A Treatise on the Binomial Theorem is a fictional work of mathematics by the young Professor James Moriarty, the criminal mastermind and archenemy of the detective Sherlock Holmes in the fiction of Arthur Conan Doyle. The actual title of the treatise is never given in the stories; Holmes simply refers to "a treatise upon the Binomial Theorem". The treatise is mentioned in the 1893 short story "The Final Problem", when Holmes, speaking of Professor Moriarty, states:
He is a man of good birth and excellent education, endowed by nature with a phenomenal mathematical faculty. At the age of twenty-one he wrote a treatise upon the Binomial Theorem, which has had a European vogue. On the strength of it he won the Mathematical Chair at one of our smaller universities, and had, to all appearances, a most brilliant career before him.
— Sherlock Holmes, "The Final Problem"
Moriarty was a versatile mathematician as well as a criminal mastermind. In addition to the Treatise, he wrote the book The Dynamics of an Asteroid, containing mathematics so esoteric that no one could even review it. This is a very different branch of mathematics from the Binomial Theorem, further reflecting Moriarty's impressive intellectual prowess.