Where did I say FA was not "useful" or "needed"? I only asked a question. I've elaborated with a bunch of buzzwords. Do you know what a Caley transform is? Have you ever asked yourself whether it was worth your time to find out? (Not rhetorical questions. Please answer yes/no.)
100 years ago there was a need to put the math of QM on a firmer foundation. Some might assume that that has largely been accomplished. Physics advances. Not sure I understand what you are getting at.
Physicists provided the motivation for studying functional analysis (FA) 100 years ago. But is an in depth understanding of FA necessary in 2024? A slightly different way of putting it would be: is there any important work being done by physicists that requires working knowledge of all the...