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Showing posts with label Fermat's Last Theorem. Show all posts
Showing posts with label Fermat's Last Theorem. Show all posts

Theorem that took 357 years to prove...!!!

Posted by Vikramsinh at Sunday, December 13, 2009



“And perhaps, posterity will thank me for having shown it that the ancients did not know everything.” -Pierre de Fermat


Man is always fascinated by complexity of mathematics. The mathematical problems, theorems, conjectures proposed are sometimes pose such a challenge that it took years of efforts of many brilliant mathematicians to solve it. People who solve it are truly obsessed with only one thought, that is solution to the given problem.

Here is world’s one of the most famous and celebrated theorem which took 357 years to prove. Statement of the theorem looks so simple that any schoolchildren can understand it, even though it poses challenge to mathematicians from all over the world. Yes...it's famous Fermat's Last Theorem...!!!



Fermat wrote, “It is impossible for any number which is a power greater than the second to be written as a sum of two like powers. I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.”

Mathematically a^n = b^n + c^n where a,b,c,n are integers have no solution for n > 2

Pierre de Fermat (1601 - 1665) wrote it in 1637 and it is very confusing if he had the proof. He wrote that he have proof but the margine of the paper is too narrow to contain it. It's mystery and different people have different opinions about it.

The proof was established by Andrew Wiles in 1994. Proof is not directly related to Fermat’s last theorem its proving another theorem that implies Fermat’s last theorem. As a child Andrew
was curious about the theorem and why it is not solved for so many years. He worked hard but found dead end. He then started to work on elliptic curves which was popular contemporary field of study and coincidently the very field leads to the proof.

He buried himself for 7 years, he left his job as a professor and sideline his social life. In 1993, he comes up with proof. But soon his dreams got bigger blow, he was devastated when one of the questions asked by colleague challenged the correctness of the proof. Once again he obsessed with his work. He started work to fix the problem. After several months efforts with his former student he comes up with the correct proof.


This incredible journey to get proof for 7 years of ceaseless efforts is captured in a movie called The Fermat's Last Theorem in 1996. Simon Singh and John Lynch's film tells the enthralling and emotional story of Andrew Wiles. Here is the link to watch the video.

This is one of the most interesting stories about mathematical proofs I came across. It’s really amazing struggle of man to get the ultimate truth ..!!! and I think that’s what makes our lives meaningful.