The Man from the Future The Visionary Life of John von Neumann

🚀 The Book in 3 Sentences

This book is about the fascinating life of John von Neumann. It describes the work and the ramifications of the work he ventured on. Things like game theory, the biology of cell automata, economics, physics, mathematics, and computer science are all fields either founded or drastically influenced by the work of John von Neumann.

🎨 Impressions

I have always had a soft spot for one of the most influential scientists of all time, and I was astonished by the amount of work that was done by John von Neumann.

This book is a goldmine of a story of the scientific and cultural shift from Europe to America, and the golden age of scientific discovery during the first 50 years of the 20th century.

How I Discovered It

I think it popped up when I was browsing around in Amason for books and it sounded like a book I would like to read.

Who Should Read It?

I think this is a good book for anyone who likes to read biographies and is interested in science. It does not contain any math so rest assured, it will be a good read.

☘️ How the Book Changed Me

It is just so interesting for me to read about how drastic the shift from Europe to America was, it was insane how much brainpower shifted to the Americas. I am astonished about how increasingly effective the purges of intellectuals from Germany by the Nazi party were, they removed most of the tools they had to contribute to their insane war effort.

Also, the tragic fate of some of the characters, such as Godel, Nash, and others, shows the dark side of the human mind and how one should be thankful for not only the gifts one receives but also the curses one does not. Reading this and seeing the movie Oppenheimer made me be aware of a lot of different aspects that the movie missed.

✍️ My Top Quotes

• ‘If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.’ John von Neumann

• ‘Von Neumann would carry on a conversation with my three-year-old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us.’ Edward Teller

• Created when the old capital of Buda was merged with the nearby cities of Óbuda and Pest in 1873, Budapest was thriving.

• In 1910, a quarter of Budapest’s population, and more than half of its doctors, lawyers, and bankers, were Jewish, as were many of those involved in the city’s thriving cultural scene.

• Equally, von Neumann had no interest in sport and, barring long walks (always in a business suit), he would avoid any form of vigorous physical exercise for the rest of his life. When his second wife, Klári, tried to persuade him to ski, he offered her a divorce.

• ‘Mathematics is the foundation of all exact knowledge of natural phenomena.’ David Hilbert, 1900

• ‘Johnny’s unique gift as a mathematician was to transform problems in all areas of mathematics into problems of logic,’ says Freeman Dyson.

• ‘My opinions have been violently opposed to Marxism ever since I remember,’ he told a congressional confirmation hearing in 1955, after he was nominated to the Atomic Energy Commission, ‘and quite in particular since I had about a three-month taste of it in Hungary in 1919.’

• Displaying a sensitivity towards the feelings of others that are not always found in those with remarkable brains, von Neumann took care not to be overbearing yet could not but help stand apart. ‘Whenever I talked with von Neumann,’ Wigner said of his friend, ‘I always had the impression that only he was fully awake, that I was halfway in a dream.’

• The next leap forward in geometry was taken by the German mathematician Bernhard Riemann in the 1850s, about twenty years after Bolyai and Lobachevsky. Riemann’s doctoral thesis, now recognized as one of the greatest ever produced in mathematics, was of a gloriously fertile originality,’ said Carl Friedrich Gauss, the most famous mathematician of the age. While Bolyai and Lobachevsky pictured planes that curved through space, Riemann’s surfaces often twisted and contorted in ways that could barely be imagined at all. His mathematics could describe space with any number of dimensions – hyperspace – just as easily as the three familiar spatial ones. More than half a century later, Riemann’s geometry would prove ‘admirably appropriate’ for describing the warped four-dimensional spacetime of Einstein’s general relativity.

• ‘Ignoramus et ignorabimus,’ as he put it: ‘we do not know and will not know’.

