There are a few mathematicians that have analyzed and wrote about their process. A recent (IMO) good writing on the subject is David Bessis' "Mathematica" (I found this review https://siliconreckoner.substack.com/p/review-of-mathematica... which I haven't had a chance to fully read). It covers both a personal perspective as well as examples from Grothendieck, Descartes and others.

Having had the opportunity to have ideas and pursue them extensively as a corporate employee, startup founder, and independent researchers, all I can say is that there seems to be a violent agreement of how stuff actually happens and that it's almost never fully made possible in either industry or academia. It's like a living irony.

For a deeper treatment of the broader subject - one of the most cited books is the "The Structure of Scientific Revolutions"