Not A Machine

It is always like this. The moment the man stands on the podium to present the results of his research in front of the other researchers of the world, the ambience of the lecture hall is transformed. Today is no exception. His lecture means an exhilarating journey to an undiscovered and mysterious island of mathematics. The mathematicians stare at him in awe. And the man effortlessly navigates one turn after another of the labyrinth to arrive at the desired conclusion, like a skilled footballer charging through the fierce defense of the opposition towards the goalpost. His amazing adventure began with his ingenuous proof of Bertrand’s conjecture. By offering a creative proof of this hypothesis, he announced his powerful arrival in the world of mathematics. The connoisseurs of mathematics got a fresh taste of his calibre at the very first proof. He followed up with other valuable contributions, especially in number theory, so much so that the society of intellectuals understood that he belonged to a rare breed of mathematicians.

That was the beginning—and now, even after crossing the threshold of 60, the man’s creativity has not ebbed. Not just for the newcomers; he is a source of inspiration even for the veteran mathematicians. ‘No mathematician should ever allow himself to forget,’ Hardy, a renowned character in the world of mathematics, had once pronounced in his book A Mathematician’s Apology, ‘that mathematics, more than any other art or science, is a young man’s game…I do not know an instance of a major mathematical advance initiated by a man past 50.’ Mathematicians, like me, have memorized each and every word of Hardy’s dictum. And so far, this comment has been pushing all the mathematicians above the age of 50 into a bottomless well of despair. When Hardy first met him, he was in the prime of his youth. If Hardy had been alive today, he would have said that this mathematician is a fascinating counter example of his famous remark.

Whenever we shower him with praise for his immaculate proofs, he just says that there is a book with the Supreme Fascist God, and the beautiful proofs of mathematics are all documented on its pages. Apparently, there were a few times when he had the opportunity to glimpse some of the pages of the book. He says, ‘Whether you believe in God or not, that is not important, but do believe in the book.’

The blackboard had been filled with his handwriting by then. His familiar handwriting—some of the letters and numbers tilting left, some completely vertical, and some others inclined to the right. The lines didn’t have a particular shape—one was straight, and the other one falling to the right. I sometimes felt as if a certain line at the bottom would storm at the one above for illegally occupying its space! The man is restless because new thoughts are always knocking on his brain, and probably this is the reason for his handwriting being the way it is. Of course, the man is not skilled at any kind of mundane day-to-day tasks. He can’t even prepare a cup of coffee, let alone cook. On the other hand, he is fond of coffee, so much so that he often says: ‘A mathematician is a machine for turning coffee into theorems.’ He once admitted that he didn’t even know how to apply butter over his bread. Once while studying in England he had to have buttered toast with his friends; being embarrassed, he had to admit he didn’t know how to apply butter to toast. He was 21 then! And whenever I think of the Chaplinian manner with which he entered the scene today, I can’t help but laugh. Mathematicians from all over the world have come to listen to his lecture. The new mathematicians are excited to catch a glimpse of him from up close. He arrived at the university by car, and when he stepped out, to our small horror, we discovered that one of his shoelaces was undone. If the other foot happened to land on the undone lace, there was high probability of the sexagenarian tumbling down and landing flat on his face. A young mathematician pointed his attention towards it, thinking he would tie the shoelace himself. But tying shoelaces is not easy like proving mathematical theorems! So, abandoning his natural walk, he limped his way towards me and pleaded, ‘Please tie my shoelace!’ Taken aback in front of the crowd of mathematicians, I hid myself in the throng. He charged at someone else this time.

That was the dramatic entry of the cynosure of today’s seminar.

He is like this. It is as if he has understood nothing except mathematics. The numbers are more melodious than Beethoven’s ninth symphony for him. If someone asks him, ‘Why are the numbers beautiful?’ he would counter, ‘Tell me, why is Beethoven’s ninth symphony beautiful? If you can’t appreciate it yourself, no one else can explain and make you appreciate it. I know numbers are beautiful—if numbers are not beautiful, nothing else can be either.’ This man of mathematics feels extremely uneasy with nonmathematicians. In those situations, his condition resembles that of a fish scooped out from water. He starts yawning if the topic of discussion of a get-together is anything but mathematics; in fact he tends to fall asleep. For him the non-mathematicians are ‘trivial beings’, and he calls children ‘epsilons’ in the mathematical language. The entire world is full of mathematics for him.

