A + J = T

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Fan Theory
Fan Theory: A + J = T
Synonyms: Aerys + Joanna = Tyrion
Origin: Usenet
Fandom(s): A Song of Ice and Fire and Game of Thrones
Dates: 2005 -
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A + J = T is a fan theory in the A Song of Ice and Fire and Game of Thrones fandoms. It posits that Tyrion Lannister is not actually the son of Tywin Lannister, but rather is secretly the bastard son of Aerys Targaryen, the Mad King, and Tywin's wife, Joanna Lannister.[1][2]

The theory was apparently first proposed in a January 2005 Usenet post by a user called Groundsel.[3] It gained traction after the release of the fifth book, A Dance with Dragons, in 2011, due to a scene in which Barristan Selmy tells Daenerys Targaryen that Aerys was "taken" with Joanna in his youth, and lamented the abolishment of the lord's right to the first night during her and Tywin's wedding feast.[2]

A corollary theory holds that Tyrion's older twin siblings Cersei and Jaime are instead the ones secretly fathered by Aerys.