A sage is wise. That young woman is clever.
Both of them (I think) are good at not getting into unwanted trouble, and both are good at solving problems.
So.. Is there a difference between being clever and being wise?
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As I use the terms -- and I grant that there may be variation in usage --
Cleverness/intelligence is the ability to solve a problem.
Wisdom is the ability to know whether the problem needs to be solved, whether it's the right problem, and whether it's a problem at all.
(MIT had many students who were extremely intelligent, but some of them didn't have the wisdom God gave a goose.)
The word clever can have a negative connotation:
Jim was a clever klepto! (i.e., kleptomaniac)
Sally had a clever way of not paying the taxes she owed.
The team was adept and clever, being able to put a positive spin on even the worst circumstances.
Clever can also have a positive connotation:
Dr. Blalock had a clever assistant who designed a special surgical tool for performing open-heart surgery on "blue babies."
I commend you, Brad, for your clever and elegant solution to an intractable problem!
The word wise can be used in a pejorative and negative sense, but it usually requires the addition of a modifier to do so. Examples one and two are negative; examples three and four are positive.
Don't be a wise-guy [or wise-a_ _], Mr. Smarty Pants.
Murphy's cracking wise was totally out of character for him.
The judge was a wise woman who made wise decisions.
We are too soon wizened and too late wise.
In conclusion, to be clever is to put knowledge to use in creative ways with outside-of-the-box kind of thinking. The use to which the knowledge is put, determines whether the cleverness is positive or negative.
To be wise is to apply knowledge to real-life situations--problems, challenges, and so on. Without the modifiers I refer to above, however, it is (almost) always a positive thing. Often, wisdom is contrasted with folly, stupidity, indecisiveness, waffling, ignorance, and other negative words (although ignorance can also be a neutral word meaning simply "not knowing").
A clever person has a quick intellect that can come up with complex solutions to difficult problems. A wise person makes good decisions. The clever solution may not be wise (it might be morally suspect, risky or overly complex) and the wise solution is often not "clever" (it may be very simple).
Cleverness is often associated with youth, and wisdom with age, although the connection is not a necessary one.
Definitions from Dictionary.com:
adjective, clev·er·er, clev·er·est.
adjective, wis·er, wis·est.
A person can be born clever, but can only become wise with life experience.
Wisdom is personally gained. Of one's own fa ulty and person/volition.
Cleverness or the wit of it is the ability to enjoin separate or distinct ideas to cohort a more plausible direction as it is in description. Often intiitive over formulaic, as there is only the self or subject to account for. Math is more formulaic due to its generalities.