John von Neumann Thought He Had the Answers

The father of game theory helped develop the atom bomb—and thought he could calculate when to use it.

Just as there are von Neumann machines and von Neumann algebras, there are von Neumann anecdotes. Here’s a well-worn favorite. Late in the 1940s, years after he left Hungary for the United States and became a lionized mathematician, John von Neumann met a group of Rand Corporation scientists who wanted to use a computer he’d helped design. They had a particular problem to solve, and it was—as they explained using blackboards and graphs—beyond the capacity of von Neumann’s computer at the moment. But perhaps the computer might be modified to address it? For two hours, von Neumann listened to the scientists, his head in his hands, his face impassive. Then he declared, “Gentlemen, you do not need the computer. I have the answer,” helped them through his thinking, and concluded: “Let’s go to lunch.”

Most anecdotes about von Neumann abide by this three-act structure: a question that baffles the best minds; their sweaty, pointless deliberations; von Neumann’s swift, soaring leap to the solution. (Sometimes, as in the Rand Corporation tale, the question itself goes undescribed. Its sole attribute of importance is its impenetrability.) For any biographer of von Neumann, these anecdotes are irresistible, because they serve several purposes so well. Most obviously, they are instant lessons on how much more brilliant von Neumann was than his colleagues—on the inscrutable speed and clarity of his brain. And how useful they are for many of us, untrained in the sciences, to glimpse his genius through this anecdotal shorthand; left to follow his work in quantum mechanics, mathematical logic, or game theory, we’d drown. But the anecdotes also carry a hidden charge. They lull us into believing that if von Neumann, the magus of logic, was so effortlessly and consummately right about these scientific problems, perhaps he was similarly right in his hyperrational treatment of the great projects of his time: the Cold War, nuclear escalation, market economics. Add to that mix the development of the computer—in which, too, von Neumann played a vital role—and the twentieth century shows itself as a distinctively von Neumannian enterprise.

The Rand Corporation story pops up in Ananyo Bhattacharya’s The Man From the Future, a lucid and rewarding new biography of von Neumann that otherwise visibly quivers from the noble effort to not use too many von Neumann anecdotes. Truth to tell, Bhattacharya, a physics scholar turned science writer, is less biographer than cartographer. The book doesn’t reveal many new details of von Neumann’s life and character, and our hero himself vanishes for pages at a time. Instead, Bhattacharya composes a rich intellectual map of von Neumann’s pursuits, shading in their histories and evolutions, and tracing the routes and connections between them. He recruits every ounce of your attention: Quantum physics, nuclear bomb-making, and computer architecture are all gnarly subjects. But through his narrative, we attend the raucous birth of these disciplines, with von Neumann hovering like a fussy midwife.

In his introduction, Bhattacharya argues that von Neumann invented his future—our present. “His views and ideas,” he writes, “inform how we think about who we are as a species, our social and economic interactions … and the machines that could elevate us to unimaginable heights or destroy us completely. Look around you and you will see Johnny’s fingerprints everywhere.” If that smells mildly of overkill—of the modern publisher’s tic of bigging up biographical figures into a burning, all-pervading modern relevance—it’s only because von Neumann wasn’t always an original thinker, and because, in his grandest undertakings, he featured as one among a constellation of other bright stars. But undeniably, von Neumann’s devotion to mathematical rationality was emblematic of, and even fed, the new American faith that cold, theoretical logic could be applied to nearly every province of human activity. Even happiness, as von Neumann once wrote to the physicist Stanislaw Ulam, “is an eminently empirical proposition.” He was referring to his own divorce.

