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.
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 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]
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]
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). 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]
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]
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.
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]
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:
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
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