Wolfgang Pauli in a letter to Heisenberg dated October 19, 1926: “One can see the world with the p-eye, and one can see it with the q-eye, but if one opens both eyes, then one becomes crazy.”
Perhaps the pair of mathematical rigor and physical intuition should be added as another example of two mutually exclusive qualities. You can look at the world with a mathematical eye or with a complementary physical eye, but don’t dare to open both. https://www.quantamagazine.org/how-quantum-theory-is-inspiring-new-math-20170330/