• ‘God made the natural numbers; all else is the work of man,’ growled Leopold Kronecker, a contemporary grandee of German mathematics who found Cantor’s juggling with infinities suspicious and distasteful

• His analysis of the paradox revealed it to be similar in form to several others, including the liar’s paradox (‘this statement is a lie’). ‘It seemed unworthy of a grown man to spend time on such trivialities,’

• In Göttingen, Hilbert reacted angrily. Whereas once he had supported Brouwer’s application for a chair at the University of Amsterdam, he now campaigned for him to be removed from the board of editors of Mathematische Annalen, one of the field’s most prestigious journals. Einstein, one of the editors, dismissed the feud as a completely overblown Froschmäusekrieg (literally a war of frogs and mice, a German phrase describing a bitter but unimportant altercation).

• I don’t maintain that I understood everything, but enough to see that this was outstanding work and to recognize ex ungue leonem.’ ‘To know the lion by his claw’ – the Latin words uttered by Johann Bernoulli 200 years earlier, on recognizing by its brilliance an anonymous work by Isaac Newton.

• After 379 pages, Russell and his co-author Alfred North Whitehead were able to prove that 1+= (‘The above proposition is occasionally useful,’ read the wry comment accompanying their proof).

• He was twenty-two. Hilbert, one of the examiners, is alleged to have asked just one question. ‘In all my years I have never seen such beautiful evening clothes: pray, who is the candidate’s tailor?’

• ‘If only I knew more mathematics!’ Erwin Schrödinger, 1925

• ‘The more successes the quantum theory enjoys, the more stupid it looks,’ said Einstein, who realized early on that the shotgun wedding of classical and quantum concepts could not last.

• The core ideas in Heisenberg’s revolutionary paper were assembled during a two-week stay in June 1925 at Heligoland, a sparsely inhabited rock shaped like a wizard’s hat that lies some 30 miles north of the German coast. Puffed up by a severe attack of hay fever, the outdoorsman had gone to take the pollen-free North Sea air, hiking and swimming and hoping for a breakthrough that would make sense of the puzzles thrown up by Bohr’s work.

• He showed what he described as his ‘crazy paper’ to Born, who encouraged him to publish, writing to Einstein that it was ‘rather mystifying’ but also ‘true and profound’. Only after the paper was in print did Born remember that he had been taught about similar arrays years earlier.

• Anxious to make his name with a big discovery, Schrödinger worked through a two-week tryst with an ex-lover in an Alpine resort that Christmas, returning to Zurich in January to apply his new wave equation to some of the key problems that were being thrown up by atomic physics. ‘A late erotic outburst’ was how Hermann Weyl, a close friend of Schrödinger (and his wife’s lover), would describe the deluge of academic papers that were to follow. Among them was a complete description of the hydrogen atom spectrum based on his theory and a version of his equation that showed how the waves evolved over time.

• Heisenberg was even blunter about the failings of Schrödinger’s wave mechanics. ‘It’s crap,’ he wrote to Pauli. He was particularly disturbed by the physical picture that Schrödinger was trying to paint of the atom’s inner workings.

• Paul Dirac, whom novelist Ian McEwan describes as ‘a man entirely claimed by science, bereft of small talk and other human skills’. His Cambridge colleagues even named a unit of speech after him: a ‘dirac’ amounted to a single, solitary word per hour.

• Paul Dirac, whom novelist Ian McEwan describes as ‘a man entirely claimed by science, bereft of small talk and other human skills’. His Cambridge colleagues even named a unit of speech after him: a ‘dirac’ amounted to a single, solitary word per hour. Dirac would later fall in love with and marry Margit Wigner, the sister of Johnny’s school friend Eugene. He would even learn to tell a joke or two. But in the 1920s, the young Dirac was a man who cared little for anything other than advanced physics and who, in the words of Freeman Dyson, ‘seemed to be able to conjure laws of nature from pure thought’.

• German, not English, was the language of science in the 1920s. Practically all the founding papers of quantum mechanics were written in it. There was a flood of congresses and conferences for young researchers to attend.

