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History of $f \circ g$
Choice of symbols can be an indicator of intellectual allegiance. Consider how, back in the day (and before LaTeX regularised things so much!), the choice of $\neg, \to$ as against $\sim, \supset$ was an indicator of how you felt about natural deduction.
A simple query some older hands here might know the answer to. When and where did the symbol for function composition as in $$f \circ g$$ originate, and when did it become common? It was used in Bourbaki, Theory of Sets (p. 78). Was this another of Bourbaki's symbolic innovations? Was early adoption of the symbol by others an indicator of Bourbachiste enthusiasm?