Game Of Thrones: 7 Fan Theories About Jon Snow 's Parents (That Aren't R+L=J)
4. Mance Is Jon's Father
There are a couple of different lines of thinking on this one, although both are rather 'out-there' even within the realms of these theories, but the base idea ends up at Mance Rayder being the father of Jon Snow.
One of these is essentially R+L=J, with the theory that Mance actually is Rhaegar Targaryen, who used a strong glamour involving rubies after his 'death', and fled Beyond-The-Wall, pointing to similarities in the personas of the two, such as their love of songs, in particular Bael the Bard.
The other is more basic, which is that on one of the occasions Mance managed to sneak his way into Winterfell, he impregnated Lyanna with the baby who would become Jon Snow. This partially stems from a quote by Alfie Allen (Theon) who said it was sort of a Luke Skywalker situation. You have Mance, who joined the Night's Watch and then betrayed them, and then Jon follows in his footsteps by taking the black. Mance does act as a father figure to Jon as they become closer, but actually being his father seems unlikely, especially considering the timeline of Lyanna's 'kidnapping'.
As for the Mance is Rhaegar theory, well, it's possible, but requires one hell of a tinfoil hat.