A Universe of Sufficient Size

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A Universe of Sufficient Size Page 2

by Miriam Sved


  Ildiko and I were both taken aback, for different reasons, when we realised Tibor’s plan to help Pali. Ildi tried to talk him out of it. In my confusion, I stayed quiet.

  I have to reveal things in this account that a more respectable girl might take to her grave, so that you can see how things are, that I have never been an innocent. I am not a victim or a dupe and my motives are not pure. Nonetheless, I was shocked, really, when I found out what Tibor intended to do, passing his opportunity with this professor on to the man who was, I suppose, in some way his rival. And a different kind of shock: what if Tibor’s plan should work and carry Pali away? But I wouldn’t stand in the way of it as Ildiko tried to do. I could see too much sense in Tibor’s arguments about Pali. Tibor had always been very good, very altruistic, but none of us thought he was giving away his whole future, all the other opportunities that would open to him. He was active in both the mathematics and communist communities. He regularly sent his work out for publication. Whereas Pali … What, we thought, would become of Pali if we let him stay trapped in this box, this series of dead ends in our country? Ildiko would argue that he was perfectly safe and well where he was: his parents supported him financially and would continue to do so even if the dreaded war did come. They were probably wealthy enough to bribe the conscription board. And I did find it hard to imagine Pali being called up to fight. He is an intrepid, independent soul in his way, but so childlike. Ildiko once told me that his mother still tied his shoes for him. Surely the army did not recruit soldiers who could not tie their own shoes.

  So Ildiko’s arguments were true as far as they went, but they did not go all the way, and the other part of the story, the part that worried Tibor, was also true: that Pali, left here in our country, was too unfocused and unworldly to get his work out to the world. It would not have occurred to Pali to enter the competition that led the professor to Tibor. He never tried to publish anything; he wasn’t properly enrolled at the university and likely would not have received a diploma, although he used to attend every lecture. It was the sort of situation Tibor could not stand: even if he didn’t know and value Pali personally, it would go against his innate belief in progress, the idea of so much brilliance going wasted. Pali had always worked simultaneously on several different theories and extensions, mostly in number theory. Tibor sent the professor some interesting results about the Mersenne primes, which he credited to his brilliant but unrecognised friend. We did not tell Pali.

  And then we waited. The four of us – Tibor, Ildiko, Levi and I – nurturing this seedling of a plan, discussing how it might grow, where it might extend its limbs to take the light. It was all rather exciting to talk about, and with Pali’s regular tardiness it was not hard to find opportunities to discuss his future without him present.

  Tibor sent his reply not long before we heard the terrible news about Vienna. We did not know what it would mean for our professor. Were the citizens still able to work, travel, correspond with the outside world? Professor Voigt was not Jewish, clearly, but one heard such things about the Germans: that they were experiencing a kind of mass hysteria, they marched about the streets in perfect order and then descended without warning into violent frenzies like their ancient Teutonic forebears. I don’t know what news you got there; here we had reports that the Austrians actually welcomed the little psychopath, that they threw flowers at the Wehrmacht. And we heard nothing from the professor. A month, five weeks passed. We had almost resigned ourselves to the seedling withering away when, finally, Tibor received his reply. There was nothing in the perfectly civil letter about the German invasion – all appeared to be calm and normal. The professor had no objection to the direction in which Tibor had steered their correspondence. Tibor read to us from the letter, going back twice to a paragraph about arranging a meeting between the professor and Pali, whom he called our young scholar friend.

  ‘If our young scholar friend has any more such promising ideas like the ones you sent me, I might be able to speak with people. I have influential friends who might arrange a fellowship in America, perhaps even at the Institute for Advanced Study.’

  Well, we all lost our heads a little at that. Even cast out of the academic establishment, bits of the work being done at the institute have floated down to us, and of course we all saw Pali following in von Neumann’s footsteps. It was a dream.

