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I hate to tell you it takes little bit more than that, but of course you were already aware it also takes a keen mind to fly a fighter aircraft,

I made light of "what it takes" in that the skills are mostly perceptual, as opposed to mental.
Strapping on a fighter makes you one with it and your abilities are its virtues and vice-versa.

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...many military pilots hold master degrees, many military pilots are aeronautical engineers.

I am reminded that nearly 100% of all airline pilots were once military pilots, the huge mass of them earning their degrees while in the military, "Free" educations we taxpayers paid for.

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It also takes certain amount of coolness under pressure to recover from an emergency. To handle high “G” forces requires one to be in good physical shape.

Agreed; which makes them first and foremost, as I have noted, physical exemplars, not necessarily mental giants, though most of them are both better educated and better pilots than say a Charles Lindberg or Dick Bong.