cars and petrol-powered cars, and the intersection would represent hybrid cars with petrol engines.