  A dream on the other side of Vienna. The Anschluss, they called it, as though the little psychopath had just clipped Austria onto Germany like an extendable limb. Tibor, of course, was the first one to raise the practical problem: Pali could not go on his own. He would most likely pace directly into the path of a German tank while cogitating on his prime numbers, or at the very least pour soup on himself in the train dining car. He would mess it up.

  I should mention that the meeting at which we discussed these things followed on from one the day before at which I had covered myself in shame during a conversation about measure theory. It was not a topic with which I felt comfortable, but I had tried to bluff my way through and made a terrible hash of it and felt like a bigger blockhead than the worst of Ildiko’s pupils. It is possible that the humiliation of that previous day’s work made me snatch at this, a job I could actually do. I could get Pali to the train station. I could order for him in the dining car so he would avoid the disastrous soup. I could even tie his shoes for him if need be.

  ‘I’ll do it,’ I said. ‘I’ll go with him to Vienna.’

  Tibor looked at the side of my face for a minute. ‘It’s true that a man and woman travelling together might attract less attention than two men.’

  (You might notice: he did not say Jewish men.)

  Ildiko, glaring up at me from the ground, said, ‘You can’t, Eszti. I heard they are taking people straight off the street, just randomly, and locking them up.’

  (Not Jewish people.)

  She reached for the letter in Tibor’s lap and went on. ‘He says something about his links to the Hungarian University. Why don’t we wait? He is sure to come to Budapest eventually and we can meet with him here.’

  ‘It could be too late by then,’ I said, not sorry to have this slight resistance to push against, to demonstrate my nerve and commitment. ‘Any day now it could be too late. We can’t miss this chance.’ And I looked into the distance, staring into the impending war like a heroine from a Jókai novel, feeling only slightly absurd.

  It had the desired effect. ‘Brave girl,’ said Levi, his handsome face glowing with approval.

  ‘She is brave,’ said Tibor with great finality, as if he had known this about me all along. Perhaps it explained why he chose me.

  And at that moment I did feel truly brave. I felt that I could face the tanks and stare them down. A new sense of determination surged through me: I could become a revolutionary, start going to Tibor’s underground meetings.

  The feeling lasted perhaps thirty seconds. Ildiko started to say something else in protest, but Tibor interrupted her. ‘Let’s discuss the details of Vienna later. I have some new work I want to show you.’ He reached into his satchel and pulled out some pages. ‘It’s not much but maybe a slight extension on Littlewood and Hardy.’

  Ildiko took the top sheet and I watched her scan it, the worry on her face replaced by the calm and purpose of work. If I ever envied Ildiko it would not be for her looks or all her strength of character but for this: her gift, her easy entry to that other world. ‘This is interesting,’ she said. ‘You’ve added odd exponents to the Vinogradov lemma?’

  Levi, reading over Ildiko’s shoulder, said, ‘Can n be 0?’

  Ildi handed the paper to me with a small smile.

  I tried to focus. It was a problem of prime sets, I could see that much (I suppose it was Pali’s influence, we were all a little obsessed with the primes). Something about summing their squares. But beyond that the substance of it would not stay in one place for me. I was used to feeling two steps behind the
others and scrambling to keep up, but this was different. I found that I was still lost in the conversation about Vienna, and suddenly thinking of Papa at our dining table back in March, the day after the little psychopath marched his troops in. Papa had the newspaper open in front of his toast, and he was reading it with little grunts of disgust and shakes of his head. ‘Well, he has done it now,’ he said, as though the little psychopath were one of Papa’s men who would have to be called into the factory office for a dressing-down. More quietly he added, ‘Rothschild and Freud. If they are not immune, all the Jews will suffer.’ I remember wondering if he meant to include us in this assessment, and your reassuring existence floated briefly through my mind. My parents had discussed emigration once or twice, when business was very poor. But Mama frowned at him and he closed the paper without further discussion: she did not like to dwell on the nasty politics that went on elsewhere. I didn’t dwell on them either. Of course it was terrible news about Austria, but at that point it felt quite distant from us. For once there was comfort in the alliance between Horthy and Hitler: we would never be invaded. My mind turned back to whether the ice would hold another week and if we might get some skating on the lake in the park.

