This title takes up anew the riddles within a number of Maya hieroglyphic inscriptions first recognised by Floyd Lounsbury. Gerardo Aldana unpacks these mathematical riddles using an approach grounded in a reading of the texts made possible by recent advances in decipherment. Using a history of science methodology, he expands upon (and sometimes questions) the foundational work of archaeoastronomers. Aldana follows three lines of investigation: a reading of the hieroglyphic inscriptions of the Classic period (ad250-900), mathematical analysis to recover Classic Maya astronomical practice, and a historiography of Maya astronomy. During troubled times in Palenque, Aldana contends, Kan Balam II devised a means to preserve the legitimacy of his ruling dynasty.He celebrated a re-creation of the city as a contemporary analogue of a mythical Creation on three levels: monumental construction for a public audience, artistic patronage for an elite audience, and a secret mathematical astronomical language only for rulers-elect. Discussing all of these efforts, Aldana focuses on the recovery of the secret language and its historical context.