This, so much. Many mathematicians and physicists believe in intuition as a function separate from intelect. One is more akin to a form of (inner) perception, whereas the other is generative - extrapolation based on pattern matching and statistical thinking. That second function we have a handle on and getting better at it every year, but we don't even know how to define intuition properly. A fascinating book that discusses this phenomena is Nature Loves to Hide: Quantum Physics and Reality, a Western Perspective [1]

This quote from Grothendieck [2] (considered by many the greatest mathematician of the 20th century) points to a similar distinction: The mathematician who seeks to understand a difficult problem is like someone faced with a hard nut. There are two ways to go about it. The one way is to use a hammer — to smash the nut open by brute force. The other way is to soak it gently, patiently, for a long time, until it softens and opens of itself.

[1] https://www.amazon.com/Nature-Loves-Hide-Quantum-Perspective...

[2] https://en.wikipedia.org/wiki/Alexander_Grothendieck