TITLE: History of $f \circ g$
QUESTION [10 upvotes]: $f \circ g$ is usually interpreted as $f(g(x))$ although, as Google shows, $g(f(x))$ is used frequently too. My question: Does anybody know who was the first mathematician to use this symbol and what was his interpretation?

REPLY [7 votes]: N. Bourbaki used $f\circ g$ with the interpretation $(f\circ g)(x)=f(g(x))$ in 1949 (Fonctions d'une variable réelle).
Looking at the Bourbaki papers, I found this example from 1944 (middle of page 5), with the same interpretation. I haven't found any older examples, although I haven't tried very hard. (Van der Waerden does not use this notation in his Moderne Algebra from 1930.)
It is certainly conceivable that the notation $f\circ g$ was invented by someone from the Bourbaki group. They were certainly very occupied with good notation, and André Weil introduced the modern symbol for the empty set in 1939 to be able to distinguish between $\emptyset$ and $0$. This notation for composition could have appeared from a similar discussion about $f(g(x))$ and $f(x)g(x)$.