The man and his mathematics are equally attractive to me. A thrilling character like him is rare in the history of mathematics. My relationship with him is close. Naturally, the reason is mathematics—it is the only recource to be close to him. No other matter can be discussed with him—anything else is in his own words ‘illegal thinking!’ It is only because of my own curiosity that I have come to know a few things about his life.

So—born in Hungary, his family was Jewish, he was pampered by his mother because his elder sisters died of scarlet fever, he was sharp in mathematics from an early age, etc.

After the First World War, Hungary’s political climate was not amenable. A few days of democratic governance was succeeded by the fascist regime of Bela Kun. Subsequently, Mikolos Horthy came to power after overthrowing Bela Kun. But Horthy was even more aggressive and fascist than his predecessor. Because his former ruler Bela Kun was Jewish, Horthy assumed that Jews were against him. So, he turned oppressive towards them. The Jews were stripped of their rights to study at a university. But this particular mathematician was successful in a national examination and was exempted from the prohibition. Because of this repressive behaviour, his heart was filled with disgust for the fascists. Once, a co-worker showed him a kitten. He picked the kitten up onto his lap, but it scratched him. Immediately putting the cat down, he said, ‘Fascist cat.’ The co-worker protested, ‘How could a cat be a fascist?’ He replied, ‘If you were a rat you would have realized.’

Even though he did his PhD from Hungary, he was trying to move away from the fascist regime. He received a postdoctoral scholarship and took the opportunity to go to England. There he met Hardy and Ulam. Even after that he couldn’t return to Hungary due to Hitler’s growing influence. He proceeded to start his research at Princeton. While he was there, Hungary allied with Germany and as a result, America cut all communication with Hungary. Inevitably, he also lost all communication with his family in Hungary. After one year was over, the Princeton administration refused to extend his scholarship for more than six months. Feeling insulted, he immediately left Princeton. And thus began his life as a nomad. He started wandering from one university campus and conference to another.

Towards the end of the Second World War, Russia liberated Hungary. Only then he received the news that most of his relatives had died in Auschwitz, and his father had also died of a heart-attack. He returned to Hungary and frequently travelled to England and America. But there came a time when America refused to give him an entry visa, and he started living in Israel. The mathematicians appealed to the American government. He once joked, ‘The American government is adamant about two matters—they will neither allow red China to enter the United Nations, nor me into the United States of America.’ At last, the prohibition against him ended, and he was able to move around freely.

Always preoccupied with mathematics, the man didn’t even marry. In fact, he ignored the advice of his well-wishers and didn’t accept any tenured position. He manages his affairs with the money he receives for research. Manages barely—as he doesn’t even have a house of his own. He wanders around, staying for one or two months at his colleagues’ homes. His life’s motto has become, ‘another roof, another proof.’ Whose home he will invite himself to as a guest and for how long—one month or two—doesn’t depend on the host’s but on his own whims. It has become an unwritten rule among his colleagues to offer him generous hospitality, whenever he lands in somebody’s home. Once he dumped his suitcases on the floor upon arriving at my house and directly made for the phone. I heard him telling someone, ‘Listen, I have arrived at Wilf’s house, you can also come.’ I didn’t know whether to laugh or cry. There was no end to the problems created by him—he was not even accustomed to the use of household items. He would get ketchup from the fridge, and there would be a blood bath on the floor all the way from the fridge to the dining table. By the time he left, the bathroom door lock, shower, etc. had to be repaired by the handyman. Still, one can’t be upset with him. During the span of those one or two months that he spends with us, he reveals to us newer ways of research, many of which we have never imagined could exist. The man is unbelievably talented. I remember one incident narrated by George Purdy at a seminar. The mathematicians were having coffee during the break between the two sessions. He came, looked at the writings on the board and asked Purdy, ‘What are these?’ That was the problem of functional analysis. A few moments earlier two researchers had offered a 32-page-long solution to the problem, and thus they were bloated with pride. He looked askance at the board for a few moments and asked Purdy the meanings of the signs and symbols used there. After that he effortlessly solved the problem within two lines. Purdy was astonished—as if he had seen magic.

Such a man with so much unique talent is completely naive in matters of everyday life. His chief assistant Graham cracks jokes with us—apparently all his cheques are signed and deposited in the bank by Graham on his behalf. Graham has been doing it for a long time and if someday he himself signs instead of Graham, then the bank would return the cheque, suspecting signature forgery!

‘Wilf, are you thinking of something else? No-no-no illegal thinking.’ And the audience laughed.