• Von Neumann’s usual approach to giving seminars was not to spoil them by over-preparing. He would often think through what he might say on the train journey to the conference, turn up at the seminar with no notes and then race through the maths. If he filled up the blackboard, he would rub out a swathe of earlier equations and plough on. Those not as quick on the uptake as he was – i.e. nearly everyone – referred to his inimitable seminar style as ‘proof by erasure’.

• Abraham Pais recalled ‘that during one walk Einstein suddenly stopped, turned to me and asked whether I really believed that the moon exists only when I look at it’.

• The scheme to entice the two Hungarians had been cooked up by Oswald Veblen, a distinguished Princeton professor of mathematics. America was an intellectual backwater and Veblen wanted to change that by poaching some of Europe’s most brilliant mathematicians with the offer of huge American salaries. He had secured millions of dollars from the Rockefeller foundation and wealthy private donors to erect a grand new building, named Fine Hall, for the mathematics department. Now he just needed the mathematicians to fill it.

• ‘Jancsi felt at home in America from the first day,’ Wigner continued. ‘He was a cheerful man, an optimist who loved money and believed firmly in human progress. Such men were far more common in the United States than in the Jewish circles of central Europe.’

• ‘I do not see that the sex of the candidate is an argument against her admission,’ he retorted. ‘We are a university, not a bath house.’

• One of the first acts of the new regime was to introduce the ‘Law for the Restoration of the Professional Civil Service’, which called for the removal of Jewish employees and anyone with communist leanings. In Germany, university staff are officially appointed and paid directly by the government. About 5 per cent of all civil servants lost their jobs. But physics and mathematics departments were devastated: 15 per cent of physicists and 18. per cent of mathematicians were dismissed.

• Twenty of the ousted researchers were either already Nobel laureates or future recipients of the prize. Some 80 per cent were Jews.

• Back in Princeton, Wigner faced a quandary. Princeton had extended his contract for five years along with von Neumann’s but he felt guilty about turning his back on Europe. He turned to his friend for advice. ‘Von Neumann,’ Wigner said, ‘asked me a simple question: Why should we stay in a part of the world where we are no longer welcome?

• In June that same year, von Neumann wrote to Veblen: ‘If these boys continue for only two more years (which is unfortunately very probable), they will ruin German science for a generation – at least.’

• The economist Fabian Waldinger recently analysed the impact of the dismissals on German research. Scientific productivity dropped like a stone: researchers produced a third fewer papers than before. The ‘Aryan’ scientists recruited to replace those forced to leave were generally of a lower calibre. He found that university science departments that were bombed during the war recovered by the 1960s, but those that had lost staff remained sub-par well into the 1980s. ‘These calculations suggest that the dismissal of scientists in Nazi Germany contributed about nine times more to the decline of German science than physical destruction during WWII,’

• Heisenberg stayed, only to be branded a ‘white Jew’ for his adherence to the theories of Einstein.

• Next year, when Rust attended a banquet at Göttingen, he asked Hilbert whether it was true that mathematics had suffered after the removal of Jews. ‘Suffered?’ replied Hilbert. ‘It hasn’t suffered, Herr Minister. It just doesn’t exist anymore

• Bohr: I don’t think anyone has yet discovered a way you can use theoretical physics to kill people. Michael Frayn, Copenhagen, 1998

• ‘You and I could have a lot of fun together,’ he told her, ‘for instance, you like to drink wine and so do I.’

• Next, there was the problem of getting about. Von Neumann enjoyed driving very much but had never passed a test. At Mariette’s suggestion, he bribed a driving examiner. This did nothing to improve his driving.

• He sped along crowded roads as if they were many-body problems to be negotiated by calculating the best route through on the fly. He often failed, and an intersection in Princeton was soon christened ‘von Neumann corner’ on account of the many accidents he had there.

