Friday, March 25, 2016

LearnNBlog: Fermat's Last Theorem

Recently read a news article about Prof. Andrew Wiles being awarded the Abel prize for his proof of Fermat's Last Theorem. I had first come across Fermat's Last Theorem in one of my mathematics textbooks in school. Apart from the various numbers and equations, each chapter had trivia about mathematicians. 

This was the theorem proposed by the French mathematician Pierre de Fermat in 1637. In the margins of the his copy of Diophantus's Aritmetica, he had left the following words 

"But it is impossible to divide a cube into two cubes, or a fourth power into two fourth powers, or generally any power beyond squares into like powers; of this I have found a remarkable demonstration. This margin is too narrow to contain it."

Enigmatic words, indeed!

For over 300 years, mathematicians across the world struggled with finding a proof of Fermat's last theorem. Empirical evidence could not disprove it either. But no proof could be found. The search for a proof of Fermat's Last Theorem became the quest for the Holy Grail for mathematicians. Many awards were announced for the person who cracked it. But Fermat's remarkable demonstration was not found since. In fact, it was thought that with the current available knowledge this theorem could just not be proved (or disproved).

In 1993, Prof. Andrew Wiles announced his proof of the theorem. However, soon after, an error was found in his proof. But Prof. Wiles was not to be deterred. He reworked and came back with a new proof, a year later. This proof was compiled over 150 pages and took in developments in mathematics from the 20th century (which would not have been  available to Fermat).

For his discovery of the proof of Fermat's last Theorem, Prof. Wiles was awarded the Abel Prize (considered to the Mathematics equivalent of Nobel prize) in 2016.

Prof. Wiles's proof was over 150 pages long, which explains why Fermat couldn't fit it in the margins of Arithmetia. Or maybe there is a simpler proof out there, which even the best minds have of the past four centuries haven't been able to resolve.

Fermat's Last Theorem (Wikipedia)
Prof. Wiles' Solution (Wikipedia)
The News Article on Abel Prize (The Hindu

P.S. With this post, starting a new section in the blog title "LearnNBlog", incorporating interesting (for me at least) learnings.

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