A portrait of Pierre de Fermat, French lawyer and mathematician. (Photo credit: Wikipedia)

**“I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.”** – Pierre de Fermat

One of Fermat’s habits was to write proofs in the margins of the books he read. He was most known for writing in his copy of *Arithmetica*. One day he came across the book and worked through the many problems published therein. The author of *Arithmetica*, Diophantus of Alexandria, shared his proofs and solutions in his text. The story is told that at some point, about 1637, Fermat decided to expand the Pythagorean Theorem to similar equations with exponents greater than 2. He concluded that there were no whole number solutions to the equation x^{n} + y^{n} = z^{n} for values of n greater than 2. However, in the margin of Book II of *Arithmetica* all he wrote was “I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.” (Singh, 62) To his successors’ chagrin, Fermat did not write the proof to this, then, conjecture. At least none that anyone have found and published. Fermat died in 1665. In 1670, Fermat’s son, Clément-Samuel, published Fermat’s discoveries, theorems, notes, and commentaries in *Diophantus’ Arithmetica Containing Observations by P. de Fermat*. In the years to follow, mathematicians would unsuccessfully attempt to prove what was known as Fermat’s Last Theorem. It was given this name because it was the only theorem that Fermat did not provide a proof for.

The quote rings out for me because it leaves an element of wonder, mystique, and brilliance, all at once. *Did Fermat have a proof? Did he write out the proof? Did he have it figured out in his mind? Was this his last puzzle for the world?*

**WHAT IS YOUR FAVORITE QUOTE? WHY?**

**REFERENCE:** Singh, Simon. Fermat’s Enigma. New York: Anchor Books, 1997

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I am a Co-founder of and Program Coordinator for Math Corps Philadelphia, a combined academic enrichment and mentoring program. I am the author of "Teacher Training Manual: Designed for Secondary Mathematics Teachers of African American Urban Students." I hold a Master of Education degree in Secondary Mathematics and have several years of experience teaching secondary and post-secondary mathematics.

June 29, 2013 at 9:54 am

I too have been fascinated for many years by this quote, but I am not a mathematician and my interest is very basic and amateurish. Nevertheless I am convinced that there is a simple proof of the theorem, and have identified some of the patterns in the number sequences which could, I believe, form the basis for the simple proof.

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June 29, 2013 at 3:16 pm

Thanks for visiting. I hope you find that simple proof! Sometimes it’s the simple things that seem so confounding. By the way, your blog is very interesting!

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August 9, 2013 at 6:39 pm

this is one of my favorite quotes:

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of a sculpture, without appeal to any part of our weak nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.” (Bertrand Russel “Mysticism and Logic”)

I really like your article, and I still am fascinated by what Fermat did and what he would have done, if he wouldn’t die… he is just one of my favorite mathematician…

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August 10, 2013 at 7:04 am

I like your favorite quote. Math is beautiful! Thank you for sharing it!

I am also fascinated by Fermat’s mind (and work) as well. Only a few people like him come along!

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