TITLE: whence commutative diagrams?
QUESTION [71 upvotes]: It seems that commutative diagrams appeared sometime in the late 1940s -- for example, Eilenberg-McLane (1943) group cohomology paper does not have any, while the 1953 Hochschild-Serre paper does. Does anyone know who started using them (and how they convinced the printers to do this)?

REPLY [32 votes]: Eduard Study in Von den Bewegungen und Umlegungen, Math. Ann. 39 (1891) 441-566, writes on p. 508:

Here $g, g^*, g'$ are rays in space with polar planes $\gamma, \gamma^*, \gamma'$, $\mathfrak P$ is the “polarity” taking rays to planes and conversely, the $\mathfrak t_i$ are commuting collineations acting on both rays and planes, and Study uses $\mathfrak t_i\mathfrak P$ to denote the composition we would write $\mathfrak P\circ\mathfrak t_i$.
(Essentially the same diagram is repeated in Study’s book Einleitung in die Theorie der Invarianten linearer Transformationen auf Grund der Vektorenrechnung (1923, p. 217), with credit to (1891).)