Fermat's Last Theorem

 was a mathematical statement.The Eleventh Doctor used its proof to convince a body of geniuses they should take his advice about how to save the world from annihilation by the Atraxi. He uploaded the proof — which the Doctor called "the real one, never been seen before" — to a secure video conference from a laptop computer in Leadworth. Simultaneously, he muttered an acknowledgment to the originator of the theorem, Fermat, and mentioned that Evarist got killed in a duel before he could write down his own proof. He claimed responsibility for the latters' death, saying that it had only happened because he had slept in that morning. (DW: The Eleventh Hour)
 * The reference here is to Fermat's Last Theorem, but many details in the Doctor's speech do not conform to known events in the real world. The theorem was actually proved in the 1990s, but the Doctor's clarification that he was sending "the real one" likely indicates he doesn't feel the 20th century solution is a particularly good one. The other reference is to Évariste Galois, a 19th century mathematician whose work on the theorem was fundamental to the 1990s proof, who was killed in a duel.