Theorem of the Day

Cameo Apperances by Theorems

Wikipedia on cameo appearances: "Originally, the phrase cameo referred to the famous person playing no character but him or herself." I would like to keep to this original sense; the portrayal must be such that any professional mathematician would agree on the identity of the theorem in question. I'm not going to verify this though; any cameos that people (whose names appear in square brackets after the entry) are kind enough to tell me about I will take on trust.

Theorems in Film

Parseval's Theorem: in the opening scene of Gus Van Sant's film Good Will Hunting, Prof. Gerald Lambeau (Stellan Skarsgård) concludes a lecture with a statement of Parseval's Theorem.

Pythagoras' Theorem: the star of a song in David Kidd's musical comedy Merry Andrew (1958). [Maths in the Movies], see also Wikipedia entry.

The Snake Lemma: in the opening scene of Claudia Weill's film It's My Turn (1980) Jill Clayburgh proves the Snake Lemma for her mathematics class before departing for a weekend (Anthony Knapp). In Mike Nichols The Graduate (1967), at the very beginning of the film, the Snake Lemma can be seen on a blackboard behind Dustin Hoffman. [Wikipedia entry]

Arnold G. Reinhold's Maths in the Movies is a good source. [Allyn Jackson]

Theorems in the Theatre

Fermat's Last Theorem: Joshua Rosenblum and Joanne Sydney Lessner's musical Fermat's Last Tango (2000) is based on the story of Andrew Wiles' proving, and repairing his proof of, Fermat's Last Theorem. There is a nice review on Simon Singh's web site. [Allyn Jackson]

Gödel's First Incompleteness Theorem: features in Hugh Whitemore's 1986 play about Alan Turing Breaking the Code. [Allyn Jackson]

Theorems in Literature

The Binomial Theorem: in The Memoirs of Sherlock Holmes (The Final Problem), Prof. Moriarty is described by Holmes as having written, at the age of 21, "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..." See also the Wikipedia entry.

Fermat's Last Theorem: in Arthur Porges' 1954 story The Devil and Simon Flagg, the latter bets the former that he cannot prove or disprove Fermat's Last Theorem in 24 hours. You can find the story, which has a delightful twist in its forked tail, in Clifton Fadiman's Fantasia Mathematica (Bob Lockhart). In Fadiman's 1962 follow-up The Mathematical Magpie, he attributes the outline of the same story to A.J. Lohwater (so whose plot is it? asks Alex Kasman).

The Four Colour Theorem: on The Island of Five Colors, a junior mathematician is distraught to find five tribes whose territories all border on each other and on the sea, even though "A professor at the University of West Virginia ... had just proved the [Four Colour] theorem up to 83 districts." You can find Martin Gardner's 1952 story in Clifton Fadiman's Fantasia Mathematica. [Bob Lockhart]

Gödel's First Incompleteness Theorem: Apostolos Doxiadis's Uncle Petros and Goldbach's Conjecture refers to Gödel's Theorem and also several theorems from number theory. [Robin Wilson]

Gödel's Theorem features in Guillermo Martinez's The Oxford Murders. [Robin Wilson]

Pythagoras' Theorem: in Aldous Huxley's story Young Archimedes, a boy genius peasant discovers Pythagoras' Theorem for himself, drawing with a stick in the earth. You can find the story in Clifton Fadiman's Fantasia Mathematica. [Bob Lockhart]

Sims' Conjecture: in Charles Wallingford's The Last Messiah, Nick Stonesmith complains that he can't use Sims' Conjecture if his subgroups are not primitive. [Charles Wallingford]

Alex Kasman's Mathematical Fiction web site is an amazing resource which I haven't explored properly yet. [Allyn Jackson]

Theorems in Fine Art

Euler's Identity: Justin Mullins produces fine art directly from mathematics (and was kind enough to let me use his Beauty -- Euler's Relation (1998) as an icon on Theorem of the Day's home page). Imelda Almqvist has illustrated the more general series expansion of e^ix in The Highlands of Imaginary Numbers, part of a series of paintings exploring the theme of language. [Pinky Sidhu]

Bernar Venet reproduces mathematical diagrams or graphs, often commuting diagrams from cohomology, on a grand scale. There is a nice AMS article by Karl Heinrich Hofman. No specific theorems involved that I have been able to track down, though. [Pierre Fauret]

Mario Merz makes art out of the Fibonacci sequence, again on a grand scale, but again without incorporating any actual mathematics. [Pierre Fauret]

Raymond Brownell makes art from combinatorial structures and designs.

The American Mathematical Society has a nice Mathematical Imagery resource which I need to look through properly. [Allyn Jackson]

Theorems in Music

This seems quite a tall order: a piece of music which embodies, at some point, a clearly identifiable theorem. There is a little theorem of Robin Wilson and Carlton Gamer relating dual projective planes to inversions of certain tone sets which is the basis for Fanovar by Gamer (1996). It doesn't quite qualify but it is very interesting nonetheless.