  It no longer felt distant that afternoon at the statue, after I had volunteered to go to Vienna. I thought of what Ildiko said: I heard they are taking people straight off the street. I had heard these stories too, and tales of random beatings, Jewish homes and businesses being vandalised.

  I don’t know if you learned, perhaps from my father, about what happened to me, to all of us, to make us leave the university. I find it difficult still to dwell on directly, but it is with me all the time. I know what people are capable of. What a fool I was to believe myself equal to tanks and heroics, even for a moment. To imagine that I could join Tibor’s movement. I was – I am – a coward.

  I think a tremor went through me then on the bench, and Tibor turned to me. ‘What do you think, Eszter?’ he said earnestly, as though my opinion might be the success or failure of his ideas.

  ‘Yes, interesting.’ I nodded, hoping to look like I was sunk deep in mathematical contemplation rather than fear.

  Luckily Levi jumped in. ‘Have you tried it for the even integers in base three?’

  I closed my eyes for a moment and tried to concentrate on the feel of the sun on my face. It occurred to me that I probably wouldn’t have been able to understand Tibor’s work anyway, even if I hadn’t been so distracted, and for once my ineptitude was strangely comforting: let the tanks come at me, it would be no loss to the world. But then I remembered that I would be with Pali when I met the tanks, and for the world to lose his mind would be an unthinkable disaster. My pulse was racing and I felt a little dizzy.

  ‘Eszti?’

  I opened my eyes. It was Ildiko. Of course she had noticed.

  ‘Are you okay?’

  She looked so concerned for me. I felt a swell of wistfulness for her. It was strange to feel bereft, when she was right there, my best friend whom I could see whenever I wanted, with whom I was used to being completely open. But I had not been open with her, not recently; I had become accustomed to guarding my secrets even from Ildiko. I noticed the dress she was wearing, an old cleaning tunic of her mother’s; she had added a drop waist and a row of buttons at the side and now it hugged her figure perfectly. I had been with her when she started working on that dress some weeks before, the two of us alone in the cramped kitchen as she laid it out across the table. What had we talked about? The new Bertrand Russell edition, and whether he had conceded defeat to Gödel. I remember we complained to each other about the various students we tutored. And Tibor was going to a meeting that night in the Eighth District; I was anxious about raids.

  Why had I not told her about all the things that pressed against me? There under the statue, with Tibor’s work still in my lap, I had a sudden urge to say to Ildiko, ‘I think I will never be a mathematician.’ And to tell her the other things. About Tibor: that I kept waiting for him to lay a hand on me romantically, that I was afraid of losing him but also perhaps a little afraid of keeping him. And Pali, of course. I don’t know how I would have explained my terrible wonderful Pali problem, but if the men hadn’t been there I would have tried. Or at the very least I would have said to Ildiko, I am terrified.

  As it was I smiled at her then looked at the sheet of workings in my lap. The Vinogradov lemma. Something offered itself up to me, a little pebble from deep in the layer of my brain that I feared washed away. I grasped the small round thing and came up to the surface with this: ‘I was just wondering about cubing one or more of the primes.’

  All three of them looked at me for a few seconds, then Tibor reached out to take the sheet of paper and studied it. ‘Interesting,’ he said. ‘I think Eszter might be on to something.’

  And a wave of pride came at me and washed everything else away, all my worries and fear and doubt. It was a shining spring day in the park with my friends; life was beautiful.

  I didn’t even realise Pali had arrived until I heard his mouth-clicking noises, the ones he always made when he was working on a problem.

  Then he said, ‘What if you use the Siegel–Walfisz theorem to extend the proof to the even integers?’

