- Wisdom is when someone, given little information, reaches the right conclusion.
- Intelligence is when someone, given lots of information, reaches the right conclusion.
- Ignorance is when someone, given little information, reaches the wrong conclusion.
- Stupidity is when someone, given lots of information, reaches the wrong conclusion.
Intelligence can reason through things quickly. Wisdom knows which details are more important, and which situations are more likely than others.
When a problem is simple enough, either intelligence or wisdom can do the job. For example, a computer program that plays tic-tac-toe perfectly will always tie with a sufficiently-experienced person.
When a problem is complex, you want both intelligence and wisdom, though perhaps at times in different proportions. When all the facts are visible, intelligence is favored: a chess prodigy can beat people far more experienced. But when a lot of the information is implicit, wisdom is more valuable: a very intelligent child is unlikely to give good advice on your office politics — you're better off asking any elder.
People who (think they) are intelligent but lack wisdom tend to undervalue wisdom, and ignore advice. This is usually bad, but can be good, like when someone accomplishes something that was thought to be impossible.
By sharing its reasoning, intelligence can "prove its answer" better than wisdom can. Reasoning is a kind of evidence, useful for convincing people. But it can also disguise uncertainty, unjustly trampling over wisdom in a disagreement.