It startled me. I know that he doesn’t like absentmindedness. Sometimes he seats his co-researchers at various desks in a room and keeps them busy with mathematical research questions while making his move in a chess game that he plays at another desk with a chess player. But if he senses somebody’s attention divert, he will shout, ‘No-no-no illegal thinking.’ It has become somewhat of a quirk. The tone he pronounces the sentence in, the expression of that exact moment—we know everything by heart. The sentence elicits acute humour even in serious situations.

I humbly let him know that I have been listening to his lecture with utmost concentration. It was an utter lie. Actually, he has already explained to me the problem on which he was delivering his lecture today. Therefore, I could indulge in the luxury of inattentiveness like a school student. Otherwise, was there any place left for anything else other than mathematics to wriggle in our brains? Probably that was why the amusing anecdotes of a mathematician like him provide our busy brains with some relief. There were many anecdotes to his credit that all of us were familiar with. Of course, he didn’t know about them. His stories spread without his knowledge. If anything amusing happened in front of our eyes, we narrated it to others with full enthusiasm. Whatever he did, he did seriously—most likely not to elicit laughter—but he was unaware of the fact that his naivety outside the world of mathematics was providing someone with so much comic relief.

‘Wilf! Wilf!’

I looked at the board.

‘No-no-no illegal thinking.’

And the audience laughed. He probably caught me looking elsewhere. Oh, whatever it is, at least he remembers my surname! Although I won’t nurture the false hope that he remembers my name. Even the most optimistic ones did not dare keep such an inordinate hope. He called us all by our surnames. He called only one person by name in the entire world—and that unfortunate soul is Tom Trotter. He called Tom, Bill! However, it is our misfortune that in spite of all this, he remembered all our phone numbers without any mistake. He knew our addresses too, to be our guest, obviously. Peter Winkler was very sad—apparently he researched with him for 20 years; still the poor fellow didn’t expect him to know his name. I consoled him, ‘You are at least luckier than Mendelson.’ He replied with disbelief, ‘How?’ and I narrated the story to him with enthusiasm—Once, upon meeting a mathematician he asked,

‘Where are you from?’

‘Vancouver,’ the mathematician replied with an awkward smile.

‘Oh, then you must know my friend Elliott Mendelson!’ he said.

The mathematician promptly replied. ‘Yes. It is indeed me who is your unfortunate friend, Elliott Mendelson!’

Peter was convinced after listening to the story and measuring out his misfortunes.

It has become like this. The numbers are his friends and relatives. As if the numbers have sucked up and exhausted all of his emotions and feelings like a vacuum pump. He doesn’t feel comfortable talking about anything else other than mathematics with people. He has become detached from the world outside mathematics. He is unable to connect with anybody with un-mathematical things. He has really become a machine producing the proofs of mathematical theorems—he has become a machine.

The conference hall roared with the sound of applause. Just then, very elegantly he presented another new proof of a theorem without any hiccups. His lecture had come to an end.

One by one, people moved towards the dining hall. I also headed in that direction.

***

It was as if the nerves of the mathematicians had come under tremendous strain after staying in the world of mathematics for two hours. To get rid of the stress, the mathematicians huddled up in groups of three or four and immersed themselves in energetic conversation while holding plates of food in their hands. And I happened to notice that the topic of discussion of all the groups was him. The discussions were engrossing. Each conversation was animated with various juicy and sometimes unconfirmed anecdotes about him. The entire dining hall resounded with gales of laughter. I also joined a group. The conversation was in full swing there. Hoffman was enthusiastically recounting an incident I had not heard before.

Once he was a guest with someone in New Jersey. While he was having breakfast with the host, there was the mention of a mathematician from California. Suddenly, he recalled that he needed to discuss something with this mathematician regarding a theorem. Immediately he got up from the dining table and moved towards the telephone. The horrified host instantaneously called out to prevent him, ‘It’s only five o’clock there—morning has not even dawned properly. The poor fellow must still be in bed.’ At this, apparently he replied very seriously, ‘That means it is sure that I will reach him on the phone.’

The four of us burst out laughing.

Then George said—

Once he had to undergo an eye surgery for cataract. He declared to the doctors—only one of his eyes would be operated on, so he would read books of mathematics with his other eye. The doctors were puzzled. At last, after a lot of searching they produced before him a local mathematician. During the operation he continued with the discussion of mathematics simultaneously with the miserable mathematician.

We came out after finishing our meals amidst fun and moved towards the conference building. There in the area in between we witnessed him coming pensively, probably to have his meal. We came face to face and he stopped. He whispered very slowly—’Herbert!’

