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Star Trek: The Next Generation :: The Royale (02x12)
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Episode Information |
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| Title: | The Royale |
| Episode #: | 02x12 |
| Production Number: | 138 |
| Original Airdate: | Monday March 27th, 1989 |
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| | Other Release Dates: (Edit) | | Country: | Aired On: | |
 CA (Télé-Québec) |
Mar 27, 1989 |
 UK (BBC TWO) |
Jun 19, 1991 |
 FR (BBC TWO) |
Jun 19, 1991 |
 IE (BBC TWO) |
Jun 19, 1991 |
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Episode Summary |
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Stardate 42625.4 After discovering debris from an old manned NASA vessel, an away team beams down to an out of place building on a nearby planet. There inside the building they discover a recreation of an Earth casino-hotel. They also discover that there is no exit from this casino-hotel.
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Guest Stars |
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Episode Notes |
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Log Entries:
*Captain's Log, Stardate 42625.4. We are entering orbit around the eighth planet of the previously unmapped Theta 116 solar system. We diverted from our scheduled course when a passing Klingon cruiser reported discovering pieces of a strange vessel in the upper atmosphere of this planet. We've come to investigate.
*Captain's Log, supplemental. We remain in orbit around Theta VIII still out of contact with the away team.
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Analysis |
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Picard: Fermat's Last Theorem. You're familiar with it?
Fermat's Last Theorem was the final remaining unproven theorem of 17th century mathematician and renaissance man Pierre de Fermat. It is an extension of the notion behind the famous Pythagorean theorem X^2+Y^2=Z^2 that every schoolchild learns. It is one of the most famous theorems in mathematics,and received the attention of almost every serious mathematician in the centuries since its proposition by Fermat. Despite a vast array of utter failures, in fact it brought forth a wealth of techniques for solving problems in number theory which, while failing to solve this specific problem, found great utility in other areas and applications. Many brilliant minds thought they had solved it, only to find upon peer review that they had made some subtle error which invalidated their proof.
Simply stated:
No three positive integers a, b, and c can satisfy the equation
a^n + b^n = c^n
for any integer value of n greater than two ("^" means "to the power of")
Fermat had a habit of scribbling things in the margins of books, and, in this case, wrote the theorem followed by a note that roughly translated as "I have discovered a wonderful proof of this which this margin is too small to contain". No further notes regarding this "elegant and simple proof" have ever been found.
While the theorem had been proven for special cases -- n=3, all even "n", and so forth, it had not been proven for the general case (i.e.,"all n") at the time of the production of this episode.
The ST:TNG episode makes a common error in SF, that of attempting a serious, clearly defined prediction, in this case that the theorem would remain unproven even until the time of ST:TNG.
In actual fact (indeed, a true "DOH!!" moment) the theorem stood unsolved well under ten years after the episode was aired, being finally solved in 1995 by Andrew Wiles drawing on work by Ken Ribet and Richard Taylor.
The techniques used by Wiles were far beyond those of any which were available to Fermat, and most have speculated (indeed, many had done so prior to Wiles' proof) that Fermat's own proof was also faulty, and contained some subtle error which has been lost to posterity. Nonetheless, Fermat's gauntlet was thrown, and it took centuries for someone to be able to pick it up and make it their own.
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