Review by Terence Jagger
This is a lively and compelling biography of one of the intellectual giants of the twentieth century, who has somehow escaped the notice of the general reader and is not as well known as Einstein, Bohr, Heisenberg and so on. But he made contributions to so many different fields that this is quite wrong – indeed he ought to be famous for any one of several achievements. Of course, the very technical nature of all von Neumann’s work is a real challenge for the biographer and his ability to get the issues and the achievements across to the general reader, but Bhattacharya does an excellent job.
Neumann Janos (the name was anglicised and reversed later) was born in Hungary in 1903, and died of bone cancer in the United States aged only 53. He had an extraordinary brain, focused on mathematics, but was also brilliant in linguistics, history and many other fields, aided by a prodigious memory which meant he could recite verbatim whole chapters of an historical encyclopaedia read decades before. He worked on widely disparate issues at the same time, understood other people’s fields almost depressingly quickly for people who had struggled for years on problems he solved within a few minutes, and often lit touch-papers in others and moved on, losing the formal credit while astonishing all around him. Jacob Bronowski, no mean intellect, calls him the cleverest man I ever knew, without exception. And it was through Bronowski’s Ascent of Man BBC documentary that I first came across von Neumann in 1973, and I will come back to his views later.
He started early; aged 17, he authored a paper on polynomials, and his style was immediately evident: “Johnny’s unique gift as a mathematician was to transform problems in all areas of mathematics into problems of logic”, said Freeman Dyson. And he quickly made a contribution to one of the pressing issues of twentieth century mathematics – could it be entirely rigorous and logical, as Hilbert demanded? Or were there things we could never know through mathematics? Bertrand Russell had run into a frightful problem with set theory – is the set of all possible sets which are not members of themselves a member of itself or not? Both answers are illogical, and this kind of crack in the foundations of mathematics worried many – but in 1921, Neumann rescued numbers from this dilemma in a confident paper. Also in 1921, he started studying – simultaneously! – for a degree in chemical engineering in Basel and a mathematics doctorate in Budapest, in both of which he was outstandingly successful.
To Göttingen – then the centre of the mathematical world – and on to Berlin; working with Dirac, Heisenberg, and Max Born, he made huge contributions to settling the mathematical foundations of quantum mechanics. But the rise of National Socialism forced him to move to the United States in 1930, where he lived for the rest of his life. He made hugely important contributions to the atomic bomb programme, both in terms of the optimum height for bomb detonation, and the exact engineering of the bombs to focus the detonation shock wave which would evenly crush the plutonium. This was extraordinary work of international importance – though now, of course, highly contentious – but his big contributions to modern science were yet to come – the invention of the computer, machines to make machines, and game theory (and this misses a lot out).
In 1945, von Neumann turned away from bomb making (although not from defence) to something he considered much more important – machines to do calculations, or computers (a word originally used to refer to the people, mainly women, who did the necessary maths in many complex scientific areas). He had met Turing in the UK during the war, and they had sparked off each other, and this may have been the origin of Neumann’s interest in the field. In post war America, he brought his genius to the development of computers, realising quickly that machines built for solving one particular problem, the normal approach in those days, could have many more applications in defence and industry. He realised that “by making use of coded instructions stored in memory, a single machine of fixed structure could in principle carry out any task for which an instruction table can be written. With [his] report of 30 June 1945, von Neumann would turn Gödel and Turing’s abstract musings into the canonical blueprint for the stored programme computer.” This “von Neumann architecture” is still the structure of almost all modern computers.
Game theory, perhaps his best known contribution to modern thinking about nuclear war, diplomacy, economics, indeed any situation in which different possible outcomes are possible without clear rules for decisions, “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 – but effective nonetheless.” Bhattacharya tells the famous story of Neumann talking to Bronowski in a taxi in London, but I will quote Bronowski himself (in The Ascent of Man):
He first talked to me about his Theory of Games in a taxi in London – one of the favourite places in which he liked to talk about mathematics. And I naturally said to him, since I am an enthusiastic chess player, ‘You mean, the theory of games like chess.’ ‘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. Now real games’, he said, ‘are not like that at all. Real life is not like that. Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do. And that is what games are about in my theory.’
And that is what his book is about. It seems very strange to find a book, large and serious, entitled the Theory of Games and Economic Behavior, in which there is a chapter called ‘Poker and Bluffing’.
The number of situations to which game theory can apply is enormous – and is still growing; in this book, examples are drawn from the Cold War, Holmes being chased by Moriarty, poker, economic regulation of oligopolies, the famous prisoner’s dilemma, and the auction of bandwidth for telephone or radio operators. Easier examples are the finger game of Morra, or Rock, Paper, Scissors, and you can google these and find some fun stuff!
Later in life, von Neumann became interested in machines which can make machines (think 3D printers which can reproduce), and naturally looked at the biological sciences, where, extraordinarily enough for someone with no background in biological sciences, he made considerable contributions. “In his usual way, von Neumann dabbled brilliantly, widely and rather inconclusively in the subject but intuitively hit upon a number of ideas which would prove to be fertile areas of research for others,” (including separation of chromosomes during cell division, bacteriophages, and protein structure). He created virtual beings, on computer screens, which could replicate and evolve, and threw up patterns we can recognise from nature, for example from seashells. And he had insights into biological structures which influenced studies into biological reproduction, including in the discovery of DNA. As Freeman Dyson said,
So far as we know, the basic design of every organism bigger than a virus is precisely as von Neumann said it should be.
Von Neumann was an extraordinary man, mathematical genius, party-goer, anti-Communist, and this book is a good guide to his life and work. However limited your mathematical or scientific knowledge, you will be amazed, and there are so many areas of modern life and modern science he has touched, it is staggering we do not know him better. But perhaps the final word should go to Klari (his second wife), from her memoir of him:
I would like to tell about the man, the strange contradictory and controversial person; childish and good-humoured, sophisticated and savage, brilliantly clever yet with a very limited, almost primitive lack of ability to handle his emotions – an enigma of nature that will have to remain unresolved.
Ananyo Bhattacharya, The Man from the Future – The Visionary Life of John von Neumann (Allen Lane, 2021). 978-0241398852, 284pp., hardback.
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