  Pali. He was leaning against Anonymous, on the statue’s other side, so I had to crane forward to see him. He hadn’t seen what we were working on, but from just a few overheard words he knew exactly where we were and how to nudge us towards somewhere more expansive. He looked typically crumpled, the clothes hanging off his thin frame like an afterthought. Also typical: he hadn’t even said hello.

  Levi said, ‘And good afternoon to you, Herr Genius.’

  ‘That way,’ Pali went on as if uninterrupted, ‘we might bypass Riemann for sufficiently large even integers.’

  I didn’t quite follow this – as usual, I was slightly overwhelmed by Pali’s presence and found myself scrambling to recall basic precepts (Siegel–Walfisz: what are the conditions of the positive constant?), and before I could catch up the others were rushing on ahead of me, past the little flicker of a contribution that had made me so proud, Levi saying something about applying Vinogradov and Siegel–Walfisz simultaneously and Pali pulling out his tattered little notebook (‘We should take a given c’). It was disheartening, but at least I could give up on following too closely. I could let my mind wander and my eyes rest on Pali.

  I should be ashamed to put this in writing. I am ashamed. But I think it is a necessary part of the story. I must be honest about how I have given way to the strange joy I found in Pali. Just watching him – for a long time I expected and hoped for nothing more. My faculties became clogged whenever he was there, especially when he was at work, and this was sometimes inconvenient because I was so confounded in his presence that it made his work harder to follow.

  As soon as he got into the Siegel–Walfisz business he began pacing around the statue – although pacing is not a very good descriptor for the irregular patterns he walked, fast and directed one way then another, branching off at acute angles with his arms waving and his face intense and animated. Even his hair, always unconfined and wild, seemed to become springier when he was in flight. And yet this whole catastrophe of movement, this human cacophony, seemed to me somehow harmonious. Somehow (I am embarrassed to use the word, but it will not make way for another) beautiful.

  He did his strange zigzagging pacing around the base of Anonymous a couple of times, then came to a stop in front of me, and I experienced that rushing sensation, as though losing myself – my awkward ungainly self – for a moment in the searchlight beam of his attention, then swinging back with a feeling of disorientation and self-consciousness. I think that I blushed.

  ‘You are on to it, Eszti, with the cubed primes,’ he said. And then something about arcs, something about Farey fractions – I don’t know what, only that in seconds he was far out beyond the exponents, somewhe
re in the realm of prime additives, while I became abruptly aware of the way Ildiko was looking at us. With her head slightly tilted and eyebrows raised, her gaze moved from me to Pali and back again, a question suddenly so clear on her face that it seemed to me she might have been standing on a dais announcing it to the group. I don’t know what she saw – the way I looked at him, the blush? But I became conscious of Tibor beside me on the bench, a terror that he would read the realisation on her face. I knew this was unlikely (Tibor was not interested in the feminine whimsy of emotion, his challenges were in the real worlds of politics and numbers), but still, I wished so fervently that I had taken the chance to speak to Ildiko alone when I could. I wished the men away so that I could get down on the ground beside her, take her by the shoulders and say, Stop looking at me like that. And, No, it is not what you are thinking. It is something, yes, but nothing like the crass schoolgirl crushes we have dealt in before. It is … pure.

  This is the crux of it, and a kind of shield with which I would try to defend myself from judgement. I would like to convey this to you before I go further into the mess of things: that my feelings for Pali have affected every action I have taken, despite being not quite real. No, that is not it: not quite of this world. You know, I suppose, that I was not brought up with any belief (poor Nagymama the last one in the family to go to synagogue with any regularity). Perhaps this is why I don’t know how to articulate it. I felt connected to Pali, and through him connected to some larger truth. It was partly about the miracle of Pali’s numbers, which I so often failed to understand. He was the embodiment of something bigger than himself, and even if I often failed to understand him, I believed in him.

 

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