Monday, September 21, 2009

QED

When doing mathematics, there is a feeling of exhilaration to confidently write QED at the culmination of an arduous proof. Whether attempting a direct proof, a proof by contradiction, or a proof by induction, the feeling is all the same when you proclaim QED at the end! The Latin phrase “quod erat demonstrandum” which literally means “which was to be demonstrated” is traditionally used to denote the end of a mathematical proof.

Alternatives to QED included a small black square, either hollow or solid. In some of my mathematics classes in college we also used three small dots arranged in a triangular fashion to denote the end of a proof. These days, I prefer the more classical QED for my proofs.

Getting to the point of writing QED is sometimes more significant than others. Some proofs are short and concise while others draw on for many pages. Thinks of how Andrew Wiles felt when he was able to write QED after proving Fermat’s Last Theorem, first conjectured in 1637 and remaining unsolved until 1995. In this case, QED spells “relief!”

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