Mathematics is generally categorized as a science, but I don't think it is only that. I admit that mathematics has contributed to the realms of physical science, and has itself been reinforced by its interactions with them, but mathematical discoveries are made regardless of their applicability or utility to the physical world. Mathematics has evolved purely for itself, with the greatest contributions to the field being those theories that put value on the beauty of the adopted logic. A theory contrived for purposes other than itself lacks natural beauty. What is mysterious is that a great theory possessed of inherent beauty transcends the subject and finds applicability in other fields.
It is impossible to put in words the intrinsic grace of a theorem. It is highly abstract and complex. I can only describe it as being akin to a perfect piece of music in which each note is irreplaceable or to a haiku in which no syllable can be changed. The beauty I speak of is like the exquisite tension that holds together aspects of a work of art; a fragile serenity that cements its perfection. And so the magnetic force that draws art—and therefore literature—to mathematics is the dignified beauty of its pure logic.
Almost thirty years ago I wrote a book about my experiences living in the US, and since then I've had many opportunities to work with literary professionals and to write essays apart from my regular occupation. I felt at ease when I first began to write because I regarded literature and mathematics as kindred art forms. Besides, having grown up with two parents who were both writers, I'd long thought of writing as instinctive to human nature. In short, I didn't expect to be challenged. But numerous obstacles confronted me in the process of writing. I began to realize that there were fundamental differences between mathematics and literature. It became hard to cope with being a writer while also being a mathematician. But writing had a bonus: I experienced first-hand the trials my parents had secretly faced as writers. I began to reassess my hardships relative to theirs.
The most agonizing aspect of being a mathematician is having to pound away at a problem without making any obvious headway. I can devote myself day and night to the problem at hand and not glimpse the solution for weeks or even months. Early periods of study tend to slip away without any serious stagnation; during this time I go through one idea after another. But once the well of ideas has run dry, I have to endure the darkest exhaustion. An invisible pressure settles on me; the anxiety of it all is suffocating. I once put aside everything for nearly six months to work on a thesis. I was contemplating the problem day and night, even in my dreams. Finally I left Tokyo and traveled to Gamagori, Inuyama, Kujukuri and the Irako Lake, but my idée fixe would not leave me. It pursued me everywhere: at the inn, in the park, on a bench, on the battlements of an old castle, at the lakeside, on the beach . . . After six months, I fell ill. I conceded the challenge and brought my journey to a close. I had made no progress in the end and I was physically depleted.
But a writer, sitting at his desk round the clock, would have made some progress, some scribbles on paper. No matter the pace, he can see the page slowly fill with words. His creative process becomes visible to him and he is comforted by it; he is strengthened to go on. My father often displayed signs of extreme distress, and it was always when he couldn't settle himself at his desk, when he couldn't get on with the writing. He lacked the encouragement he would otherwise have been given by the sight of his own rough drafts. At the start of a new novel he would be in a bad mood for more than a week. It was only when he warmed up to the work that he would return, steadily, to his natural and gentle self.
My father used to say the most strenuous part of writing was the beginning. He called it 'the birth pangs of creation.' For mathematicians too, the early part is the most trying, when one has to distil from the fluid of vague thoughts the essence of an idea. Writing a treatise is rather easy. Even a prolific mathematician would spend no more than a month each year writing up all of his studies. What we suffer from is a never-ending succession of 'birth pangs.'
Mathematics is an all-or-nothing business: either one can prove one's theorem or one cannot. There is no grey area. One cannot 'almost prove' or 'nearly resolve' anything. No compromise is permitted. The completed theory must be free of ambiguity. Nothing but the absolute—and therefore beautiful—proof is of any value to mathematics. In literature, however, it is not important that everything be explained. In fact, room for the reader's imagination is left open. This might suggest that literature is more flexible, somehow easier to tackle than mathematics, but I imagine that room for anything other than what is in the story can be disquieting to a writer.
