A lecture by Rudin Is it available a written version of this lecture by Rudin on the relation between Fourier analysis and the birth of set theory?
https://youtu.be/hBcWRZMP6xs
If not Rudin himself, maybe someone else has collected these ideas in an article?
 A: I extracted the written text from Rudin's lecture, it starts out like this (see below). If there is an interest, with some effort I can provide the rest of the text, but it requires some editing and I'm unsure this is what the OP wants... Perhaps just listening to the talk is good enough?

It is a real honor to be invited to give this lecture and I'm sorry
professor Marden couldn't be here to listen to it.
I'm a bit out of my depth here today because I intend to give a talk
which is more historical than mathematical. I was told that there
would be many non mathematicians here in the audience and that I
should not write too many formulas.
A warning: the history of mathematics is a difficult field and it's
one that has been neglected and I think there are good reasons for
that. Mathematicians don't pay much attention to history. We name
theorems after someone and sometimes that someone has something to do
with the field and sometimes he didn't. Sometimes somebody later
proved what the first guy should have proved if you see what he was
really doing, and we don't ever go to the first original sources. I
think we read what someone said about it, so mathematicians are not
really qualified to do the history of mathematics. Historians are
maybe even less qualified because you can't write about it unless you
understand it and once you start studying mathematics for its own sake
you become interested in it and you don't want to take time to go to
the history.

