Vitya had never read the well-known lines of Mandelstam, but he experienced the same emotion the poet describes in his obscure, redolent, pulsing words:
And I step out of the space of the world
and into the garden of magnitudes
and I rend the illusory permanence
and self-evidence of reasons.
And your very own primer, eternity,
I read all alone, in solitude—
Wild, leafless book of medicinal lore—
problem set of enormous roots.
In short, he had ended up in that garden. It was impossible to imagine anything more wonderful.
By the tenth grade, Vitya had become a real mathematician. His massive, somewhat convex forehead—like that of a child with a mild case of hydrocephalus—contained the brain in which the expanding universe moved, breathed, bubbled, and frothed. All other natural functions of the organism—eating, drinking, sleeping, etc.—were mere obstacles to the constant working of the rest of his highly functioning mind. Very little interested him apart from mathematics, and even his friendship with Grisha waned a bit. Grisha no longer satisfied him as an interlocutor. To be more precise, the pleasure he got from the music of mathematics so exceeded all other joys, including that of spending time with other people, that he began avoiding everything “extraneous.” Even physiological growth into manhood was an inconvenience or a malady to him, something like tonsillitis, which prevented him from studying. During that period in adolescence when young people are in the throes of hormonal revolution, Vitya found a simple method for releasing the tension that gripped him: overtaxing his mind.
Nora, who inhabited the outskirts of the world of Vitya’s interests, took the initiative at this timely moment to change her status from tutor in literature to friend and companion in sexual activity, and readily accepted his newfound manly maturity. She was a premature, illegitimate offspring of the sexual revolution, of which she knew nothing—if you didn’t take into account Marusya’s bold but old-fashioned pronouncements about the full emancipation of women in the socialist world, spoken in a whisper for fear the neighbors would overhear her.
Vitya was grateful to Nora for liberating him from the yoke of his hormones, a relief he experienced immediately after each one of their short, stormy meetings. Business meetings … The marriage prank they staged for the graduation ceremony had no effect on their relationship. Sometimes Vitya went to see Nora, with a friendly but purposeful aim; sometimes Nora would call him. They would come together, then part ways, without discussing when they would see each other again. Sometime or other … Vitya devoted all his energy to another romance—mathematics. Nora did her artwork with supreme pleasure, attended lectures on the history of theater, and read books.
Vitya was admitted to the Department of Mathematics and Mechanical Engineering, and from the first year of his studies dived headlong into set theory, a field of mathematics that had arisen relatively recently, in the mid-nineteenth century—a field that seemed to appeal greatly to madmen and suicides. It also beckoned to Vitya. Human fates, characters, and biographies did not yet stand behind the names of theories. It wasn’t until a few years later, when the Russian translation appeared of a multivolume work on mathematics and its history written by a group of mathematicians who had adopted the pseudonym Nicolas Bourbaki, that Vitya found out about the founder of the entire field. Georg Cantor, born in St. Petersburg, was the originator of the notion of actual infinity. A philosopher, musician, and Shakespeare scholar, he lost his way in the world of his own creation and died in a psychiatric clinic in Halle. He left behind (in addition to all of the above) what is known as Cantor’s Problem or the Continuum Hypothesis, which, as the next generation of mathematicians would claim, was possible neither to prove nor disprove. Vitya learned about the death of Felix Hausdorff, who took his own life in 1942 before he could be sent to a concentration camp, about Hausdorff spaces and the Hausdorff Paradox, which were his legacy to his descendants, and much else besides, concerning not so much mathematics as mathematicians.
Vitya spent the entire fourth year writing about computational functions, which thrilled his department chair, who was also quite an eccentric fellow.
The university administration, forced to consider the outstanding achievements of the department head, a world-renowned scholar, forgave his eccentricity; but Vitya, his student, did not get off so lightly. In those days, the Communist Party representative called the shots, and the dean’s office was beholden to him. The students were kept on a tight leash—mandatory Komsomol meetings, political briefings, “volunteer” social work. From time to time, Vitya was taken to task for disregarding the laws of existence. Once, he was barred from taking an exam for skipping PE classes. Another time, he was nearly expelled from the university for what became known as the “potato-carrot incident.”
Every September, all the students were sent “potato-picking” on communal farms. Those who were best suited to the conditions of Soviet life managed to procure medical exemptions beforehand. As secretary of the Housing Management Committee, Varvara Vasilievna had connections all over the district, and getting hold of the desired certificate would have been a breeze for her; but Vitya hadn’t even thought to ask for one, and now he had to fulfill his Komsomol obligations.
The students worked with great enthusiasm this time, since Dennikov, the Komsomol organizer in their class, promised that they would be released as soon as they dug up all the potatoes from the immense field. Inspired by this promise, the young people worked from sunrise to sunset, took in the entire harvest in two weeks, and were glad that they had earned fifteen extra days of free time. Toward the end of the harvest, however, Dennikov disappeared. He had been recalled on important Komsomol business, and the Party comrade who replaced him announced that now they would pick carrots. The rains started the same day.
The students howled and went into the carrot fields. Not all of them, however—some of them refused on principle, and left for home. Vitya also left—not out of principle, but because of illness. He had a terrible cold and a fever, so he took to his bed and gave himself over to mathematical dreams. He experienced what in later years he would call “intuitive visualization.” He even attempted to describe this experience of the world of sets as forests or lacework of profoundly beautiful ties and nodes, moving in space, and having no connection whatsoever with crude reality, where the teakettle boiled, and sometimes all the water boiled off; where the indestructible cockroaches persecuted by Varvara Vasilievna roamed the kitchen; where the exhaust fumes from Nikitsky Boulevard came in through the window and filled up his ground-floor basement room. The attempt failed.
Misty visions the mind couldn’t comprehend alternated with a semiconscious state in which the shadow of Nora was present. She offered him amazing objects on a large flat plate made of bright metal, and these objects were algorithms, and they were alive—they stirred slightly and interacted with one another. Vitya felt that there was some exquisite idea he had to write down, but something was missing, something was always missing. A tall man was walking down a long corridor with a shining hole at the end and carrying the same dish that Vitya had seen in Nora’s hands, and on the dish were the same creatures—which were the theory of functions and functional analysis. The man’s name was Andrei Nikolayevich, and Vitya desperately needed to have this man notice him, but because of some unspoken law he didn’t dare call out to him, so Vitya had to wait until the man noticed him first. Then the scenery changed, and the tall man went away; the dish with the algorithms ended up in Vitya’s hands, only they were all dead and didn’t stir any longer, and horror engulfed him.