Sure, there are intelligent children and stupid adults. But the virtue adulthood is not defined by intelligence (for intelligence is a rare condition indeed) but by experience.
Amongst prodigies and geniuses, there have been child mathematicians, painters, scientists, linguists, musicians and so, but I noticed that on the list of child prodigies, how few writers or leaders military or otherwise there were. Sure Christopher Paulini wrote a book, but as any look at Tv tropes will tell you his books are awful for reasons other than poor grammar or spelling... On fanfiction.net there are 12-13 year olds writing who presumably get adults to correct the technical aspects of their writing (spelling, grammar and so on) but their stories still lack the mature and complex characterisation, plots, themes that and older writer will have because these aspects of writing are not based on your technical ability to write but by observations of people as the author matures and ages aka experience that one gains as one reaches adulthood. Which brings me to leadership:
Good leadership requires several characteristics more commonly found in adults than children: consideration for others as opposed to selfishness that to be honest children (and sociopaths who have many child like characteristics) lack, the ability to listen but still remain firm and detached and not be swayed by their emotions but what is necessary all of these things are based on maturity (unless you are a sociopath in which case you're morals fail to grow as you body does). Military tactics are not like painting or music (which is something that genius pick up quickly because they learn quickly) but are gained through experience, study of previous generals, knowledge of local terrain, weather conditions, coordinating politics (which is basically to manipulate people an ability that requires experience) and so on... The lack of children in leadership position is not for want of trying either: numerous kings and queens have begun their reigns young (some even before they were born or Mary Queen of Scots at 6 days old) but they have been advised and helped by adults, sure Edward IV of England (Henry VIII son) was a good king (but many child monarchs mature quickly in the role) but he still relied on a lot of advice and help. The only military prodigies I can think of are Alexander the Great and Akbar... but they're both older than other prodigies and Akbar reigned for a long time.
