Fermat's Last Theorem in Star Trek

[master_q 0]

It has been a while since I last posted (besides posting on these subjects as it relates to trek trivia) on such related topics as science and/or mathematics, but that does not mean that I have abandoned these topics in "real life" and whatnot (obviously).

 

I was doing some searching in Wikipedia for topics related to mathematics. And, I thought I would share the entry on Fermat's Last Theorem. Why? For the Star Trek trivia gurus out there, you know why. But here is Wikipedia...

 

In fiction

 

In "The Royale", an episode of Star Trek: The Next Generation, Captain Picard states that the theorem had gone unsolved for 800 years. Wiles' proof was released five years after the particular episode aired. This was subsequently mentioned in a Star Trek: Deep Space Nine episode called "Facets" during June 1995 in which Jadzia Dax comments that one of her previous hosts, Tobin Dax, had "the most original approach to the proof since Wiles over 300 years ago." [1] This reference was generally understood by fans to be a subtle correction for "The Royale".

 

Fermat's What?

 

Fermat's Last Theorem is one of the most famous theorems in the history of mathematics. It states that:

 

It is impossible to separate any power higher than the second into two like powers,

 

or, using more formal mathematical notation:

 

If an integer n is greater than 2, then a^n + b^n = c^n has no solutions in non-zero integers a, b, and c.

 

Despite how closely the problem is related to the Pythagorean theorem, which has infinite solutions and hundreds of proofs, Fermat's subtle variation is much more difficult to prove. Still, the problem itself is easily understood even by schoolchildren, making it all the more frustrating and generating perhaps more incorrect proofs than any other problem in the history of mathematics.

 

The 17th-century mathematician Pierre de Fermat wrote in 1637 in his copy of Claude-Gaspar Bachet's translation of the famous Arithmetica of Diophantus: "I have a truly marvelous proof of this proposition which this margin is too narrow to contain." (Original Latin: "Cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.") However, no correct proof was found for 357 years, until it was finally proven using very deep methods by Andrew Wiles in 1995 (after a failed attempt a year before).

 

All the other theorems proposed by Fermat were proven, either in his own proofs or by other mathematicians, in the two centuries following their proposition. The theorem was not the last that Fermat conjectured, but the last to be proven.

 

[For More http://en.wikipedia.org/wiki/Fermat's_last_theorem ]

 

For a laymen (on this specific topic ---- that is about all I could take) book or two on this subject, I recommend, "Fermat's Enigma" by Simon Singh. Also, see Keith Devlin's fantastic "Mathematics: The New Golden Age" (Chapter 10)

Edited December 13, 2006 by master_q