A Treatise on the Binomial Theorem is a fictional work of mathematics by the young James Moriarty

Professor Moriarty

Professor James Moriarty is a fictional character and the archenemy of the detective Sherlock Holmes in the fiction of Sir Arthur Conan Doyle. Moriarty is a criminal mastermind, described by Holmes as the "Napoleon of Crime". Doyle lifted the phrase from a real Scotland Yard inspector who was...

, the evil archenemy

Archenemy

An archenemy, archfoe, archvillain or archnemesis is the principal enemy of a character in a work of fiction, often described as the hero's worst enemy .- Etymology :The word archenemy or arch-enemy originated...

 of the detective Sherlock Holmes

Sherlock Holmes

Sherlock Holmes is a fictional detective created by Scottish author and physician Sir Arthur Conan Doyle. The fantastic London-based "consulting detective", Holmes is famous for his astute logical reasoning, his ability to take almost any disguise, and his use of forensic science skills to solve...

  in the fiction of Arthur Conan Doyle

Arthur Conan Doyle

Sir Arthur Ignatius Conan Doyle DL was a Scottish physician and writer, most noted for his stories about the detective Sherlock Holmes, generally considered a milestone in the field of crime fiction, and for the adventures of Professor Challenger...

. 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 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

Binomial theorem

In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with , and the coefficient a of...

, 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.

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

The Dynamics of an Asteroid

The Dynamics of An Asteroid is a fictional book by Professor James Moriarty, the implacable foe of Sherlock Holmes. The book is described by author Arthur Conan Doyle in "The Valley of Fear" when Sherlock Holmes, speaking of Professor Moriarty, statesWith this class of talent, Professor Moriarty...

, 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 has been claimed to be one of the colleges
that later comprised the University of Leeds

University of Leeds

The University of Leeds is a British Redbrick university located in the city of Leeds, West Yorkshire, England...

. However, in Sherlock Holmes: The Unauthorized Biography, the "smaller university" is said to be Durham

Durham University

The University of Durham, commonly known as Durham University, is a university in Durham, England. It was founded by Act of Parliament in 1832 and granted a Royal Charter in 1837...

.

Review and discussion

Doyle, in his works, never describes the contents of the treatise. This has not stopped people from speculating on what it might have contained. Science Fiction writer Poul Anderson

Poul Anderson

Poul William Anderson was an American science fiction author who began his career during one of the Golden Ages of the genre and continued to write and remain popular into the 21st century. Anderson also authored several works of fantasy, historical novels, and a prodigious number of short stories...

, for example, wrote about the treatise for the Baker Street Journal.

Treatise is sometimes used when a reference is needed to a non-specific example of a scientific paper.

Other references

In The Seven-Per-Cent Solution

The Seven-Per-Cent Solution

The Seven-Per-Cent Solution: Being a Reprint from the Reminiscences of John H. Watson, M.D. is a 1974 novel by American writer Nicholas Meyer. It is written as a pastiche of a Sherlock Holmes adventure, and was made into a film of the same name in 1976....

, a Holmes pastiche

Pastiche

A pastiche is a literary or other artistic genre or technique that is a "hodge-podge" or imitation. The word is also a linguistic term used to describe an early stage in the development of a pidgin language.-Hodge-podge:...

 by Nicholas Meyer

Nicholas Meyer

Nicholas Meyer is an American screenwriter, producer, director and novelist, known best for his best-selling novel The Seven-Per-Cent Solution, and for directing the films Time After Time, two of the Star Trek feature film series, and the 1983 television movie The Day After.Meyer graduated from...

, Moriarty in conversation with Watson denies any treatise on the binomial theorem, saying: "Certainly not. Who has anything new to say about the binomial theorem at this late date? At any rate, I am certainly not the man to know."

External links

• A list of many references to this work, as well as to other works of Moriarty's such as The Dynamics of an Asteroid.