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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.

I will not vouch, either, for the mathematical accuracy of any of these cameos: they are artists' responses to mathematics, so accuracy may not have been the first imperative.

 

Some General Links

John Lienhard's radio programme Engines of our Ingenuity is a stupendous source of material on science and engineering and human culture with almost 2500 episodes available online in audio and transcript.

The general issue of mathematics in popular culture was the subject of an interesting research project Mathematical Images and Identities carried out recently by Heather Mendick, Debbie Epstein, Marie-Pierre Moreau and Teresa Carbajo-Garcia.

 

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.

The Pythagorean 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 the 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]

Maths in the Movies by Maths Masters Burkard Polster and Marty Ross.

Maths-et-tigues has a good list of French maths-related films.

 

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.

Euler's Identity: in Yoko Ogawa's The Housekeeper and the Professor Euler's Identity represents an important point of intellectual and spiritual contact between the two protagonists.

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). Arthur C. Clark's last novel, completed just before he died, co-authored with Frederik Pohl, is The Last Theorem, which describes the discovery of a short proof of Fermat's Last Theorem and the resulting cryptographic fall-out.

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]

The Pythagorean 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]

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

David Leavitt's The Indian Clerk must include some of Hardy's and Ramanujan's theorems - but I need to check...

 

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 series expansion of eix in The Highlands of Imaginary Numbers, part of a series of paintings exploring the theme of Mathematics. [Pinky Sidhu] There is a striking redition Euler's Formula by the South African artist Peter van Straten.

Fermat's Last Theorem: Imelda Almqvist's A Mammoth Callenge (in her Mathematics series) depicts the case n=3. For good measure A Mammoth Callenge II is the same but with n=37 (the first irregular prime).

Raymond Brownell makes art from combinatorial structures and designs.

Helaman Ferguson is a mathematician and scultor whose art is often based in mathematics.

Edmund Harriss is an expert on tiling and creates art from this and related mathematics. He maintains, with Dirk Frettlöh, the visually stunning Tilings Encyclopedia.

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

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]

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

A good source of information is the European Society for Mathematics and the Arts.

 

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 (see John Fauvel, Raymond Flood and Robin Wilson (eds.), Music and Mathematics: From Pythagoras to Fractals, Oxford University Press, 2003.)

 

Theorems in Heraldry

This would seem an even more elusive category but the subject of scientific heraldry is dealt with extensively at Numericana. Only one example is found there:

The Pythagorean Theorem: featured in the coat of arms of the Swedish engineer Christopher Polhem (1661–1751) and also, according to Rietstap's Armorial General, in the arms of the "Seissenegger" family, which is (most probably) the way Rietstap himself misspelled the name of the Austrian painter
Jakob Seisenegger (1505–1567). [Gérard Michon]


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