• Envious Princetonians dubbed the moneyed academy a stone’s throw away ‘the Institute for Advanced Salaries’ and ‘the Institute for Advanced Lunch’. Unused to the gilded existence, some professors would lapse into somnolence. ‘These poor bastards could now sit and think clearly all by themselves, OK?’ wrote one critic, the Nobel Prize-winning physicist Richard Feynman. ‘They have every opportunity to do something, and they’re not getting any ideas … Nothing happens because there’s not enough real activity and challenge:

• He feared that during that war, European Jews would suffer a genocide as the Armenians had under the Ottoman Empire. In 1940, he predicted that Britain would be able to hold a German invasion at bay (far from obvious at the time), and that America would join the war the following year (as it did after the bombing of Pearl Harbor).

• ‘Johnny preferred admirals to generals, because the generals drank iced water for lunch, while the admirals when ashore drank liquor,’ said Leslie Simon, a director of the BRL.

• The massive effort to build the atom bomb, codenamed Project Y, would cost the US $ billion (more than $ billion today) and at its height employ more than 100, people. In September 1942, the forty-six-year-old Army engineer Leslie Groves was appointed to lead it. The very next month, Groves chose Oppenheimer to head the top-secret laboratory that would develop the bomb.

• Worst of all, from the military’s standpoint, he was a left-winger whose closest associates – his girlfriend, wife, brother and sister-in-law – had been, and perhaps still were, members of the Communist Party. Even Oppenheimer’s landlady in Berkeley was a communist.

• These facts would be used to strip Oppenheimer of his security clearance in 1954, a public act of humiliation that effectively ended his work for the government.

• Von Neumann was irked when newspapers reported that he had received the medal for showing that a ‘miss was better than a hit’. He had actually discovered that large bombs cause far more damage over a wider area when they are detonated in the air above their target than on the ground. The principle was well known, but von Neumann showed that the effect of an airburst was much larger than previously thought,

• Oppenheimer reached for poetry, recalling a verse from ancient Hindu scripture, the Bhagavad Gita, which he had read in the original Sanskrit. ‘Now I am become Death,’ he said, ‘the destroyer of worlds.’ Bainbridge was pithier. ‘Now we are all sons of bitches,’ he told Oppenheimer.

• In the end, Truman sidled over to the Russian leader and told him that the United States now possessed a ‘new weapon of unusual destructive force’. Stalin, completely unperturbed, told him to make good use of it. Spies in the Manhattan Project had long ago told Stalin everything he needed to know.

• Shortly after the end of the war, Stalin asked Truman to grant his ‘modest wish’ to occupy Hokkaido, Japan’s second-largest island. Truman refused. Possession of the atom bomb had stiffened the resolve of the American government.

• On 6 August, the Enola Gay took off before dawn from Tinian. Good weather allowed Little Boy to be dropped on the primary target of Hiroshima, but a crosswind blew the bomb away from the aiming point, Aioi Bridge, so that it detonated 1, feet ( metres) above Shima hospital, modelled by its founder on the Mayo clinic in Rochester, Minnesota.

• The explosion, equivalent to about 17, tons of TNT, and the resulting firestorm killed some 70, people, mostly civilians. Many thousands more would die from burns and radiation poisoning by the end of the year.

• Little Boy and Fat Man claimed more lives in minutes than the senseless firebombing of Dresden by hundreds of Allied (mostly British) aircraft. No decision of such magnitude should pass into the annals of history unscrutinized, and no schoolchild taught to accept uncritically that the horrors visited on the citizens of those two cities can be justified.

• ‘I began to look backward and ask myself how it happened that I let myself become involved in this crazy game of murder,’ he says. ‘Since the beginning of the war I had been retreating step by step from one moral position to another, until at the end I had no moral position at all.’

• intellectually dynamic but psychologically frail Austrian mathematician Kurt Gödel would demonstrate that it is impossible to prove that mathematics is either complete or consistent. Five years after Gödel’s breakthrough, a twenty-three-year-old Turing would attack Hilbert’s ‘decision problem’ (Entscheidungsproblem) in a way completely unanticipated by any other logician, conjuring up an imaginary machine to show that mathematics is not decidable

• One can,’ he ventured modestly, ‘even give examples of propositions (and in fact of those of the type of Goldbach or Fermat) that, while contentually true, are unprovable in the formal system of classical mathematics.’ In other words, there are truths in mathematics that cannot be proven by mathematics. Mathematics is not complete.

