The Man from the Future: The Visionary Ideas of John von Neumann

John von Neumann’s second wife, Klári, called him a “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.” The Man from the Future deftly presents his era, his vast intellectual scope, and the impact of the scientific revolutions “Johnny” sparked. Londoner Ananyo Bhattacharya, a science writer and physicist, is the perfect guide.

 

Born in 1903 in Jewish Budapest, young Jancsi displayed a prodigious intelligence and appetite for mathematics. His banker father agreed to a mathematics doctorate (which “does not make money”) in Budapest only along with chemistry in Berlin, followed by a chemical engineering doctorate in Zurich. Jancsi throve on the imposing workload and frenetic travel, an insanely rapid pace he kept throughout his life.

 

Quickly publishing on the zeros of Chebyshev’s polynomials, the young scholar turned to the foundational crisis that had captivated every ambitious peer. The resulting articles confirmed he was a rising star. The subtleties of the topic showcase the author’s creativity and skill as he illustrates, for example, von Neumann’s recursive definition of ordinal numbers and the concept of cardinal numbers using LEGOs.

 

Upon settling in Gottingen in 1926, Jancsi became a favorite of the world’s most influential mathematician, David Hilbert. Intrigued by new work on quantum mechanics, the young scholar established a rigorous mathematical proof that the two leading, and apparently opposing, theories (Schrodinger’s wave mechanics and Heisenberg’s matrix mechanics) are basically two sides of the same coin. His 1932 book, Mathematical Foundations of Quantum Mechanics, is a masterpiece. Bhattacharya closes this plunge into quantum physics with an evenhanded discussion of disputes over von Neumann’s theorem that a quantum theory with hidden variables is impossible.

 

While developing the mathematics of quantum mechanics, von Neumann was briefly but deeply absorbed by operator algebras on Hilbert spaces (a term he coined) and their properties. His pioneering classification and study of these algebras, which exceeded 500 pages, is his most voluminous contribution to pure mathematics.

 

Brief appointments at the Universities of Berlin and Hamburg led to a visiting professorship at Princeton University. The outgoing, high-spirited man immediately felt at home in America, taking the name Johnny, though never losing his heavy Hungarian accent.

 

In 1933, a permanent position was offered at the new Institute for Advanced Study. While many eminent professors saw their ideas dry up in that ivory tower, von Neumann had a constant overflow of ideas, offset by a tendency to quickly lose interest. With every breakthrough (and his repeated flashes of genius brought many), Johnny snatched a few large juicy fruits and left the gleanings to others more patient and persevering. His most important contribution during this period was within ergodic theory. After the American George Birkhoff used it to establish a more robust theorem, von Neumann’s great sense of courtesy led him to quietly renounce a claim of co-authorship on the second incompleteness theorem.

 

The Hungarian foresaw in the early 1930s how events in the European theater would have disastrous consequences, and in wartime Von Neumann put his immense talent at the service of his adopted country. Well-versed in the mathematics of shock waves from bomb explosions, he became a world expert on shaped charges, which proved critical to the Manhattan Project. His post-war work at Los Alamos on the H-bomb confirmed that the complex design calculations demanded new computer technologies, and von Neumann used his impressive network of contacts within the government to ensure sufficient funding. 

 

Bhattacharya contends that von Neumann’s work in mathematical logic and set theory early in his career prepared him for the advent of the modern computer. In a 1945 memo, von Neumann drew on the abstract work of Austrian logician Kurt Gödel and British mathematician Alan Turing to produce the canonical model for the stored-program computer. The preliminary draft, leaked to dozens of scientists and engineers, greatly accelerated the development of computers, but cost computing pioneers their competitive edge. The ensuing battle over intellectual property and patent rights continued long after Johnny’s death, and not until 1973 was the electronic digital computer ruled to be in the public domain. The author also includes Klári von Neumann’s contribution to the development of programming.

 

Besides computer design and consulting activities in and outside the government, von Neumann continued his initiatives in theoretical computer science. His paper for the Hixon Symposium on Cerebral Mechanisms in Behavior in 1948 asked whether it was possible to design an automaton capable of creating copies of itself or variants at least as complex. An unfinished manuscript published posthumously in 1966, Theory of Self-reproducing Automata, demonstrated the logical possibility of self-replication, and his detailed master plan for assembling a self-replicating virtual creature within a cellular automaton captivated imaginative, original scientists such as John H. Conway and Stephen Wolfram. Johnny thus inspired the very simple (and yet Turing complete) Game of Life as well as the highly controversial Theory of Everything. 

 

Von Neumann’s famous mini-max theorem in 1926 was the first mathematical formulation of individual cooperation and competition, and he remains inextricably linked with game theory. But having reduced the strategy game to its simplest device, von Neumann as usual let his attention drift away. It took a fascinated and tenacious German economist to draw him back for an atypically long period of intensive work. The result was a seminal text in 1944, Theory of Games and Economic Behavior, but von Neumann never achieved a complete and definitive description of rational games, nor a general theory covering any number of players. Still, the book won critical acclaim and drew many mathematicians to the field of economics, transforming this discipline with new mathematical methods.

 

Throughout this well-crafted biography, the author skillfully highlights von Neumann’s political discernment and his ability to disregard the incidental to better focus on the essential. Von Neumann is often portrayed as a war hawk who argued for a pre-emptive nuclear strike against the Soviet Union, whose ideology he abhorred. Yet when J. Robert Oppenheimer, the former scientific director of the Manhattan Project who now advocated nuclear disarmament, was accused of being a Russian spy, Johnny organized his defense. Bhattacharya finds little support for the charge that the Hungarian applied a rigid analytical grid drawn from game theory to the Cold War.

 

In 1955 von Neumann was diagnosed with aggressive bone cancer that soon metastasized to his organs. To the surprise of those close to him, he asked for a Catholic priest. Was he making Pascal’s wager? No one can say. In any case, his love of life and fear of death did not leave him until his legendary mental faculties failed. Just 53, the Hungarian genius died on February 8, 1957.

 

Norman Macrae’s portrait, John von Neumann: The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More, puts into perspective some familiar anecdotes about the subject’s computational and mnemonic feats. Istvan Hargittai’s Martians of Science and The Martian’s Daughter: A Memoir, by the economist, businesswoman, and academic Marina von Neumann Whitman (Johnny’s only daughter), also shed light on the society that shaped him. However, for a scrutiny of every sphere explored by the Hungarian prodigy, as well as a clear and up-to-date summary of his impact, Ananyo Bhattacharya’s The Man from the Future is the ultimate reference.

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Frederic Morneau-Guerin is a professor in the Department of Education at Universite TELUQ. He holds a Ph.D. in abstract harmonic analysis.