### The First Commutative Diagram?

#### Posted by Tom Leinster

At lunch today at Category Theory 2013 in Sydney, a bunch of us were talking about the mathematical work of Bertrand Russell, and I remembered this:

It’s from Russell’s 1919 book *Introduction to Mathematical Philosophy*, and it’s essentially a commutative square in the category of sets and relations, although the notation is very slightly different from how we’d do it now. Click on the image to see the whole page.

I was very surprised to see a commutative diagram from 1919. This was more than twenty years before the birth of category theory. Indeed, I’m not sure that the arrow notation for mappings was commonplace back then. Does anyone know of an earlier example of a commutative diagram in print?

Posted at July 8, 2013 5:38 AM UTC
## Re: The First Commutative Diagram?

Not an earlier example, but, Mac Lane [

Concepts and categories in perspective] did suggest that the arrow notation comes from the 1930s/40s.