• Gödel had announced one of the foremost intellectual feats of the twentieth century. He must have been rather piqued when the response to this revelation was even more muted than the perfunctory praise that had greeted his thesis. The assemblage politely ignored his carefully prepared one-sentence bombshell as if he had cracked a bad joke at a dinner party.

• Yet it appears that only one person grasped the import of Gödel’s achievement well enough to want to know more. After the round table was over, von Neumann, there as a trusted evangelist for Hilbert’s programme, grabbed Gödel by the sleeve and steered him to a quiet corner to grill him about his methods.

• The following day Hilbert gave his retirement address, a passionate speech in which he declared again there were no unsolvable problems in mathematics and uttered the words that would become the epitaph on his gravestone: We must know – we will know. But Gödel had already proved him wrong.

• At the heart of Gödel’s proof was a restatement of the liar’s paradox. In its usual form, the paradox can be phrased: ‘This sentence is false.’ Awkwardly, this is only true if it is false – a fact that has tied grammarians and logicians in knots for centuries.

• While others were still grappling with Gödel’s work, von Neumann immediately understood what Hilbert, and even Gödel himself, would struggle to accept. ‘My personal opinion,’ he said, ‘which is shared by many others, is that Gödel has shown that Hilbert’s program is essentially hopeless.’ Von Neumann called Gödel the greatest logician since Aristotle and gave up working on the foundations of mathematics.

• When, after Austria was annexed into Nazi Germany in 1938, Gödel was denied a post at the University of Vienna partly for having ‘always travelled in liberal-Jewish circles’, von Neumann would campaign to bring him to the IAS. ‘Gödel is absolutely irreplaceable; he is the only mathematician alive about whom I would dare to make this statement,’ he wrote to Flexner. ‘Salvaging him from the wreck of Europe is one of the great single contributions anyone could make to science at this moment.’

• He was successful. In Princeton, Gödel became convinced that the radiators and refrigerator in his home were emitting poisonous gas and had them removed, shivering through his first few winters. He would sometimes wander into von Neumann’s house in his absence, pick up a book and start reading. Once he had finished, he would replace the book and leave – all without saying a word to von Neumann’s young wife.

• He was successful. In Princeton, Gödel became convinced that the radiators and refrigerator in his home were emitting poisonous gas and had them removed, shivering through his first few winters. He would sometimes wander into von Neumann’s house in his absence, pick up a book and start reading. Once he had finished, he would replace the book and leave – all without saying a word to von Neumann’s young wife. He often walked home from the institute with Einstein, engrossed in gentle disagreements about politics, physics and philosophy. The solemn young logician and the gregarious physicist, now in his sixties, made an odd couple but nonetheless derived great pleasure from each other’s company.

• Like Schrödinger’s famous description of an alive-dead cat, published exactly twelve months earlier, Turing’s machine was a thought experiment. ‘Schrödinger was not trying to advance the state of the art of feline euthanasia,’ says Haigh. ‘Neither was Turing proposing the construction of a new kind of calculating machine.’

• Computer designers now refer to the whole configuration as the ‘von Neumann architecture’, and nearly all computers in use today – smart phones, laptops, desktops – are built according to its precepts.

• Computer designers now refer to the whole configuration as the ‘von Neumann architecture’, and nearly all computers in use today – smart phones, laptops, desktops – are built according to its precepts. The design’s fundamental drawback, now called the ‘von Neumann bottleneck’, is that instructions or data have to be found and fetched serially from memory – like standing in a line, and being able to pass messages only forwards or backwards. That task takes much longer than any subsequent processing. That handicap is outweighed by the architecture’s considerable advantages, which stem from its simplicity.

