divergence in top talent

Being a sloppy mathematician is a precondition for being a superb physicist. All the greatest ideas in physics involved huge discreet intuitive leaps. Mathematics always came later to bridge and formalise the gaps. 

Einstein doggedly went ahead with his gut feelings. It took him and his mathematician friends years to formalise his intuitional ideas about gravity. Feynman did the same thing in quantum mechanics. He went ahead with his path integrals which mathematicians have still not been able to make rigorous despite continuous attempts during the last seventy years. (Einstein and Feynman are not some random physicists. They are the best humanity could come up with in the twentieth century!)

What seems like a positive correlation in the middle talent range becomes negative at the top. Good math and physics skills go hand in hand until you reach the top echelon of each discipline. Best physicists are not mediocre but horrible mathematicians, and vice versa.

There are similar examples from other domains as well. I will provide you with two. I am sure you can come up with more.

• Good business and political skills often go hand in hand. This leads most people to mistakenly conclude that top businessmen can become top politicians and vice versa.
• Best performers on stage are timid and awkward in social contexts off stage.