Rota said something similar in this essay about mathematicians and their bags of tricks: https://www.ams.org/notices/199701/comm-rota.pdf https://www.ams.org/no

Rota said something similar in this essay about mathematicians and their bags of tricks: https://www.ams.org/notices/199701/comm-rota.pdf https://www.ams.org/notices/199701/comm-rota.pdf But I think they also have their intuitions built from experience in the sense of Tao's post-rigorous stage: https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/ https://terrytao.wordpress.com/career-advice/theres-more-to-...