Legend has it that the first Adams was tied by Leonard Halladay of Mayfield, Michigan back in 1922 for his friend Charles F. Adams of Lorrain, Ohio. It's believed that Adams was the first to fish the pattern, thus the fly's name. Halladay was a fishing guide & most likely guided Adams on fishing trips to Michigan.
Today we know the Adams mostly as a very generalized mayfly imitation. It looks like no specific mayfly while at the same time it looks like a lot of different mayflies. However, it's thought that the first Adams fly could have been tied to copy some type of grey caddis.
There's a lot of controversy over the design of the wings of the original Adams. Some believe that the wings were divided & slanted forward, towards the eye of the hook. Others think the wings were divided but slanted back, delta-wing style. What we do know is that the body was grey in color, the hackle was like it is today, & the wings (whichever way they pointed) were the same, barred color we still use. It's believed that the tail was made from golden pheasant tippets.
No matter what the exact pattern was originally, there's no reason why you can't try them with wings going in either direction. Personally, I like the idea of the delta-wing style. I think that might work very well for my local caddis, when I'm not in the mood to try an elk hair caddis dry.
The Adams is a very versatile pattern that can be adapted any way you want or need. The fact that there's disagreement over the original pattern just proves how many different ways you can tie this fly & have it still be productive in fooling fish.