Looking back, von Neumann’s rise to scientific eminence seems as fluent and foreordained as his resolution of thorny problems. His early career met no hiccups: He wasn’t raised in poverty, as Srinivasa Ramanujan was; he failed no exams, as Einstein did; he came down with no immobilizing disease, as Stephen Hawking did. Even as a boy, von Neumann had a blistering-fast mind and an adhesive memory. By some accounts, he could multiply two eight-digit numbers in his head by the time he was six, and he absorbed a 45-volume history of the world so thoroughly that, decades later, he’d quote whole entries word for word in the midst of arguments. He was born into a Jewish family in Hungary in 1903—among the best of all possible times to be a Hungarian Jew, although mere decades before the worst of all possible times to be a Hungarian Jew. The Budapest of von Neumann’s childhood, the fin of a buoyant siècle, was a cosmopolitan idyll in which Jews were able to prosper, and the von Neumanns could afford tutors, country homes, and private libraries. They could also send their bright little son to Budapest’s most elite “gymnasium,” a high school that Eugene Wigner, a Nobel-winning physicist a year senior to von Neumann, thought was the best in Hungary, if not the whole world.

These gymnasiums turned other wealthy Jewish boys into towering scientists as well. Leo Szilard came up with the idea of a nuclear chain reaction while crossing a London street in 1933. Edward Teller figured out how to make a hydrogen bomb. Theodore von Kármán refined the principles of aerodynamics and co-founded the Jet Propulsion Laboratory in Pasadena. Von Kármán aside, the rest all worked on the Manhattan Project, sorting out the science with such liquid ease and conversing with one another in such unfamiliar accents that their colleagues called them “Martians.” Even among these intellects, von Neumann’s was esteemed as special. Someone once asked Wigner: Why did Hungary turn out so many geniuses during his generation? Wigner claimed he didn’t understand the question. He knew only one Hungarian genius, he said: von Neumann.

His early energies were drawn to the liveliest mathematical debate of his day, about the essence of the field itself. By the early 1900s, so many barnacles had clung to the keel of mathematics—so many paradoxes, and theories that were true but unprovable, and strange new geometries—that the vessel itself seemed in danger of sinking. One group of Europeans, led by the German theorist David Hilbert, wanted to salvage mathematics—to define it afresh with rigorous logic so that one axiom followed tidily from others, anomalies dissolved, and everything felt complete, consistent, and shipshape once again. “If mathematical thinking is defective,” Hilbert once wondered, “where are we to find truth and certitude?”

The doubt must have felt profound, existential. In parallel, physicists were struggling to reconcile Newtonian laws with quantum theory, and biologists to figure out how Mendelian inheritance fit with Darwinian selection, so the whole venture of human knowledge was suddenly quaking underfoot. Von Neumann, studying for degrees in two different universities at once, naturally plumped for logic—for the view that mathematics had to be smooth and consistent. His first major paper, published in 1925, set about refurbishing set theory along clean, logical lines. It was complex, elegant work—a senior mathematician understood just enough of it to compare von Neumann to Newton—and it continues to be foundational in set theory today. But if anyone hoped that the paper would light the road toward final proof that all of mathematics was similarly watertight and consistent, they were soon deflated by Kurt Gödel’s theorems of incompleteness, which showed that some assertions could never be proved or disproved using mathematical tools. Von Neumann, armored in self-confidence, learned from it and took it in his stride. It never did to take anything as immovably certain, he wrote later: “I know myself how humiliatingly easily my own views regarding the absolute mathematical truth changed during this episode.”

To the sharp, sure quality of his analytical thought, von Neumann added a capacity to marry and advance the concepts of others. Show him an idea, an assistant once recalled to an earlier biographer named Norman Macrae, and “he was in a short while five blocks ahead of you.” In the 1920s, too, von Neumann wrestled into sync two competing approaches to quantum mechanics, the emerging, probabilistic science of how energy and matter acted at the subatomic level. One physicist, Werner Heisenberg, cast the properties of particles as numbers in rectangular arrays called matrices, to better calculate their behavior; another, Erwin Schrödinger, treated particles as traveling energy and drafted a wave function instead, claiming he was “repelled” by Heisenberg’s method. Von Neumann, who saw the underlying mathematics better than almost anyone, showed how wave and matrix mechanics were essentially the same, and how one could be expressed in the other’s language.

