Fermat's Last Theorem

Fermat's Last Theorem was a mathematical theorem whose proof the Doctor once used to convince a body of geniuses that 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 noted that the originator of the theorem, Fermat, got killed in a duel before he could write down the proof. He claimed responsibility for the death, saying that it had only happened because he had slept in that morning.

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" may be an allusion to this 20th century solution. Also, Fermat himself was not killed in a duel. Instead, the reference to a duel seems to be a reference to Everiste Galois, a 19th century mathematician whose work on the proof was fundamental to the 1990s proof.