Game Of Thrones: 10 Most Believable Fan Theories

Ok, so we know R+L probably equals J, but could A+J=T? Or, to put it another way, is Tyrion's father not Tywin, but instead the Mad King Aerys II Targaryen. That may just be the case. 

Tyrion and the man we know as his father have always had an uneasy relationship, with Tywin resenting him because of the fact he was a dwarf, and that Joanna died giving birth to him. However, numerous times throughout the series he refers to Tyrion as not being his son, or at least being unable to prove this is the case. He despises him, and refuses to acknowledge him as heir to Casterly Rock. 

Tywin was Hand to King Aerys, and it's said by Barristan Selmy that the Mad King was infatuated with Joanna, and took certain liberaties during the bedding after her and Tywin's wedding. It's not specified what these were, but it doesn't take much imagination to guess. It's possible that Aerys continued to further abuse her throughout the course of their marriage, leading to her falling pregnant with Tyrion. 

There's also the Imp's appearance to consider. In the books his hair is described as being pale blonde, unlike the golden crown of hair his siblings have. He also has mismatched eyes (a signifier of mixed blood), a bookish nature - like Rhaegar - and a fascination with dragons. He, Jon, and Daenerys have all had to kill someone they love, and their mothers died giving birth to them (if Lyanna is Jon's, anyway). 

It's certainly possible, even if it would diminish his and Tywin's relationship and his eventual murder of him, and you can read more about the theory here.