It was among the last pieces of work he would complete in Europe. In 1933, he accepted a lifetime professorship at the Institute for Advanced Study in Princeton, New Jersey, that unending summer camp for geniuses who were requested to do nothing but think around one another. Von Neumann and his family had converted to Roman Catholicism in 1928, but that would hardly have mattered to the Nazis. As a speculative exercise, the reader may wonder what would have become of the American century if the war had never happened, and if there had been no westward stream of scientists who feared their futures in Europe, and who were outrageously prolific because, as von Neumann said, of “a feeling of extreme insecurity … and the necessity to produce the unusual or face extinction.” But there was something especially fortuitous about the match made between the United States and von Neumann—a man who fell in love with the country as soon as he set foot on its soil, and whose powers of calculation and synthesis were exactly what American science needed for its monumental new schemes, schemes that promised, in von Neumann’s favored phrase, to “jiggle the planet.”

One of the finest aspects of Bhattachar­ya’s book is his delineation of how the nuclear bomb and the modern computer flowered in parallel, and how von Neumann buzzed between the two, cross-pollinating and nurturing until one now seems inconceivable without the other. His own contributions were, as was often the case, nimble and inventive answers to questions that others had slogged through. He perfected the calculations showing that big bombs wreak more ruin when they explode at an optimum altitude, rather than on the ground—a result that, to his chagrin, newspapers understood as “a miss [being] better than a hit.” At Los Alamos, working on the bomb, von Neumann devised an ingenious arrangement of wedge-shaped explosives that could implode in such synchronicity that the shock waves set off a core of plutonium—the mechanism in the bomb that eventually flattened Nagasaki. He liked being at Los Alamos, not so much to revel in the sere beauty of the New Mexican landscape—for he was, after all, the man who once wore a business suit on a mule ride up a mountain—but because he was in the thick of heated, urgent science. For their part, his colleagues treated him like a human computer. Whenever they heard that von Neumann was returning to Los Alamos, an unnamed source told Macrae, “they would set up all of their advanced mathematical problems like ducks in a shooting gallery. Then he would arrive and systematically topple them over.”

For his own sums, which ramified as these projects grew more complicated, von Neumann relied heavily on both punch card machines and the first electromechanical computers—to the point that whenever other scientists visited a computer installation, it was already running a shock wave problem for von Neumann. The progress of the computer was sweetly timed, occurring just at the moment when it was called upon to handle nuclear bomb calculations and not just estimate artillery trajectories.

Much of this activity happened at the University of Pennsylvania, which offered von Neumann one of his numerous consultancies. In 1945, riding a train to Los Alamos, he drafted a report laying down the logical design for a “stored-program” computer—a computer that holds both data and the instructions on how to act upon the data, the sort of computer that had first taken shape in Alan Turing’s broad theoretical vision. In the years after the war, this document was invaluable. It guided the engineering of several new computers, including one at the Institute for Advanced Study—where, as Bhattacharya shows in a small, firm act of historical restitution, Klára Dán, von Neumann’s second wife, worked as one of the chief programmers. But von Neumann’s report also incensed some colleagues, who thought he’d merely rendered their concepts into print—and worse, profited from them through other consulting contracts. In any case, posterity has had the last word. That model of the computer, which prefigured the devices we employ today, is still called von Neumann architecture.

After the war, a strange feat of transmutation took place. The cool, logical precepts driving the computers that engendered the bomb were turned into the basis for a kind of amoral thinking about the use of the bomb itself—a calculus that could discount the lives of civilians in the quest for nuclear supremacy. Other scientists, such as Robert Oppenheimer and Leo Szilard, had misgivings about this.

Von Neumann, though, was enthusiastic about the arms race—about bigger and bolder bombs, certainly, but also about the strategies of deterrence and first strike. “It will not be sufficient to know that the enemy has only fifty possible tricks and that you can counter every one of them,” he wrote in a paper titled “Defense in Atomic War” in 1955, “but you must also invent some system of being able to counter them practically at the instant they occur.” Pouncing first might even be pragmatic, for after all, as von Neumann believed: “With the Russians, it is not a question of whether but when.”

