Dirac admitted it in public. The way he put is is that what people call "physical intuition" is knowing what the solution looks like without solving the equation.

Seeing how some of my classmates who were better than I was at symbolic algebra and functional analysis and never got caught by a trivial counterexample, but were mystified by even slightly nontivial PDEs, I came to the conclusion that I did the right thing studying physics before mathematics. Physical intuition allow the mathematics to come alive.

We have met the enemy, and he is us — Pogo