**Fermat's Last Theorem **

Dare your friends to take a cube of blocks and make two cubes, using up all the blocks. You'll win every time. Mathematicians have suspected as much for hundreds of years, but have only recently found the proof. A mathematical mystery - after this on Earth and Sky. **
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(Tape 0:16:18-0:16:25) *Fermat's Last Theorem is one of the great stories on so many different levels in the history of mathematics. *

JB: This is Earth and Sky, and you're listening to Dr. Robert Osserman of Berkeley's Mathematical Sciences Research Institute. He spoke with us about a famous math problem - the proof of Pierre de Fermat's Last Theorem. After Fermat's death in 1665, his son found that Fermat had posed a problem in the margin of a book - along with the note that he had a proof which the margin was too narrow to contain. Well, that proof has kept mathematicians busy for hundreds of years. Dr. Osserman explains a part of the problem that Fermat posed:

(Tape 0:17:19-0:17:55) *So just what does the first case say, that a cube cannot be the sum of two cubes. You picture say a whole bunch of cubical building blocks and you make a large cube, say 10 by 10 by 10. So you have a thousand blocks piled up. And then you ask yourself, suppose you separate it, dismantle it into two piles, can you reassemble those into a pair of perfect cubes, say a 5 by 5 by 5, and a 9 by 9 by 9, or any other combination. And each time you try it, you discover you cannot do it - there will always be some leftover. *

JB: Dr.Osserman added that in 1994, Fermat's Last Theorem - which, in part, says that you can't make two cubes out of one without leftover blocks - was finally proved to be true. Thanks to Robert Osserman for speaking with us. And with thanks to the National Science Foundation, I'm Joel Block, for Deborah Byrd, for Earth and Sky.

Author(s): Beverly Wachtel

Thanks to the following individual for aiding in the preparation of this script:

Dr. Robert Osserman

Mathematical Sciences Research Institute

Berkeley, CA

Osserman@msri.org

If you enjoyed this program, you may be interested in the following: *
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Fermat's Enigma*, Simon Singh & John Lynch. NY: Bantam Books, 1997. *
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Poetry of the Universe*, by Robert Osserman. NY: Anchor/Doubleday, 1996.

Mathematical Sciences Research Institute website:

Fermat's Last Theorem website:

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html