I recently visited the Rock and Roll hall of fame in Cleveland and saw 2 of Duanes guitars.One 1959 Les Paul was strung oddly. Instead of a direct insertion to the tail he entered the tail piece via the bridge side and wrapped the strings over the tail piece and on up the neck. Anyone know why he strung this guitar in this fashion????

In this picture it's hard to tell but it looks like he strung them that way.
There is argument both ways but it produces less bridge to tailpiece angle.
It's a sustain argument. Personal preference I think.

i want to take a guess..i believe it was to raise the strings higher from the fretboard in order to use a heavier glass slide which normally would ground out on the frets from the weight. and i know from experience that the heavier the glass the longer and richer the sustain and tone.

It is usually used to decrease the break angle to the bridge to facilitate
a higher bridge for playing slide.

I think it goes guitar by guitar basis just from what I have heard from a couple of local luthiers. It depends on neck angle and other factors I cannot recall. More angle on the bridge equals more tension increasing tone quality. That's what I have been told anyway. I saw them and noticed the same thing and inquired about it when I was getting my quarterly set up done on my 335. I wanted to do the same thing but was advised against it as my particular guitar was not optimal for it. Again, I just play them and let the experts set them up!

It can be strung either way. My guess is that when you wrap over you get a different type of tone, maybe more sustain. You lower the tailpiece a bit to compensate for the higher attack on the bridge saddles