Wisdom has no necessary relationship to age or profession.
That is despite our difficult-to-escape and very banal stereotype of someone who is wise. An aging professor in an esteemed institution’s philosophy department, for instance, may more often than not be someone whom we would go nowhere near with the word.
For wisdom is only wisdom when it links a deeper view of the world, picking up on subtleties usually missed, with outward action. The philosopher may have bountiful knowledge of wisdom, but that does not mean they are wise.
That deeper, more subtle view of the world is more likely, it is true, to come with age. But it shouldn’t be assumed, as the stereotype pushes us to.
We do not think of education as being about wisdom; but we should. Since one need not be old to be wise, and since wisdom is likely the most important trait in living one’s life (because it affects all else), there seems no larger or nobler purpose of education than gaining a more subtle view of the world and learning how to apply that to life as it is lived.
Wisdom as a single idea cannot be taught, but it seems more possible for those constituent parts to be.
There is an opportunity cost to all that is taught and studied in formal education. So while there may be nothing wrong with what is taught, it must be weighed against what could be taught. In this light, it is the humanities that make more of a claim through that larger vision of education.