• What had become the longest trial in the history of the federal court system concluded with the ruling that the most valuable invention of the twentieth century could not be patented. The open source movement, born a decade or so later, would soon shun corporate secrecy, lauding the benefits of freely sharing information to drive forward innovation. Thanks to von Neumann those principles were baked into computing from the very beginning.

• Around this time, he met an old friend, Gleb Wataghin, a Russian-Italian physicist who had recently returned from Brazil. ‘I suppose you are not interested in mathematics anymore,’ Wataghin teased. ‘I hear you are now thinking about nothing but bombs.’ ‘That is quite wrong,’ von Neumann replied. ‘I am thinking about something much more important than bombs. I am thinking about computers.’

• Ulam realized that many real-world problems are surprisingly similar in nature to working out the chances of winning solitaire. A complex situation can be made tractable by setting up a model that is then run repeatedly to reveal the most likely outcomes. ‘It’s infinitely cheaper to imitate a physical process in a computer and make experiments on paper, as it were, rather than reality,’ Ulam explained later. Monte Carlo made simulating a chain reaction possible for the first time. There are a vast number of different ways in which an assembly of neutrons might behave – too many to calculate.

• By the 1960s, IBM manufactured about 70 per cent of the world’s electronic computers. ‘Probably’, Teller told his biographers, ‘the IBM company owes half its money to Johnny von Neumann.’

• ‘A tidal wave of computational power was about to break and inundate everything in science and much elsewhere, and things would never be the same.’

• ‘Omar Little: I got the shotgun. You got the briefcase. It’s all in the game, though, right?’ From The Wire, 2003

• child custody arrangements that he and his first wife Mariette came up with for their daughter, Marina, when she was just two years old. The two agreed that until the age of twelve, Marina would live with her mother and spend holidays with her father. After that, when she was ‘approaching the age of reason’, Marina would live with her father to receive the benefit of his genius.

• ‘It was a thoughtful and well-intentioned agreement,’ Marina says in her memoirs, ‘but they were too inexperienced to realize that adolescence is often the stage in life farthest removed from the age of reason.’

• Game theory sprang from von Neumann’s urge to find neat mathematical solutions to knotty real-world problems during one of the most ‘disorderly and irrational’ periods in human history. The answers of game theory sometimes seem cold, unconventional, shorn of the complexities of human emotion

• ‘No, no,’ he said. ‘Chess is not a game. Chess is a well-defined form of computation. You may not be able to work out the answers, but in theory there must be a solution, a right procedure in any position.

• ‘It is not enough to succeed. Others must fail,’ Iris Murdoch once wrote.

• Von Neumann coined the term ‘zero-sum’ to describe such games of total conflict, in which one person’s loss is the other’s gain. One indication of the influence of game theory is that ‘zero-sum’ has now passed into the vernacular.

• ‘Other mathematicians prove what they can,’ she declared, ‘von Neumann proves what he wants.’

• He delivered the unscripted talk in German, and though most present could be expected to have understood him, von Neumann’s machine-gun delivery accompanied by his usual habit of wiping the blackboard clean before anyone could catch up with him probably explained why his thoughts did not immediately reach a wider audience.

• Privately, he was less diplomatic. ‘If these books are unearthed sometime a few hundred years hence, people will not believe that they were written in our time,’ von Neumann confided to a friend in 1947, referring to some of the discipline’s most lauded contemporary works. ‘Rather they will think that they are about contemporary with Newton, so primitive is their mathematics. Economics is simply still a million miles away from the state in which an advanced science is, such as physics.’

• discovered principally through the Jewish economist Ludwig von Mises the classical liberalism of the Austrian School. Mises’s belief in the power of free markets put him at odds with other Jewish professors, who were mostly left-leaning progressives. Without their support, Mises was unable to overcome the general antipathy of the gentile faculty and never secured a tenured position. He was still extraordinarily influential.

• Morgenstern was deemed ‘politically unbearable’ and summarily dismissed from his job. The Anschluss appears to have cured Morgenstern of his anti-Semitism. The snide jibes aimed at Jews largely disappear from his diaries after 1938. His own family in Austria were forced to prove their Aryan ancestry (which they did, back to the 1500s).

