Wisdom versus Intellect. Does wisdom truly exist?

It is said education offers intellectual development. You see the results or non-result depending on how you apply your mind. Are intellectual minds guaranteed "wisdom?"

How do we prove its existence? How do you recognize wisdom? Why is it accepted by humanity that there is such an attribute to the makeup of a human being.

Scientific minds say "show me the proof. Show me the matter connected with the experiment, show me the results….then it is recognized."

How do you prove wisdom exists? And if you accept it as a human attribute, is it then spiritual and not scientific?