One day I was sitting in my study trying hard to come up with an idea to
write an article on. I knew it had to be on Fermat's theorem. This theorem was
so very peculiar because, it was found written in the small top-left margin of
his notebook. without a proof, without any preceding thought.It was written as a
matter of fact.Great mathematicians have since tried their lives out in proving
the theorem or maybe disproving it, without success.
Maybe I was trying too hard, or maybe i was disillusioned by exhaustion, but i saw a shiny warp in my garden , just outside the window. I could not resist so i went near it and before i knew through it, and literally before i knew, i came out of it, knowing not what just happened. I looked in front of me and saw an old house.I had learnt owing
to my last article in the paper on medieval architecture that this house was about 400 years old.I entered the house, to find out more. ya i am inquisitive,
if you haven't figured out yet.
Inside the house, it was creepy, as if no one lived there. For once i believed that i did not actually time travel but teleported just to a wrecked abandoned house. Then i saw an almost balding man sitting on his table dozing off into his thoughts.I could not see his face because he had covered it with his fingers. After another 5 minutes, while I was debating whether to wake him up, he woke up with a sudden inhalation and started writing into his notebook.Then , when he was done, he looked at me, and was
surprised, not because i wore clothes of another generation but because, he saw
a man in his house.Immediately I recognized that he was the great Pierre de
Fermat. After the initial hello-how are yous and other mechanisms for
ice-breaking, we started talking.We mixed up well because we shared a interest -
After only one hour he showed me his notebook with the recent
thought he had come up with . I read it and knew that I had read it before ...in
college. Then I remembered about how fun it would be to ask Mr. Fermat how he
came up with the idea of the Fermat's principle.So I asked him. He did not know
what principle I was talking about because obviously it was named that after he
died. So I explained him that the principle told that x to the power n plus y to
the power n is equal to z to the power n for integer values of x,y and z was
never possible for any value of n greater than 2.He looked interested and after
a moment, took the notebook from me and wrote it down in the margin of his
After that I had coffee, meal, talked more, exchanged goodbyes,
entered the warp in his garden , exited out of my garden's warp, reached my
study and wrote this article.I wanted a punchline to end the article so I wrote:
"If I learnt the Fermat's principle from the notebook's margin which was written
because I told it to Mr. Fermat. Where did the principle come from? I mean who
thought about it?"
The most common and the most skeptical explanation to this paradox till now is Time travel is not possible.
The second most common but most elegant explanation to this paradox till now is (as pointed out by Shamukh in the comments) the theory of parallel universe. It goes as follows.
The action of my telling the theorem to ermat just broke me out of the original universe into a parallel universe, in which Fermat did not come up with the thought.The source of the thought is in another universe altogether ( the original one).
Anyways I wanted to come up with another explanation. It starts with how western thought considers time as linear from big bang to big crunch, from zero to infinity. On the other hand the eastern thought has always been cyclic.. Like birth , life, death, something here, rebirth..and the cycle continues.
So there can be a circular interpretation to this. In fact what I am proposing is there is never a single point from where the idea is generated. Never Eureka. Any idea is always ivolving.
To explain it better lets go back to fermat's theorem. When I first learnt about the theorem. The theorem was not exactly for me what it was for Fermat. He had his interpretation based on his environment and his resevoir of thought. I on the other hand perceive the theorem from my point of view. So though there is similarity, the fermat's theorem is quite different for me then it was for Mr. Fermat.
Now going into recent past (400 years) and telling him the theorem may be weird because of any of the above reasons. I am hypothesising , consider a time loop of thousands of years.It is impossible for us ,'using logic', to extrapolate what would be the environment for Fermat's theorem then.Maybe someone would come up with a very simple to understand proof of the theorem. maybe it will then become a theorem which is as obvious as say 2+2 makes 4. Then people would forget , rather stop bothering about the proof. then in thousand years when several such theorems and principles have been discovered, Fermat's theorem would die.Not completely though. It will always remain as part of some or the other process it had caused .Now when the jumbo time cycle starts to repeat again. It will reach a point of Fermat sitting on his desk and thinking. While his mind is going on full throttle, maybe some remaining ansh (a part) of the theorem comes to his mind. When he adds his perspective to it, it is again reborn as the Fermat's principle.
This is the very basic idea of what I am thinking. I will think about it more and write it down later.