Intelligence is being able to successfully reason your way from A to B to C. Wisdom is being able to navigate safely from A to C when B is missing.
In real life B is always missing. That is to say life is much messier than the homework problems you are given while in school. Teachers go to great pains to test us only over that which they have taught us. But real life will ask things of you which you are completely unprepared to answer. There is no rhyme or reason to the tests it will give you, and more is at stake than a gold star.
You will never have enough information to be 100% sure of your decisions, nor will you always be able to gather it no matter how much effort you make. Sometimes it simply does not exist. When it does exist, you will often need to weigh conflicting information and conflicting goals or values. The answer is never as obvious as it is in the classroom and there is rarely either one wrong, or one right, answer. For this we can be grateful or otherwise we would almost certainly be doomed to failure in all of our endeavors.
The best you can do is to try to take the experience you gain in many areas and apply it as a filter to help you sort the wheat from the chaff. You will have to learn about human nature to know the ways in which people can disappoint you or surprise you. You will have to learn about human behavior to spot the clues as to which course they are intent upon. You will have to acquire experience to gauge whether they will be successful. And you will have to be comfortable operating in perpetual uncertainty for that is what it means to be human.
You will be institutionalized for the first third or quarter of your life and will be deprived of opportunities to gain much wisdom as your environment is carefully controlled and all of the answers are fed to you for you to regurgitate at the proper time and in the proper form whether you have fully digested them or not. The thing you must realize is once you are done with your education you will still know nothing, or close enough to it as to make no difference. You will have been deprived of the opportunity to hone your judgment, to bite off more than you can chew, to pursue a path which leads to a dead end. You will have been sheltered and protected from failure. For this I hope you will forgive me for it was not my doing.
You may have wondered at times why I did not always provide you with the answers to all of your questions, or why I eschewed making decisions for you in some instances while countermanding your decisions in others. You may have wondered why I was sometimes infuriating in answering a question with a question instead of saving time by providing a simple answer. This is why. The beginning of wisdom is in knowing which questions to ask… and in knowing who to trust. It is in being allowed to fail where failure is not fatal.
All of this is a pretty shoddy explanation. It is poorly crafted like a shack which houses something essential to a purpose, but which is itself poorly constructed. I trust you are wise enough to figure out how to peek through the windows to see the content… despite how poorly I have constructed things for you.
Some years after I wrote this I learned Einstein had come up with a similar formulation. He is supposed to have said something along the lines of “logic can take you from A to B, but imagination can take you anywhere.” Which I guess is true enough. But wisdom assures that the anywhere your imagination takes you to is the one where you wish to be
In fairness though, imagination is a large part of wisdom. Most of the mistakes intelligent people make are in not accounting for other every possibility. The truly wise man will be able to think of many more possibilities, assign a likelihood of those factors playing a part, and then understand that he likely still forgot a bunch of things that will come back and bite him in the butt one day. Thus he always tries to maximize his margin for error. Failure to account for these other possibilities at all, whether you can think of them or not, normally means failure. This is why scientists always couch things in caveats “if A pertains, then B likely follows given c, d, e etc…” If anyone speaks about a complex and unsettled subject with certainty then he is not a scientist and he is certainly not wise.