The Dream Proof

"I dreamt it."

"You mean to say you actually saw the proof in your dreams?"

"I cannot explain how, why and all those questions that you may have. But what you see in your hand is exactly what I saw in that dream."

Standing before me was one of the younger members of the staff. He had burst into my office that morning, looking as he had just got up from the bed. His clothes were a mess but what caught my eye was the look on his face, one that a child that has just taken its first step, horrified but excited at the same time.  And the reason for this lay in front of me.

"Now tell me again, slowly what this is all about. And please have a seat." I said, motioning to his right.

"Okay," he said, sitting down, and taking a deep breath, "I had been reading up on Number Theory as a possible area for my doctorate research, and I came across Fermat's last theorem. The more I read, the more I became intrigued by this simple looking theorem."

I nodded my head, understanding the amazement in his voice. Here was a simple, inconspicuous-looking theorem, written in the margin of a copy of Diophantus's Arithmetica, but it was this simplicity that had mathematicians from all across the world, as well as across time, stumped to say the least. For more than three centuries, mathematicians worldwide, both amateurs and professionals had tried to put forward a proof, only to be disappointed. Only recently had a proof withstood the scrutiny of the mathematical society at large, a proof that was more than a hundred pages long, filled with peculiar symbols and notations of various theories, making it difficult to grasp for even seasoned mathematicians in the first few reads. But it was interesting to note that many of the techniques used in the proof had not been developed when Fermat had jotted down the theorem in the margin.

Fermat had once remarked that he had a truly remarkable proof which this margin is too small to contain. And statements like this get us mathematicians all worked up. And this young man standing before me had handed me a notebook in which he claimed was a proof, a much simpler than that of Wiles, one that he had dreamt up of.

"… and I woke up suddenly," his voice drifted in slowly, waking me up from my thoughts, "in the middle of the night, and wrote in the notebook, being as accurate as I could, what I had seen in the dream. Since then, I have been trying to decipher what on Earth I had written, but I could make head or tail of. That's why I brought it to you hoping you could help with it."

"I can't promise you anything. I hope you know how crazy it all sounds to me. All the same, I will have a look at it, and tell you later. Now if you would excuse me, I have a class to take." I said standing up, putting the notebook in the drawer. His eyes followed my hand, and it seemed for a moment he would protest, but he thought better of it.
Flushed, he got up, groping for words, "I … well… just… Just get back to me as soon you are finished sir."

The whole day, the idea of the notebook and the possibility of its contents were always at the back of my mind. There was a huge likelihood that it would have nothing but unclear scratching of a half-asleep man, but somehow I just wanted to be sure. So, as soon as the day ended, I raced back to my office and turned the key.

I opened my drawer to see the notebook sitting smugly as if it knew what it had inside of it and was sure of it. My hands trembled as I opened it, my fingers tracing the letters scrawled on the top of the first page,



if x^n + y^n = z^n , and n>2 then x,y,z ∉ Z



What followed for the next few pages were barely recognizable equations, half written and all jumbled up. I took up a pen and paper and got to work.

After nearly eight hours of trying to work out what was written in the notebook; I got up and went to the window, numb. Incredible! The proof he had given was simply incredible! The very fact that it seemed to prove the theorem for all the positive integers in a few pages of an old notebook was mind numbing. And to top it all off was the dubious fact that it had come to him in a dream. Excitement was rising like bile in my throat. Here I was, holding a proof that would blow away the community. But I had to be sure.

It had been almost a month from that fateful morning, when he knocked at my door.  I had reworked the theorem from scratch for what seemed the umpteenth time, always arriving at the same answer. Deciding that I needed fresh eyes on these I had sent it to an old and trusted friend, who drove up in the middle of the night, flabbergasted at the pages in his hands. I knew now what need be done.

"As you can see, by doing this, we can finally prove Fermat's Last Theorem." I turned around to a standing ovation, with the claps resounding in the auditorium. The Chairman of the Council leapt up to the stage, his face flushed from the excitement, shouting to be heard over the din, "Well done my boy! Well done!" The ovation continued for a few minutes more, and all I could do was stand there, with the board behind me filled with equations upon equations, proving the theorem. I bowed once more, trying to hide the joy that seemed to radiate from my face.  The Chairman took my arm and guided me to the podium.

Silence soon reigned over the hall once more; as the mathematicians from around the world sat down to hear the Chairman speak. But one lone figure kept standing up, waiting for what it seemed the right moment.

"FRAUD!"

A hush fell over the crowd. You could almost hear the ticking of the big clock on the side wall of the hall.

"You have something to say, young man?" asked the Chairman, clearly surprised at this sudden declaration.

"I do! He has stolen my work!" shouted the figure, hoarsely.

"Your work?" asked the chairman, glancing at me, his eyes clueless. I leaned forward into the mike, trying to keep my face straight. "And then he would say he dreamt about the theorem. "

Laughter erupted in the crowd. Many turned around to look back at the figure, who seemed to be at a loss for words. He came suddenly to life, as if he had decided something.

"Yes! I did dream about the proof. THIS IS MY PROOF! YOU STOLE IT FROM ME!"

The Chairman looked towards me, with a incredulous look in his eyes. I shrugged and muttered to him, "Lucky guess. He is surely a lunatic, dreaming about a proof? Come on!"
The Chairman seemed satisfied, for he motioned to the security head to escort the figure outside. They dragged the still screaming figure of my junior staff member out of the door, and silence still regained in the hall.

"I guess we all needed a little bit of entertainment tonight. Anyway, let's not dwell on that right now. Join me in congratulating our distinguished member for this great achievement!" One more time that night, the hall erupted in claps.

Based on a dream I had.
(Yes. I have pretty weird dreams.)