No writer is absolutely confident in his story, no matter how much he has devoted himself to the piece, how many times he reworded and rearranged it. In my case, I cannot hand over my draft to the editor unless someone else has checked it first. This someone is usually a member of my family, so I ought to feel relaxed, but I am always afraid of being criticized for having left some ambiguity in the piece. I remember my father also being anxious about initial reactions to his work, particularly during the first few days after he submitted a draft, even after he had become an established writer. But once the editor's favourable verdict was delivered, he would grin childishly, his anxieties erased, and say, 'How about that? I did it! This is the Jirō Nitta!
In mathematics, no one assures you that you will definitely achieve something after striving for a long period. If his attempted theorem transcends the standards of modern mathematics or is beyond the mathematician's resources, it may never be proven, regardless of the amount of work invested. Worse, the theorem to which he dedicates himself for so long might prove, in the end, to be mercilessly wrong. The fear of this uncertain result can swell into a terror so numbing, it chips away at the mathematician's ambition. On top of this, he has to endure the pressures of academia. A mathematician must therefore be a man of patience and of courage. Personally, I have not always had the mental stamina to bear these internal terrors and external pressures, and have abandoned some projects in the past.
I know of a mathematician who went through great difficulty to produce a work of extraordinary genius. Professor S. now works at MIT, but he was once attached to the University of Michigan as an assistant professor. While at Michigan, he challenged himself to work on a particularly difficult classical problem, one that had been left untouched for decades by other mathematicians. His devotion to the problem was so great that he failed to write the thesis expected of him and was therefore dismissed from his post at the university. But not long after that, he found a ground-breaking solution to the problem, one so spectacular that a number of related problems began to be solved. It was as if a great silence had been disturbed. As a result of his success, Professor S. was offered a post as full professor at MIT. But this is a rare case. Most mathematicians would not have had the tremendous self-reliance and confidence it took to risk a job for such an uncertain goal.
Writers, on the other hand, have clearer goals, as long as they dedicate themselves to the task. The knowledge that I can complete a task to the extent my talents afford assures and encourages me. There is, however, in literature the hurdle of the deadline, particularly when writing for a magazine or newspaper column. My father's mood changed dramatically depending on whether he was writing a novel for himself or a story for a newspaper. He was enthusiastic no matter the task, but the impetus seemed to be different in each case: He was fuelled by an inner urgency when writing a novel, but committed to something outside of himself when writing for a paper. Sometimes he simply could not go on when writing a column; he would obsess, fearing that he would somehow let down the paper. Even his family could not ease his anxiety. A scene is stuck in my head in which my father shuffles upstairs without a word. The sight of his back, clothed in an oversized old kimono, taught me that writers are always wrestling with deadlines; they would rather be on top of them than be enslaved to them.
The defining feature of a mathematician's stress is the fear that he will produce nothing, even after suffering 'birth pangs.' For a writer, it is the pressure of having to complete a work within a certain period of time. What is common to both is the struggle to sleep free of concerns. When I am obsessed with a mathematical problem, I work on it even as I dream. Sometimes a flash of inspiration will strike me when I'm in bed. The French mathematician Jules-Henri Poincaré experienced much the same thing, and it is said that most of the ideas that struck him this way proved to be correct. Unfortunately in my case, nine out of ten ideas are not worth pursuing. That one idea, however, can be of use to the work at hand and may even yield the right answer. So I always keep a notebook by my bed and reach for it when even the whisper of an idea enters my head. There is another reason for this: if I didn't commit the new idea to paper, I wouldn't be able to calm myself and go back to sleep.
When I am in the midst of writing, the lines I have written during the day return to me in my dreams. If in my dreams I encounter the perfect way to render a line I couldn't arrive at when I was awake, I wake up and take notes. In the case of writing, seven out of ten ideas that come to me in dreams turn out to be good, a ratio that is dramatically better than the one for mathematical inspirations. I don't know why this is so. Perhaps dream-thoughts are composed not of logic but of subconscious aesthetic sentiments, better-suited to literary creation than mathematics. And yet we cannot ignore the fact that one-tenth of all mathematical inspiration that occurs in dreams (or ten-tenths in Poincaré's case) works. I'd say that the aesthetic sensitivity is a factor in mathematics just as it is in literature.