Bhattacharya devotes perhaps a few too many pages to the circuit of Rand analysts, military officials, and government committees all studying nuclear war; the bureaucracy of plotting mass killings is unsurprisingly dull. But this was von Neumann’s postwar life, and he enjoyed it—not just because it made him feel important to be sought out by generals and to hear, as a friend once said, the “thump of helicopters on his lawn,” but also because he was sure of the virtues of pursuing war against the Soviet Union. In Dr. Strangelove, Stanley Kubrick mashed up several German and Mitteleuropean scientists to create his titular, near-mad scientist, and while von Neumann wasn’t a primary inspiration, he’s in there somewhere—in Strangelove’s expositions on computers and tape-memory banks, in his quicksilver doomsday calculations, in his gamed-out scenarios of nuclear attack. “Deterrence,” Strangelove says, “is the art of producing in the mind of the enemy the fear to attack”—a line of dialogue shining with the von Neumannian certainty that logic can regulate the instincts and foibles of humans.

That certainty was also at the heart of Theory of Games and Economic Behavior, a text that von Neumann wrote jointly with the economist Oskar Morgenstern. (Incredibly, the book came together in the mid-1940s, even as von Neumann was shuttling between bomb labs and computer facilities.) Game theory, faithful to its name, treats every human context as a game—a self-contained situation in which your sly rival must lose for you to win, and in which the nature of these losses and wins can be always summed up in precise numbers. Morgenstern and von Neumann offered mathematical blueprints for victory, or at least for the least bruising of defeats. These weren’t just to be consulted by a pair of prisoners in separate cells, wondering whether to rat each other out—the Prisoner’s Dilemma, the classic thought experiment, framed in 1950 by Princeton mathematician Albert W. Tucker, that introduces game theory to students even today. For von Neumann, game theory was an affirmation of humans as rational actors who weigh utility and risk in a world that is perpetually zero-sum, and who can make optimal decisions—optimal, that is, for themselves—about bombing other countries or buying new cars.

When von Neumann framed (if only theoretically) the consumer as rational, he helped endorse the free market itself as a rational, self-correcting, self-optimizing place. But the real world and its various markets are bigger and more intricate than the models of game theory, of course: No one has perfect information or consistent beliefs, no one acts in the realm of unalloyed reason. One game theorist, Ariel Rubinstein, called his field “a collection of fables”—very useful for detached analysis, but useless to reach conclusions about “what to do tomorrow, or how to reach an agreement between the West and Iran.” Von Neumann implicitly wanted, however, to apply game theory to the full-blown war with the Soviet Union that he thought was imminent—and game theory recommended a surprise, preemptive attack by the United States. “If you say why not bomb them tomorrow, I say why not today?” he said in 1950. “If you say today at 5 o’clock, I say why not one o’clock?”

It’s hard to know if von Neumann truly believed that—and truly believed, more generally, that life and society are best organized by mathematical logic. He was fond of provocation, and his proposal of a lunchtime nuke over Moscow may have been made for sheer effect. But he also seemed to conduct his own affairs on the basis of pure mind. In his work, Macrae tells us, von Neumann never had strokes of irrational intuition, the kind that result in startling new ideas; his friend Einstein had many, and von Neumann envied them. With people, he was gregarious and charming, but “he tended to be oblivious to the emotional needs of those around him,” his daughter, Marina, said to Bhattachar­ya. (Marina was two when her parents divorced; her father agreed to let her live with him only after she turned 12, when she was “approaching the age of reason.”)

Von Neumann’s colleagues joked that he was a visitor from some species with an advanced intellect, and that he’d merely studied humans in enough detail to imitate them to perfection. The jibe hinted at an image of a man somehow displaced in space and time. Bhattacharya locates that space and time in the future—the future as seen from the 1940s, certainly, but also the future as seen from 2022. One of von Neumann’s last essays, titled “Can We Survive Technology?” and published in 1955, discusses the adverse effects of climatic shifts; other papers dwelled on artificial intelligence, technological singularities, and self-replicating automata, the obsessions of our coming decades. Von Neumann isn’t done with us yet.

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