I think there's a lot of fascinating mathematical "dualism" in how many of those were developed at the same time together by both "practical" mathematicians (such as physicists) and "theoretical" mathematicians. You feel it is easy to argue that because the practical mathematicians had an easily defined "need" (hypothesis/experiment) they were the "leaders" and the arrow flowed from them to the theoretical mathematicians working with them, but there's just as much evidence in some of those cases that those theoretical mathematicians were already doing the theory building on their own and had a "need" to find practical use cases/outlets. In some cases we know the theoretical mathematician sought out the physicist to try to find ways to test a theory and were really the ones building the hypotheses. In some of the cases we know that though both are generally credited for "deep" collaboration after the fact, because they never really worked together and did all of their work in parallel and it is likely both would have completed just about the same work even if they never crossed paths. Newton and Leibniz famously never corresponded until after both published their own takes on the fundamental principles of The Calculus. Alonso Church had already developed the Lambda Calculus before corresponding with Alan Turing on the fundamentals of Computing and Alan Turing couldn't even share most of his practical work because it was still state secrets (and there was an ocean's distance in their correspondence anyway).

I think as often as not the "arrows" in the diagram point both directions at the same time: the practical needed the theorist to explain the patterns they were seeing and the theorist needed the practical to take the simple beautiful thing they were working on and make it practical and find the edge cases and complications.

That sort of "dualism" seems an interesting pattern in math.