Having writers in my family and being a mathematician myself, I thought I had a good sense of what they were about when I began to enter both fields. But I was too optimistic. Although both literature and mathematics involve creativity and both evaluate beauty and harmony, their methodologies are poles apart. Mathematics is based on a universal logic pursued by the mathematician's instinct and aesthetic sensitivity whereas literature demands originality and sensitivity to words. So, for a few days after working in mathematics, I find it impossible to produce anything literary, and vice versa. I need some time to switch from one mode to the other and during this period of transition, things go round and round, and I spend most of my time fretting away. It's a sheer waste of time, but I seem incapable of occupying both fields at the same time. Perhaps I am the only one to blame for the imperfections of this system, but I don't think it's as simple as that.
In my opinion, the essence of all literature, no matter the form it takes, is the realization of one's own mortality. Without the notion of death, almost all our sorrows, our desperation and loneliness would disappear. If we were phoenixes with eternal life, we would never experience dark days or broken hearts, nor would we be capable of absolute joy or delight—all vital components of literature.
Literature is deeply bound to the notion of death and writers consciously and unconsciously weave strands of human destiny into their stories. Masterpieces like Genji Monogatari, Turezuregusa and Oku-no-Hosomichi all study the transience of human life. This awareness of one's mortality can be seen in contemporary literature as well. In fact, with careful observation, even the most casual description can reveal the writer's understanding of the finitude of human life. In his novel, Takeda Shingen, my father wrote a scene depicting the march of the Takeda army across a bridge towards the Kanto region. When the troop reaches Kanto, one of Takeda's soldiers, who has never before left his hometown in the Koshu region, mutters, 'There are no rocks here.' One critic praised this as an example of the writer's scientific precision in depicting the scene. I remember feeling dejected by this remark. I was sure my father intended to do more than make a geological observation. I felt that he wanted to portray the soldier as a man struck by a sudden and intense nostalgia for his hometown, sending his heart far beyond the scenery that surrounds him. The flatness of the Kanto plains make him think of the stones and rocks of the Koshu region; he remembers a mountain, a river, a valley, and then the lights that illuminate his hometown, the wind that rushes through. He remembers the family he has left behind. In those few moments, his imagination goes far beyond the comparison of two topographies. In effect, the soldier is faced with the transience, smallness, and desolation of his life in contrast to the everlasting dignity of nature. A few small words uttered by a solder so dextrously convey the author's obsession with his own mortality.
Imagine a strange land that stretches endlessly before your eyes, a massive army of soldiers traversing the land on their horses, and one soldier amid that army wrapped in his solitude. With this, you have traced the writer's course of observation: from a distant view, moving to a middle, then a close-up shot, and arriving at a psychological insight. In this way, my father implied the subtle awakening of philosophy in an unknown soldier. It was his forte to hint at melancholia, the sense of Wabi, and the tranquility of life, by contrasting grand sceneries. This is what I believe struck the hearts of readers.
Writers and mathematicians both long for eternity, the difference between them being that the former seek it in their own lives while the latter look for it beyond individual human life. When a mathematician begins to explore universal truth, he must abandon his inner chaos. No mathematician will spend time on the emotional implications of the finitude of human life, but he may hypothesize the infinity of truth. Mathematicians rise above the world; time is irrelevant to them. They adapt their minds to a state that transcends the space-time dynamics of the material world. They burn with devotion for this state; else no truth will be discovered.
It must be clear now how demanding it is to come and go between literature and mathematics. It does not involve merely the techniques of each field, but a total qualitative transformation of the mind. I have yet to master a smooth transformation. Sometimes I find that it helps to listen to music when I shift from a mathematician's mindset to that of a writer's. But not any music will do. I need something like old folk songs that affect me emotionally rather than classical masterpieces by Bach or Mozart. I wish there were a wonder drug for this transformation, or that I were a fast-moving ninja rather than the awkward sheep I am, lingering on the bridge between mathematics and literature. Then again, part of me refuses to admit that there could be such a drug. After all, I may still be on this bridge, moving this way and that, hesitating between two sides, and reaching neither side of the river. And yet, I seem to be enjoying it.