• position at the Institute,’ he grumbled. Morgenstern found Princeton to be much as Einstein had described it five years earlier; ‘a quaint and ceremonious village of puny demigods on stilts’.

• ‘Economists simply don’t know what science means,’ he complained privately. ‘I am quite disgusted with all of this garbage.’ John Maynard Keynes, whose thinking shaped government policy the world over for much of the twentieth century, was ‘one of the biggest charlatans who has ever appeared on the economic scene’, said Morgenstern. ‘And everybody is on their belly before him.’

• Between helping to invent the design principles of digital circuits and modern information theory, American mathematician Claude Shannon calculated that there are at least 10120 possible games of chess – comfortably more than the number of elementary particles in the universe.

• Poker is a game of imperfect information. In many ways, it is the game of imperfect information. That a player does not know what cards other participants are holding is what makes the game fun and exciting at all. An optimal strategy for poker must embrace this uncertainty.

• However, a smart opponent will quickly depart from their ‘optimal’ strategy by passing whenever the non-bluffing player bids high and throwing in more bluffs themselves. As Binmore says, ‘The point of bluffing is not so much that you might win with a bad hand, as that you want to encourage the opposition to bet with middle-range hands when you have a good hand.’

• ‘Zero-sum games are to the theory of games what the twelve-bar blues is to jazz: a polar case, and a historical point of departure,’ says economist Michael Bacharach.

• By the time von Neumann and Morgenstern embarked on their opus in the 1940s, economists had begun to recognize that monopolistic competition was not the exception but the rule. In the mid-twentieth century, the Big Three or Four were the behemoths of the oil and car industries – Standard Oil, or Ford and General Motors. Today the monopolists are more likely to be drawn from the ranks of tech giants such as Facebook, Apple, Amazon or Google.

• Theory of Games illustrates why, without tough anti-trust laws and incessant vigilance, monopolies and oligopolies spring up like weeds. In a market dominated by one or a few big firms, each would naturally use its heft to maximize profits. Even with no active collusion, they push up prices for consumers as if they had formed one of von Neumann and Morgenstern’s coalitions.

• Despite the many plaudits, game theory did not immediately catch on with economists. The book was too mathematical. Even at Princeton, where the mathematics department quickly became a hotbed for research on the subject, the economics department was hostile.

• Ostrom described how locals invented ways to protect such resources. In Nepal, for instance, she found that cattle belonging to farmers who had failed to follow rules for water usage were interned in a ‘cow jail’ until a fine was paid to secure their release.

• Others took Hamilton’s work forward, including George Price, a chemist who worked on the Manhattan Project before moving to Britain and making some decisive contributions to evolutionary theory. First, Price wrote an equation that extended Hamilton’s ideas to include all evolutionary change – not just traits that benefit family members. This elegant mathematical interpretation of natural selection is now known as the Price Equation.

• Hamilton would, among other contributions to the field, produce a mathematical model of altruism based on the degree of relatedness (kinship) between different organisms. He showed that genes for self-sacrificing behaviours would spread as long as they benefited blood relatives (who were also likely to carry the same genes

• Price became so appalled by the idea that altruistic behaviour could be adequately explained by selfishness, rather than by the existence of some nobler motivation, that he took to performing random acts of kindness in a bid to convince himself he was mistaken. He ultimately became so depressed that, in 1975, he ended his own life by slitting his carotid artery with a pair of nail scissors.

• The Soviet newspaper Pravda once branded the organization based at the pink and white stucco building the ‘American academy for death and destruction’.

• RAND for ‘Research ANd Development’.

• There was even resistance to the idea of ordering blackboards and chalk (which the academics wanted in four different colours).

• The game, later named ‘So Long, Sucker’, was designed to push people to their psychological limit: some married couples reputedly went home in separate cabs after a night of play.

