A mystery – three centuries old!!

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What if someone told you – “I know a huge secret, but I’m not telling you now” OR “ I know where this treasure’s hidden, but gotta catch a bus so tell you later”.
How would you feel? Of course you’d be intrigued – and probably set out to get to the bottom of the mystery.
Now this is the story of one such mystery that sent the best mathematicians on a ‘treasure hunt’ for 350 years.
To understand the mystery you should first recall good old Pythagoras theorem.


So if a = 3 and b = 4,
2 + b 2 = 32 + 42 = 9 + 16 = 25 = 52
So c = 5
Thus we have 3, 4, 5 – a Pythogorean triplet- three numbers such that if we add the squares of two of them we get the square of the third.
What other numbers could a, b, c  be? Just google it and you would find that there are infinitely many Pythagorean triplets. This means there are so many triplets out there in Integer Number land, such that adding the squares of two of them gives the square of the third.
Now Pierre de Fermat, on a beautiful day long long ago, wanted to find a triplet that would answer
3 + b 3 = c 3
That is, the sum of cubes of two numbers giving the cube of the third number. He could not find any. In fact he soon concluded it was almost impossible to find integers x, y, z such that
x n + y n = z n, for n > 2
Now, for Mathematicians, “could not find” is not same as “does not exist”. To prove that it is impossible to find triplets similar to Pythagorean triplets for powers of 3, 4 etc, he had to give a mathematically solid proof that they did not exist.

And one day in 1637 it dawned on him – the proof. “Tadaaa!!!” he would have said(though, being French, he would have in all probability said ‘Voila!’). So he noted on the margin of the book he had with him:
‘ …I have discovered a truly marvelous proof of this, which this margin is too narrow to contain’.
They discovered this note thirty years after this death, but could not find any further detailing of the proof mentioned, among any of his books.
And thus began the mathematical treasure hunt that lasted centuries. It even got a place in the Guinness Book of Records as the most difficult math problem, owing to the number of unsuccessful attempts to solve it.
Sometime in the early 1960’s, Andrew Wiles, a ten year old, in England, stumbled on to this theorem and the story that followed. He was excited and decided that HE would be the one to solve it. But soon he realised that it was much beyond his knowledge and dropped the idea  as an impossible childhood fantasy.
Later he went on to graduate in Mathematics from Oxford and even got a PhD from Cambridge. Later he joined Princeton University as a Professor. In the late 1980’s he was reminded of his dream by some discussions about the theorem. He started to work on it secretly and finally in 1996, he did it- he found a proof to Fermat’s last theorem, thus solving a 350 year old mystery.

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In March 2016, he was awarded the Abel prize( as prestigious as the Nobel prize)- truly deserved , don’t you agree?
The Fermat theorem puzzled Mathematicians and the race to solve it gave rise to many new areas of Mathematics. The image shows a stamp in honour of Fermat and Wiles, and also some humour (yes, mathematicians laugh too) inspired by this fascinating theorem

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