Wisdom does not come with age automatically, but more accurately comes about with an accumulation of experiences. Age is an inevitability whereas experiences are infinitely acquired or missed. Obviously as people grow up they experience many things - riding a bike, tasting chocolate ice cream, visiting a foreign country, falling in love - the list goes on and on. Until someone reflects on these experiences and what value it holds to the self, they have only gained knowledge, not wisdom. Knowledge is then just the information gathered throughout one's lifetime through had experiences.
The world is full of knowledgeable people - auto mechanics, doctors, and academic professors are just a few specialized groups with an acquired set of information and skills that we trust and rely on to help society function properly. Being a knowledgeable mechanic, doctor, or professor does not necessarily make one wise. Wisdom goes further to explore deeper questions and what they mean to the individual, as well as the greater sphere of human life (or even the Universe). The more interested in a topic one gets, the more they research and seek out information (ie, the more knowledgeable
one becomes). When that person finally realizes that the deeper he searches for answers, the more questions he finds in its place, something new has blossomed.
Wisdom begins here, when the individual embraces the notion that he actually knows very little. Therefore wisdom does not rely on age, but tends to come later in life when the individual has had enough experiences and time to reflect on the mysteries of space, time, and the human spirit. This explains the classic description of how we envision wise people - they are old yet childlike, talk profound yet simply, and even sometimes reply with another question answering nothing at all. Wise people embrace the absurdity of the Universe and its inability to provide answers (in regards to humans making any sense of it at least).
We are floating through space on a giant rock without a road map.
So just sit back and enjoy the ride.