A Doubter's Almanac Read Online Free PDF

rocky start in the department. He was still drawn to numbers, of course. This part was unwavering. Number theory. The charismatic singularity of primes and semi-primes. The inevitability of numeric functions and their astounding analytic capture of the world—the V-shaped cadres of flying geese he’d watched as a boy, the fragmenting clouds yielding to disorder high above the two glass-paned graphs through which he now gazed hour upon hour. It was as though the numerals had been expressly fabricated, like more-perfect words, to elucidate the details of creation. He wanted to say this to someone. Instead, he sat in his thrift-store chair and watched the passing legs: steps, random crossings, the probability of flows. Mathematics not only described it all but could in large terms predict it. In his bed sometimes he wondered absently if it could be developed to alter it.
    He was interested in other fields besides topology. Commutative algebra, for one: the work of Gauss and Cayley and Lasker. But whenever he spoke with Hans Borland about it, the old man seemed irritated.

    “Topology’s the one for you, Andret,” the professor said brusquely, the next time they met. “I guarantee it. Forget algebra. Forget Gauss. Lasker was just a chess player with airs. Topology’s a perfect suit to your gifts, man. That sense we both have of the world. The rest’s a waste of your time.” He exhaled tiredly. “And talent.” A glass of sherry stood on the polished desk. He raised his left hand again, dramatically, as though it affirmed his conclusion. “Should have been a topologist myself.”
    “You still can be, Professor.”
    “A wasted thought.” He sipped from the narrow glass, then set it down carefully, as if balancing an egg. “Have you read Bott and Kuratowski and the rest on the list?”
    “Yes.”
    “And what did you find there to work on?”
    “I guess I haven’t settled on anything. Nothing specific yet, anyway.”
    “Well,” he sniffed, “focus yourself. Settle on something.”
    —
    N OW AND THEN, one or another of the graduate students in his department would stop by for an assignment or to discuss a problem. The conversation would begin optimistically; then it would falter, as conversations had all his life. Milo watched his colleagues walk back up the stairs of his apartment into the hectic brightness of the day. Satchels swinging at their sides. The spring-loaded door whooshing and slapping.
    He needed something to fill the hours. Borland’s admonition breathed steadily in his ear. Startling. He’d somehow not fully appreciated that a graduate student was obligated to write a dissertation. How insanely idiotic to be unaware of a requirement like that. He needed something to unbind his thinking.

    One day in Evans Library, he noticed that a girl was watching him. She was sitting at a desk by the window, and he was standing all the way across the room at the shelves along the far wall, looking at a book about Tycho Brahe, the great sixteenth-century astronomer. When he glanced over again, the girl was still looking in his direction. Dark hair and a man’s button-down shirt. That’s all he could see. He shifted his gaze.
    Brahe had used a quatrant to define the orbits of the planets. Milo flipped a page and found a drawing of the instrument itself, which looked like a mariner’s sextant but was many times larger. Onto the palm of his hand, he sketched the spoked arms and the notched, chordal circumference.
    When he walked back out of the stacks, she was gone.
    That afternoon, at a lumberyard near the bay, he bought some cheap lengths of maple from a scrap pile. In a trash can behind the five-and-dime he found a sheaf of balsa. From there it was straightforward. A couple of weeks later, the arc and axis had emerged from the maple, and the calibrated rim from the balsa. It was scrupulous work—but so was a wooden chain and so was a mathematical proof. Puny assaults on the heavens.
    Distractions, too. He