I recently read Gleick’s biography of Newton and highly recommend it. It’s pretty short, quotes part of this article by Keynes with a lot more context, and paints a portrait both fascinating and disturbing: to come from nothing, to start with nothing, not even having the concepts of velocity or force; to invent them, and calculus, and to develop such a deep understanding of nature to successfully compute the shape of the earth as an oblate spheroid, all from first principles, in the 1600s; to conceal nearly all of these discoveries; and then pursue things that “should all seem a crass and empty ambition once you have written a Principia.”
Which only seems like a weird conflict from modern eyes, obviously. The ideas that, paraphrased, "the world is made of math" and "spirituality and science are one" are at the heart of western mathematical mysticism, from the 6th century BC Pythagoreans onward.
BTW, if you want your mind blown, check out Penelope Gouk's "Music, Science and Natural Magic in Seventeenth Century England". It deals with the magical ideas that were present at the formation of the Royal Society.
Note that we consider magic today to be "that which doesn't exist". Natural magic then was "that which works through unknown forces".
Although rather dysfunctional as a human being, Newton is undoubtedly the greatest physicist of all time. And probably one of the greatest mathematicians. I wonder what else he would have achieved if he hadn't so much of his time and energy on alchemy and bible study.
I also wonder what benefit the study of alchemy, the Bible etc may have had on his other discoveries? Sometimes ‘flashes of insight’ come from patterns developed in other fields.
Gutenberg, for example, made a breakthrough with the printing press because his earlier career as a goldsmith taught him enough metallurgy to develop movable type; Charles Babbage credited his work on silk weaving machines with helping him visualise his adding machine (with Ida Lovelace, creating the first ‘computer’).
The thing with Newton's Principia is that's an exposition of the laws of his dynamics using proofs from elementary geometry but no calculus as such.
Newton and Leibniz separately discovered calculus but the calculus they created had no rigorous basis - it took until the middle of 19th century to formulate the axiomatic system that calculus is framed in today.
So it's natural Newton would want to write his results in a form that was rigorous and unassailable. But this meant that, as Keynes says, the final form didn't bear a relationship to intuition it was taken from.