It made me laugh. He hadn’t called me by my surname ‘Wilf,’ as he usually did. He called me by my name—that too without any error! I readied myself for another anecdote. Such anecdotes are the ones which keep our hearts jovial. I replied with great hope—’What happened, Paul?’

‘Can I tell you something?’

It was as if he was asking for permission, which was against his nature. There was no instance till now of him waiting for somebody’s wish or permission to talk about mathematics. I had just finished my lunch, and my body and brain were not ready yet for mathematics. I was merely a human—not a machine like him for proving mathematical theorems! I tried to hide my annoyance with a thin smile and said, ‘Tell me.’

He hesitated a bit. After some time he said very slowly, ‘Herbert! My heart is heavy today!’

I recalled that he had been much occupied with a complicated problem of number theory. The problem had been almost solved but last night, someone found a flaw in the solution. I consoled him that there was no reason to be upset or despair over such a trivial issue for a mathematician of his calibre. That was a part of our lives as mathematicians, we were constantly striving towards perfecting the proofs—

‘No—no, Herbert. I am feeling low because of something else. Feeling really low.’

This made me chuckle. Something else? That meant there was little room left for additional things in his brain crowded by numbers! And what was even funnier was the thought that for him to feel heavy or low, his heart was more than the normal blood-pumping machine and carried emotions, which were buried somewhere under all the numbers.

I smiled and asked, ‘Why—what happened, Paul?’

He said with an uncharacteristic tone of resignation, ‘I am feeling very lonely, Herbert.’

I reminded him that the atmosphere at the university was one of celebration. The whole place was teeming with the 200 mathematicians from all over the world. If he wished, he could spend whole days discussing different aspects of research with them. After which our roofs are always there for his various proofs. ‘No—no, Herbert. It is something else, something else.’ It was as if he was unable to make up his mind and express himself. I too couldn’t understand. After some time he again said, like an exhausted person,

‘I feel very lonely, Herbert.’

I kept staring at his eyes amidst my confusion, as if his face was pale from the fatigue of travelling a long distance. He said with a heavy voice,

‘I am missing my mother an awful lot today, Herbert.’

I felt a tremendous thrust on my chest and looked away from his eyes. I recalled—his mother followed him like a shadow, taking care of him. She did everything for him, right from tying his shoelaces to applying butter on his bread. Probably because her other children died untimely deaths, his mother pampered him like a baby. But it had been five years now, since his mother had died of an ulcer.

I said, discomfited, ‘But, Paul, it has been five years since your mother passed away!’

‘You are right; it has been five years. I often miss Anya; today, more so.’

A few uncomfortable moments of silence passed. He said indistinctly,

‘Under that—that tree.’

With one of his weak and curved fingers he tried to point towards the lonely pine tree in front of the conference hall. I looked at him, unable to understand what he was saying. He answered very shyly, like a teenager newly in love,

‘I met her for the first time.’ After waiting for a bit he said,

‘But she left me one day. Can anyone actually stay with me, Herbert?’

I felt my heart wring. As if, my chest was pressed down with a bundle of unknown something. He continued on with his ruminations like a soliloquy, forgetting my presence. ‘Whenever I was studying, Anya often used to come near me hesitantly and say, “Paul—someone else—another girl.” ’

I felt I would also hold his hands and say, ‘Why it didn’t happen, Paul; why not—some other girl!’

‘And I used to say to Anya, “No-no-no illegal thinking”—it became sort of a game towards the end—I study, Anya arrives and teases me—son, another girl! And I mock-scold her and say—No-no-no illegal thinking. I laugh; Anya laughs.’

I saw his face brighten with a child’s smile. And at the same time, I saw his eyes brimming with tears.

‘Fascist God. Fascist God.’

He soliloquized with a mumbled voice. And fell silent.

All that for only a short amount of time. Suddenly he regained his infinite strength like a wave—pulling out a handkerchief from his pocket and offering it to me he said with a smile,

‘Herbert, no-no-no illegal thinking.’

I could not smile at his quirk this time.

‘I have resolved the flaw from the proof this very morning; I will show you tonight.’

I realised tears had welled up at the corners of my eyes once I took the handkerchief offered by him in my hands. I felt like grabbing his hands and asking him—’Paul—no-no-no illegal thinking—at least for today!’

I saw him rushing away very busily. And I saw one of his shoelaces untied and dragging along the ground. If his other foot happened to land on the untied shoelace, there was a high probability of the sexagenarian tumbling down and the crowd of mathematicians heading towards the lecture hall bursting with laughter after being witness to the scene. I raised my right hand and with a shivering voice shouted—’Paul!’

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Illustration by Griselda Gabriele