Von Neumann's most exceptional and underappreciated trait was that he embraced applying mathematics to real-world problems, unlike most mathematicians who prefer to stay in an 'ivory tower'; this engagement with reality (including military work) was the source of his most interesting and original output rather than a distraction from it.

Von Neumann's actual game theory, as developed with Morgenstern, centered on cooperation and stable coalition solutions (e.g., players in a multiplayer game ganging up on the leader), not zero-sum thinking; the zero-sum/prisoner's-dilemma framing of nuclear strategy came from others inspired by him, and the prisoner's dilemma itself is non-zero-sum, so the 'Dr. Strangelove' caricature of him as a cold zero-sum thinker is mistaken.

Von Neumann was born in Budapest around 1903 to a wealthy Jewish family and showed prodigious ability early: six-figure mental calculations by age six, calculus by eight, and teaching set theory to the older Eugene Wigner by around eleven.

Von Neumann was a comparative outlier among the era's left-leaning, socialism-sympathetic scientists because his formative experiences—Hungary's brutal six-month communist regime, the even worse authoritarian Horthy counter-regime with public hangings and killings of Jews, and the Nazi destruction of German science—made him deeply allergic to authoritarianism and suspicious of Stalin from the start, so as a committed democrat he sought to put his expertise in the hands of the elected US government rather than make decisions for it.

Von Neumann lost interest in game theory once computing came to the fore, instead computing solutions to military duels (e.g., when a plane and a tank or submarine and ship should fire) and helping RAND realize their own computer ambitions.

Von Neumann's self-reproducing automata / universal constructor was an idea ahead of its time whose influence is only now becoming visible—seen in xenobots (stem cells designed by neural nets that gather other stem cells), nanotechnology's molecular constructors, the RepRap self-printing 3D printer, and self-replicating space probes.

The cluster of Hungarian Jewish 'Martian' geniuses arose because growing up amid Central European anti-Semitism between the world wars created relentless psychological pressure to 'succeed or face extinction,' combined with elite private (mostly all-boys) schools that nurtured exceptional talent.

Von Neumann's extraordinary productivity depended on a historical moment that cannot be repeated: he arrived during the logical crisis in mathematics and the explosion of quantum mechanics into the atom bomb within ~25 years, plus massive new science funding, and increasing specialization since then means no single genius could now contribute across pure math, quantum mechanics, physics, computing, and automata as he did.

Von Neumann's apparent advocacy of a preemptive strike on the Soviet Union ('if you say bomb them tomorrow I say why not today') was a rational response to context: he had successfully predicted WWII and the Holocaust years in advance and was convinced a nuclear third world war was inevitable within a decade, so weighing 100,000 immediate deaths against millions of future deaths and the end of civilization could appear coldly rational—and this preemptive-strike view was surprisingly common in late-1940s America, even shared by pacifist Bertrand Russell.

Von Neumann's mature (1950s) nuclear strategy paper rejected an all-out preemptive strike in favor of graduated, restrained escalation—if one side destroys a city the other responds proportionally rather than launching everything at once—anticipating the more complex strategic thinking that developed at RAND, because he believed it would be insane to go all-out when multiple sides could destroy the world many times over.

One should not draw self-help lessons from von Neumann's lifestyle: his incessant morning-to-night thinking cost him his human relationships (his first wife left him because he was too busy thinking), and he died in abject terror of mortality as cancer eroded his mind, so a sustainable, individually-fitting work schedule is preferable to imitating a superhuman.

Game theory was driven by an early-20th-century mathematical confidence that math, having been so successful, could be applied to anything—including human behavior, which psychologists had failed to understand—so von Neumann sought to do 'the maths' on conflict and cooperation, ultimately recasting economics in mathematical terms.

Stephen Wolfram is the only other person comparably gifted mathematically with interest in practical affairs, and might have become a von Neumann-like figure had he been born in 1903 rather than at 'the wrong time.'

Von Neumann was a deeply conflicted but quietly generous person—privately arranging for math textbooks to be sent to a Hungarian builder in America, writing references long before his death that later helped Mandelbrot get work, and helping scientists including Gödel escape Nazi Europe—so he cannot be reduced to either the Dr. Strangelove caricature or a bleeding-heart liberal.

Von Neumann's grandfather, though not academically successful, possessed mental calculation abilities that exceeded von Neumann's own, suggesting a genetic predisposition to such abilities in the family.

Von Neumann's productivity at the Institute for Advanced Study contrasted sharply with Einstein and Gödel, who became unproductive there despite the ideal environment, whereas von Neumann invented whole new fields and birthed the modern computer there.

Von Neumann can be considered a godfather of the open source movement because his proof that automata could reproduce themselves and evolve emerged from deep engagement with real-world problems.

There is no general 'Hungarian phenomenon'; the only phenomenon needing explanation is von Neumann himself, as Wigner remarked when asked about the Martians.

Von Neumann's father, a self-made investment banker, invested in technology firms including a Jacquard loom company that used punch cards to program looms, which influenced von Neumann's later thinking.

Von Neumann resolved an incredibly difficult paradox in set theory by about age 22 in his PhD, then produced the first mathematically rigorous version of quantum mechanics a few years later at Göttingen.