• Nash nervously started to present what would turn out to be his greatest – and final – contribution to game theory. He had come up with a mathematical framework allowing the analysis of any type of game – whether zero-sum or not – with any number of participants, and showed that there are certain outcomes for all games in which no player can do any better by unilaterally changing their strategy. These kinds of solutions to a game are now called Nash equilibria. It was a staggering accomplishment, though no one, least of all Nash, had any idea how thoroughly useful his idea would prove to be. There was one catch: in Nash’s scheme, players were not allowed to communicate or team up – almost as if they were caught in a perpetual final round of ‘Fuck your buddy!’ Von Neumann hated it.

• ‘His hatred, his loathing for the Nazis was essentially boundless,’ says Klári. ‘They came and destroyed the world of this perfect intellectual setting. In quick order they dispersed the concentration of minds and substituted concentration camps where many of those who were not quick enough … perished in the most horrible ways.’

• Ironically, just as von Neumann was abandoning the doctrine of preventive war, it effectively became US policy.

• The four-week hearing had begun on 12 April 1954. Oppenheimer’s security clearance was stripped on 29 June. In 2009, historians with access to the KGB archives found that Soviet intelligence had made many attempts to recruit Oppenheimer – but failed

• LeMay’s preferred nuclear strategy, the ‘Sunday Punch’, was ‘Massive Retaliation’ by another name: a no-holds-barred attack on the Soviet Union with every atom bomb at SAC’s disposal in response to any aggression. If there was, as RAND now claimed, a risk of a Soviet surprise attack then, why, that was sufficient reason to hit them first. It was not so much a war plan, Kahn told SAC officers, as a ‘war orgasm’.

• Three hundred years earlier, when the philosopher René Descartes declared ‘the body to be nothing but a machine’ his student, the twenty-three-year-old Queen Christina of Sweden, is said to have challenged him: ‘I never saw my clock making babies’.

• Or, as Freeman Dyson put it, ‘So far as we know, the basic design of every microorganism larger than a virus is precisely as von Neumann said it should be.’

• ‘Floccinaucinihilipilification’, meaning ‘the habit of regarding something as worthless’, was Conway’s favourite word

• I heard about one mathematician who worked for a large corporation. He had a button concealed under his desk. If he was exploring Life, and someone from management entered the room, he would press the button and the machine would go back to working on some problem related to the company!

• The 1,-page tome starts with characteristic modesty. ‘Three centuries ago science was transformed by the dramatic new idea that rules based on mathematical equations could be used to describe the natural world,’ he declares. ‘My purpose in this book is to initiate another such transformation.’

• ‘There’s a tradition of scientists approaching senility to come up with grand, improbable theories,’ Freeman Dyson told Newsweek after the book’s release. ‘Wolfram is unusual in that he’s doing this in his 40s.’

• ‘If people do not believe that mathematics is simple,’ von Neumann once said, ‘it is only because they do not realize how complicated life is.’

• Schelling had produced two powerful conclusions with a fairly elementary model. First, cities can become segregated along lines of race even if no one minds living in a mixed community. Second, only an active desire for diversity leads to diverse neighbourhoods. Indifference results in segregation.

• Brains don’t look so impressive. A neuron can fire perhaps 100 times a second, while the best computers at the time were already able to carry out a million or more operations a second – and a modern laptop is at least a thousand times faster than this. Worse, neurons were billions of times less accurate than computer components: every time a signal is transmitted from one neuron to another, there is a risk that errors are exacerbated.

• ‘Von Neumann, when I was there at Princeton, was under extreme pressure,’ says Benoît Mandelbrot, who had come to the IAS in 1953 at von Neumann’s invitation, ‘from mathematicians, who were despising him for no longer being a mathematician; by the physicists, who were despising him for never having been a real physicist; and by everybody for having brought to Princeton this collection of low-class individuals called “programmers”’. ‘Von Neumann,’ Mandelbrot continues, ‘was simply being shunned. And he was not a man to take it.’