There are many wonderful passages in the book "Genius" by James Gleick that describe Richard Feynman's deep intuitive understanding of calculus. He also talks a

There are many wonderful passages in the book "Genius" by James Gleick that describe Richard Feynman's deep intuitive understanding of calculus. He also talks about it a bit in his own works such as Surely You're Joking Mr. Feynman. Highly recommend if you want to see lots of interesting answers to this question. His key approach was that he always wanted to understand things based on "first principles". So he would usually take on a new mathematical frameworks by breaking them down and re-deriving them on his own from scratch. Reminds me of how Ben Franklin taught himself to write by reading famous passages and then attempting to write them from memory, comparing his version to the original version afterward and seeing what he did differently and why.