The mathematician John von Neumann had an intellect of almost otherworldly proportions. A new biography describes where he made his mark. The reader does not learn much about Von Neumann as a person.
The Rand Corporation is an American think tank that was infamous during the Cold War for its nuclear war strategies. One day, the Rand researchers approached the mathematician John von Neumann with a problem they could not solve on their own. It would take a computer, they thought. And Von Neumann was the computer expert at that time, in the late 1940s.
They had been talking to him for some time when Von Neumann interrupted them and asked what exactly the problem was. What followed was an exposure that lasted two hours. The Randmen filled boards, showed maps and sea charts. Von Neumann sat with his head in his hands and listened. When they finished, he wrote on a piece of paper, stared into the room, and then said, “Gentlemen, you don’t need a computer. I already answered.”
The anecdote illustrates John von Neumann’s almost otherworldly intellect. His colleagues at Princeton’s Institute for Advanced Study often joked that he descended from a superior species that had studied humans closely so that he could imitate them perfectly. In any case, they thought he was smarter than famous Princeton residents like Albert Einstein or the mathematician Kurt Gödel.
Model for dr. Strange love
Yet John von Neumann is hardly known to the general public. At most, perhaps if one of the scientists who modeled Dr. Strangelove, from the Stanley Kubrick film of the same name. And it is true: Von Neumann had concluded with the iron logic of his game theory that the only way for the Americans to escape a devastating nuclear war was a pre-emptive nuclear strike against the Soviet Union. “If you say why don’t we bomb them tomorrow, I say why not today?” he reportedly said in 1950. “If you say today at 5 o’clock, I say, why not at 1 o’clock?”
But those who only see John von Neumann as an unearthly iron eater are shortchanging him, writes Ananyo Bhattacharya in his biography The man from the future: “He was also a cheerful man, an optimist who loved money and believed strongly in the progress of mankind.”
Bhattacharya does not delve very deeply into Von Neumann’s soul. He has decided to chart his scientific legacy. And he needs a whole book for that. Bhattacharya does not limit himself to the achievements of his protagonist, he also outlines the genesis of each field in which Von Neumann has made his tracks. And how science has been able to build on its pioneering work for decades. In that respect, the book reflects Von Neumann’s life. Just as he regularly wrote a standard work, which provided many scientists with years of work, while he himself had long since done something else, he also disappears from view for pages of biography.
Quoting entire chapters from history books
John von Neumann was born János Lajos Neumann on 28 December 1903 in Budapest; when he fled Europe in 1933 and moved to Princeton, he adopted an American first name. As the child of wealthy parents, he learned Latin and Greek and quickly spoke French, German and English. He had a fabulous memory and could quote entire chapters from history books. The story goes that a professor of Byzantine history, who was invited to one of Princeton’s famous parties, only wanted to come if von Neumann promised not to talk about this field. The professor feared that people would doubt his authority.
All these unusual talents paled before his gift for mathematics. At the turn of the century, the philosopher Bertrand Russell had discovered a paradox in the so-called set theory. Mathematicians interpret the concept of quantity very broadly. You have the set of integers, but also that of all blue footballs. Or the collection of sentences consisting of ten words. Russell’s paradox is based on the fact that he had constructed a collection that was supposed to contain a certain object and at the same time could not contain it. In essence, it is similar to the statement: “This statement is a lie.” You cannot say whether it is true or not.
Russell could not mitigate his paradox, any more than his peers, but the seventeen-year-old student János Neumann did. He was still in high school when he dissected and reformulated set theory, making Russell’s paradox disappear like snow in the sun. Almost then, but a few years later – he had already graduated – he completed the article and gave the subject a solid foundation on which it still rests.
One masterpiece after another
With this bang, von Neumann stormed into the world of science. But where others continue to work quietly after a roaring start, things never went quiet around Johnny. He was not yet thirty when he was able to add the next masterpiece to his list of achievements. Physics was turned upside down in the early twentieth century by the development of quantum theory.
Physicists had wrestled with the question of how to describe the world of atoms and molecules for decades. In 1925, there were suddenly two theories on the table, Werner Heisenberg’s matrix mechanics and Erwin Schrödinger’s wave theory. The theories were not quite the same, but both worked very well. It was a mystery until Von Neumann proved in 1932 that they were essentially equal.
So he rambled on. In the same 1930s, he converted the mathematical paper of his British colleague Alan Turing into a plan for a working electronic computer. He then laid the foundations of game theory that would revolutionize the social sciences and developed an idea to create self-replicating entities. In between, he was one of the driving forces behind the Manhattan Project, the secret operation that resulted in the first atomic bombs.
Take a break after each chapter
Bhattacharya takes the reader on von Neumann’s journey through the exact sciences. So this one will be a lot to digest. Non-Euclidean geometry, Hilbert space, Kurt Gödel’s incompleteness theorem, Bertus Brouwer’s fixed point theorem, Nash equilibrium. It doesn’t hurt to take a break after each chapter to process what has been offered. Fortunately, you don’t have to understand everything. Even without a complete insight, the awe of von Neumann’s enormous brain grows.
But as a reader, you hardly get to know Von Neumann the person, and you have to make do with anecdotes. About his driving style, e.g. Von Neumann had never taken a driving test – he had bribed his censor – and caused many accidents in his life. Miraculously, he himself almost always remained unscathed and came home with the most improbable explanations. “I drove there,” begins a legendary apology. “The trees on the right passed me nicely at 60 miles an hour. Suddenly one went up the road on my side. Boom!’
Not even his second wife got hold of her husband’s character. In his memoirs, this Klári Dán wrote: ‘I want to tell about that man, the strange, contradictory and controversial man; childish and good-humoured, sophisticated and fierce, brilliant and yet with a very limited, almost primitive lack of ability to handle one’s emotions – a natural riddle that must remain unsolved’.
Ananyo Bhattacharya, The man from the future – The Visionary Life of John von Neumann. Publisher Atlas Contact, Amsterdam/Antwerp, 392 pp. €29.99
Scientists have managed to make ‘living’ robots reproduce
In the 1950s, the Hungarian-American mathematician John von Neumann foresaw the possibility of machines that could make copies of themselves from separate parts. Much research is now being done into this in the field of robotics.