I had seen the old man quite a few times before the day in question. He’d walk in at a brisk pace, purposefully, and make a beeline for the section devoted to number theory. This in itself was quite remarkable. Half the people who visited the math wing were tourists who invariably sat down with the largest coffee table book on cosmology they could find, and most of the rest were the physics bunch — that side of the aisle lacked sufficient seating for their lot. A further minority comprised of those such as myself — dabbling in algebra, analysis and topology. A taker for number theory was the rarest of sightings.
It is possible to reasonably correlate people’s seating preferences with the purpose of their visit – with caveats obviously applying to the availability of their choices. The casual folk tended to pick the ones near the exit, for a speedy escape when they got tired of looking at pictures of nebulae. The laptop fiends optimised their proximity to the few charging outlets available. The crammers went for the so called study booths for a distraction free experience. I went for the most isolated seat that offered a view of the skyline and the eventual sunset.
Our subject was most unusual in this respect too. Armed with his few chosen tomes, he would scout for compatible company: by their profile and by looking over their shoulders. Compatible company referring to people who were likely to be interested in math and preferably not too engrossed in what they were doing. (The old gent loved to hold energetic, extended discussions with his companions, which made him the bane of the librarians.) I satisfied both requirements admirably, but it was to be a while before it was my turn.
I was done with math for that day, ’twas one of those days. My idle eye caught him scoping for his books, and my mind wandered into a conjectural haze. Was he a professor? (his wizened countenance suited this hypothesis.) If so, what sort of collection did his department have that he had to travel to a public library to satisfy his bookish needs? Or was the reading just a ruse to find willing students to talk to? Did his college have a dearth of that too? (this, unfortunately is more than likely to be true.) Could he, most graciously, provide me with a Letter of Recommendation? (this was that period of my life when I dreamed of Letters of Recommendation like Swami dreamed of his elysian cycle wheel.)
I was soon to resolve this mystery, for he was making his way towards me, having been rebuffed by a most studious girl, who (I later discovered) was a physics student.
“Have we talked before? Would you mind if I take a seat?” I assured him that I had dedicated the rest of my day to the art of navel gazing. I introduced myself. His face lit up when he saw the topology books in front of me. “Tell me, do you like number theory?” I replied that I did, but deeply regretted that I never got the chance to study it in an academic setting.
“Do you know Fermat’s Last Theorem?”
I cannot recall how I responded to this.
“There are others studying here. And the librarian here is not too fond of me. Let us take this discussion elsewhere.” And so we went to the other side of the floor, which overlooked a distant sea.
He had been a bank manager, I learned. A student of mathematics in the sixties, circumstances had steered him away from academia. But after retirement, finding too much time on his hands, he went back to mathematics: this time as a hobby. He was completely taken with Fermat’s Last, which had been briefly mentioned as an unsolved problem in a book he was reading. For five years he had toiled away at the problem, before someone told him that it had been settled almost a decade ago. Wiles’ proof he found to be intimidating and disappointing. “Fermat, was a lawyer. The statement of the theorem is instantly comprehensible. I am convinced that there has to be a proof that reflects this elegance and simplicity.” And thus, he had worked at his own elementary proof for the past decade.
I was quite impressed by his enthusiasm and determination. I was also thrown into a fit of melancholia. A misguided obsession with rigour had exterminated a schoolboy-like aspect in me: I had learnt to venerate the masters and their words. Rightly so, but perhaps a touch too much. I was increasingly convinced that I could, at best, only appreciate and understand mathematics – creation seemed a few ballgames out of my league.
And here was an old man, an amateur, it was just him versus an old problem, and he believed that he could do it. Fermat himself would have approved of him. While it would have been premature or even wrong to sound a eulogy to the spirit of the amateur mathematician, I could certainly see that the spirit had died in me. (Not insinuating that I had turned professional. Someday, I shall, hopefully.)
He spent the better part of the next hour explaining the historical lore of the problem, the innumerable stalwarts who had turned their attention to it, the crucial breakthroughs and the false victories. It was like being waylaid by Simon Singh. I could totally see an uninterested person muttering softly, “Unhand me, [you] grey beard loon!”. But I was enjoying it immensely.
He then offered to show me his proof. A personal diary was opened, stuffed with scraps of paper containing hand done calculations. His proof lay obfuscated within that book and was intelligible only to himself.
He began.
I must confess that I did not understand a whit of it. The notation was non-standard to say the least (“I have named these variables F,E,R,M,A and T; it’s my small way of paying homage to the great mathematician.”). Assumptions were lathered on unabashedly, new variables were introduced at the drop of a hat. He did attempt to explain a few of the assumptions in the beginning; further in they were dispensed with appeals to reasonableness/obviousness. I was aware that I could be really dense at times, so I bore it and persisted — and soon lost the thread entirely. The proof seemed to lack definitive purpose or direction, there were pages upon pages of mind-numbing manipulations. Several minutes later, I was asked if I understood what a particular line implied. My bewildered look and shake of the head must have disappointed him terribly, for he grew anguished and cried,
“That means the equation has tilted! It can have no solutions!”
I had no clue what a tilted equation was.
He had gotten in touch with a reputed, local, mathematician who granted him audience a couple of times. “Professor Bouillablasè is the top number theorist in this country. He was kind enough to guide me a bit, informally. He doesn’t respond to my mails or calls nowadays — he’s a very busy man. I must respect that.”
He had submitted an older version of his paper to a number of journals worldwide — and had received a response from just one, from Japan. Their reply was terse, amounting to just a sentence, but it had filled him with a great admiration for the Japanese. “In one single sentence, they told me what my approach was missing. I have since worked on it, and I think I have fixed it.”
“I am not a crank.”, he informed me sternly,“You do know who a crank is, right?” I nodded and smiled, having been caught unawares — the word had been niggling away at the back of my head. “If there is an error in my work, I would like to be told about it, so that I can fix it.” And so I was invited to critique his proof. I informed him that I was in no position to check the veracity of his work; but maybe perhaps he ought to re-check his assumptions so that he may not have proven the theorem for a smaller set. I soon got carried away and lectured to him at length about journals’ notorious obsession with pedantry, and about LaTeX and arXiv and blogging. I told him to post his problem to Stack Exchange, insisting that the Internet was full of people who would be willing to knock holes in his proof, for free.
He seemed apprehensive of the last bit – “What if someone steals my proof?”
It was nearly closing time, and he was in a hurry to get home. We had said our goodbyes, and he’d already turned around and left. I was picking up my stuff, ruminating on the day’s strange exchange, when I saw him coming back towards me. He asked me:
“Do you know why I hang around the library so often and discuss this problem with students?”
I turned and waited for an answer.
I was staring straight into his old cataract-tinged eyes, and I felt uncomfortable. His eyes betrayed his age, and a certain sadness.
He said: “I come here everyday so that I can talk to people about my proof. Sometimes they aren’t interested. Sometimes they are, despite not knowing rudimentary mathematics. It might even be that my proof is correct, and that I do not need to validate it.”
“But — “, he now tapped his breast, “ — the heart cannot bear to keep silent. The heart yearns for a ear to speak to, to share, and to participate. It is a human failing. And I can do nothing about it.” And saying so, he left.
I stood there transfixed, my hairs on end. His words stirred something within me – it resonated with something deep within, something I cannot pin down.
I felt a silent horror.
Perhaps you do not find this moment particularly disturbing, for my words do a shoddy job conveying that moment and the horror I felt.
Maybe if you had been there, & heard his exact words, staring into his old eyes.
Maybe if you had been me.