If there is one space where it shines, sure it’s mathematics. But even there, the most notable mathematicians highly rely on some intuitions far before they man

If there is one space where it shines, sure it’s mathematics. But even there, the most notable mathematicians highly rely on some intuitions far before they manage to prove anything, as well as while selecting/creating their conceptual tools to attempt to build the proof, and rarely go to the point of formalizing their points through Coq/Isabelle or even with meticulous paper craft à la Principia Mathematica from Russel and Whitehead.