From: https://math.stackexchange.com/questions/132967/history-of-f-circ-g
N. Bourbaki used f∘gf∘g with the interpretation (f∘g)(x)=f(g(x)) (f∘g)(x)=f(g(x)) in 1949 (Fonctions d'une variable réelle). Looking at the Bourbaki papers, I found this example <http://math-doc.ujf-grenoble.fr/archives-bourbaki/PDF/nbt_010.pdf> 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∘gf∘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 ∅∅ and 00. This notation for composition could have appeared from a similar discussion about f(g(x)) f(g(x)) and f(x)g(x)f(x)g(x). answered Jul 4 '12 at 16:46 <https://math.stackexchange.com/users/33572/per-manne> Per Manne <https://math.stackexchange.com/users/33572/per-manne> Skip Cave Cave Consulting LLC On Wed, Mar 17, 2021 at 10:49 AM Roger Hui <[email protected]> wrote: > Does anyone have information on when the composition of two functions was > first denoted by f∘g (f jot g)? A 1-hour search (admittedly not very > through) in Cajori's *A History of Mathematical Notations* leaves me no > wiser. > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
