HISTORY OF MATHEMATICS? Need a mathematical historian. Boole onward, through Hil

HISTORY OF MATHEMATICS?

Need a mathematical historian. Boole onward, through Hilbert and Broewer.

When Boole, Frege, Peano Russell, Hilbert et al, developed boolean algebra and set theory, cumulating in ZFC+AC, theory did they understand WHY their solution worked, but was now disconnected from reality, correspondence, and truth?

I can’t find anything but it’s got to be there. It looks like it starts with Frege? How did they categorize the problem?

Is this one of those things like property rights, that we didn’t understand the cause, but talk about incessantly?

Or is the reason that boolean (binary), and sets, solve the problem of precision in context?

Someone smarter than I am had to solve this already….. But if not Broewer, who?