Introduction, lame segue, wise.
Wise comes from the Old English wis, wise—at least as an adjective. Further back, it’s the Proto Germanic wissaz and Proto Indo European weid, to see. That word happens to be the origin word for vision, by the way. So someone who was wise was someone who could “see”.
But, like I said, that’s just the adjective. Not that the other forms aren’t related, it’s just that they have a slightly different history. There’s both a noun and a verb of wise, although I haven’t really heard either one used in a sentence. The noun means a manner of proceeding and it comes from the Old English wise. Before that, it’s the Proto Germanic wison, which means appearance or manner and is related to wissaz. And finally, there’s the verb, which comes from wisean, just another version of wis.
Wisdom: the ability to see ahead. I guess.
Tony Jebson’s page on the Origins of Old English