It doesn't actually work like that since topics are interconnected.
Maths > physics > chemistry > biology
Specializing too much can be counter productive.
In theory is is ideal to have the country governed by maybe 15 individuals that each have specialist advisors, these advisors are the rulers stay out from areas where government actions would be harmful.
You can left a lot too the free market, ancaps think government isn't needed for everything but i dont actually think that's true.