In the fiction of Arthur Conan Doyle, Sherlock Holmes is the great detective, Professor James Moriarty is his evil arch-enemy, and A Treatise on the Binomial Theorem is a brilliant work of mathematics by the young Moriarty. The treatise is mentioned in The Final Problem, when Sherlock 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.

Professor 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 review it. This is a very different branch of mathematics from the Binomial Theorem, again showing his impressive intellectual prowess.

The "smaller university" involved is sometimes claimed to be one of the colleges that later comprised the University of Leeds. ^*.

Review and discussion of the treatise

Although the treatise itself appears to have been lost, a review of a later journal version of the paper still survives. The review is still used as an example in modern computer science publications. (In PDF format.)

There has been considerable speculation on the contents of the treatise. See, for example:

• Anderson, Poul. A Treatise on the Binomial Theorem, Baker Street Journal, 5, No. 1 (January 1955), 13-18.

A list of many references to Moriarty's work on the Binomial Theorem can be found in:

• ^* Lists many references to this work, as well as other works of Moriarty such as The Dynamics of an Asteroid.

Fictional books