Wednesday, August 17, 2011

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.)

Thursday, June 23, 2011

प्रिय भगवन

प्रिय भगवन,

आशा हैं ऊपर सब खैरियत हैं। ओसामा का तबादला हो गया धरती से चंद दिन पहले। अमरीका वालो ने उन्हे आने-जाने में काफी मदद की। बड़े भले लोग हैं ये अमरीकी। ई-फोन बना कर बड़ा भला किया इन लोगो ने काला बाज़ारीयो का। और तो और हर देश के निजि मामलों को अपना बना लेते हैं, दुख-दर्द बाटने मे विशवास रखते हैं।

वैसे सुना है, विश्व का विनाश होने वाला हैं कुछ दिनों में? बढ़िया है। आपने तो अच्छा-खासा प्लान कर रखा होगा, क्यों? बात भी सही है, कोई एक दो दिन का काम थोड़े ना है। समय लगता है, पर सोच और हिम्मत से काम ज़रुर सम्पूर्ण होगा। मेहनत करने वाले को भगवान... खैर छोड़िये इन सब बातों को। बुरा ना मानिये तो फिर आप से एक दरख्वासत है। क्या इस विनाश का पोस्टपोनमेंट पॉसिबल है?

बात दरअसल यह है, कि, अगर विनाश कुछ सात-आठ महीने के लिए पोस्टपोन हो जाता है तो फिर मैं ज़रा इंजिनियर बन जाऊगां। डिग्री हाथ मे आएगी तो फिर अच्छा लगेगा। लगेगा की जो कमर तोड़ मेहनत की है उसका फल मिल गया है। रात रात भर जाग कर मूवी देखना, दिन भर क्लास मे सोकर थक जाना, बहुत मेहनत का काम है ये इंजिनियरिंग। धरती तबाह हो गई तो बुरा लगेगा। तब तक तो लोकपाल बिल पर बहस खत्म हो जाएगी, अगर आपने चाहा तो।

देख लीजीएगा। कुछ दिनों की ही तो बात हैं, कौनसा कोई बॉस है, आपको, जो डेडलाइन की चिंता हो आपको। रात को चार बार बिजली कड़का दिजीएगा, पता चल जाएगा ये पत्र आप को मिल गया।

आपका भक्त,
प्रशांत





Tuesday, May 24, 2011

The Man Who Couldn't Dream

He couldn't dream.

He could dream per se, day-dream about his job, his future life, his girlfriend, and all that but ever since his crash he was unable to dream in his sleep. And that to him, it was as if someone had cut off a vital part of him. Before the fateful night of the car crash, almost two years ago, he had a very active dream-life. Monsters leapt out from unknown places, people whom he had met only once would come into his dreams and play havoc.

But all that was missing now. No more going to bed and waking up in a strange wondrous land, beyond his wildest imagination. He had tried everything. From holy men who had been sitting in a lotus position for the last twenty years, to herbs that promised to renew his dreams, to weird postures during sleeping, he had tried it all. But none of them worked. Something was missing inside him and he couldn't get it back.

Dejected, he turned to drinking. Day after day, bottle after bottle, he tried to drown himself. One day, he was out drinking at his favorite haunt just outside the city, which eerily smelled just like his old house. He was at his fourth bottle, when a strange man approached him.

"I believe you have been looking for a cure for your problem."

The stranger had a kind of an aura around him, more attenuated by the white clothes the stranger wore. Stung both by the stranger's sudden appearance and the bottles he had downed, he wordlessly watched as the stranger down on the opposite seat.

Grappling for a minute, he tried to find the words. "No one can cure me! No one! Leave me alone."

"I can."

The stranger simply leaned forward and touched him on the forehead with his index finger. A strange feeling emitted from that focal point in his body and spread all over. His fingers tingled and he fainted.

When he came around, the stranger was gone. Flinging a wad of notes onto the table, he walked over to his car, deep in thought. He tried to find words to express what was going on inside him, but no matter how hard he tried, he just couldn't.
That night, he dreamt.

For the first time in two years, he finally dreamt.

The dream was a weird one. He was on a white bed, and white walls, lying there as if asleep. He tried to move his arm, but all he could move was a finger, barely lifting it.

"This particular patient," he said, pointing to bed, behind him ", has been in our care for the last two years. He suffered a near-fatal accident that reduced him to a comatose state, with a GCS of one. I wan-", the doctor was cut short as one of interns yelled, "His finger! It's moving!"

The senior doctor, annoyed at this intrusion, turned around to see just in time to see the finger move. In the commotion that followed, no one saw the man dressed in white leave.

Tuesday, May 17, 2011

She said yes.


She said yes.

Not exactly said it, but nodded her head from across the room in affirmation.

I brushed off a tear, as I took out an old engraved case from the drawer in my desk. It had been my father's, and his father's before that. My hands traced the wooden carving on the top of the case, intricate yet subtle, work of an artist long forgotten. The levers creaked as I pulled back the lid, revealing what lay inside. Exhaling deeply, I picked the object inside. I had the habit of keeping it ready for emergencies, but not once had it entered my mind that I would have to use it.

Once again I looked at her, standing there, across the room, in her favorite pink dress, one I had given her on her tenth birthday. She once had told me that this was her favorite dress, and she would wear it almost every day after school. The color had almost faded now, and the ribbon almost frayed at the end, but still, now it seemed that it was radiating some kind of glow.

"I love you," I said, my voice slowly cracking.

She just smiled back.

It was this smile that had captivated me over all this years. I would jump and dance around just to have her smile. She had her mother's eyes, big brown eyes that would light up whenever she saw me. Ever since her mother had died, it was as if she had forgotten how to smile. It was on rare occasion that she would tilt her head, and give a little smile, her eyes twitching on the corners.

A tear slowly rolled down her cheek.

Even before, I just couldn't see her cry. Every time those beautiful eyes watered up, I would do anything just to have her happy. I once had painted my entire face with black paint and made faces at her all day long until she smiled.

"Don't worry baby, Daddy's coming," I said, unable to stop the tears that were now falling down my cheeks.

I slowly brought the gun to my temple, and closed my eyes. Just before my eyes closed, I saw her disappear slowly, as if smoke was being swept away by a draft of wind. I pulled the trigger and a strong white light flashed in the front of my eyes, and then there was nothing.