The Trojan Horse was a hollow woodenstatue of a horse used by Agamemnon and the Greek army to invade the city of Troy. The First Doctor did not, at the time, believe the Trojan Horse to be an actual historical event, but rather an invention of Homer for his account of the Trojan War. Threatened with execution by Agamemnon and Odysseus if he did not devise a method to swiftly defeat the Trojans, the Doctor first hoped to create flying machines for the Greeks. However, when Odysseus insisted the Doctor be the first test pilot, the Doctor reluctantly designed the Trojan Horse for the Greeks. (TV: The Myth Makers)
Technically, the Doctor is accurate in denying the idea for the Trojan Horse was his. The Doctor's creation of the Trojan Horse is an ontological paradox; the Doctor did not come up with the idea, but knew of it from Homer, telling Steven Taylor that he thought it was fictional. However, Homer's account was based on the real Horse, which the Doctor designed for the Greeks. Thus, neither the Doctor nor Homer can truly be credited with the invention.