John von Neumann Shot Lightning From His Arse
Pop-hereditarianism is built on selective credulity
The movie Braveheart has a great scene where, by whispers and tales, the legend grows of the Scottish rebellion leader William Wallace (played by Mel Gibson in one of his best roles).
First that he killed “50 men,” and then no, “100 men!” and was “seven feet tall;” he even, as Gibson jokes, shoots “fireballs from his eyes” and “bolts of lightning from his arse.”
And that’s what I think of when I hear the legends of John von Neumann.
“He could remember every book he’d ever read verbatim!”
No, of course he couldn’t. Indeed, as we will see, John von Neumann, despite being (inarguably) a genius, didn’t even invent the “von Neumann architecture” for computers. He’s just credited with it, as he is with so much else.
Why Does This Matter?
A decade ago, in the grand Nature vs. Nurture debates, proponents on the Nature side regularly said this about the “Blank Slate” side:
“Hey! Those blank slatists over there, those biased journalists and gatekeeping editors of scientific journals, they’re the unreasonable ones! We’re just arguing that Nature is non-zero!”
And that’s sympathetic, for who can argue with “non-zero?”
But with the rise of a new pop-hereditarianism, which has undergone virulent growth on social media websites like the former Twitter, the reverse is now just as true: Pop-hereditarians scoff at the very idea that Nurture’s contribution might be non-zero, fanatically dismissing that even the best education—gasp—could have an effect. Given an inch, they’ve taken a mile, and become annoyingly identical to the blank slatists they once criticized. Much like blank slatism, pop-hereditarianism is built on selective credulity: holding things like meta-analyses of the positive effect of education on IQ to the highest possible standards, while meanwhile, happily accepting the results of poorly-recorded half-century-old twin studies (where the “separated” twins already knew one another and self-selected into the research).
When it comes to the Nature vs. Nurture debate, the truth is in the middle. It will always be in the middle. Yet middles are unsatisfying.
Like most arguments online, facts matter less than symbology. And John von Neumann has become a symbol of pop-hereditarianism.
The funny thing is that, as one of the best educated people of all time, Johnny (as he preferred) is a poor choice as a symbol for pop-hereditarianism. He certainly wasn’t genetically perfect (as we will see), and he wouldn’t have agreed with them anyway, as he also thought education and parenting and cultural milieu matter.1
Last week, when I pointed out that “von” was a marker of nobility on X-Twitter—and that his childhood would make a tiger parent green with envy—this was apparently too much bubble bursting. I got dozens, maybe hundreds, of responses like “cope” and “communist” and some less polite words and a bunch of tall tales as if they were facts.
Here are a few gems I heard from the brain trust on social media:
He could do 8 digit calculations in his head as a 6-year-old (false)
He was fluent in 8 languages as a child (false)
He could recite any book he’d ever read, including telephone books (false)
His first math teacher wept when he met Johnny (false)
The von Neumanns were humble upper-middle-class who purchased a noble title (false)
I’m going to give a history of Johnny that debunks all these. I’ll also correct a great deal of bad scholarship along the way, and show you don’t need to invoke spooky rare variants or genetic dark matter to explain John von Neumann. You just need to do a little research yourself, and accept that places and eras can be just as exceptional as brains.
The Best Education of All Time
The most definitive biography we have is John von Neumann, by economist Norman Macrae. It was supposedly approved of by Johnny’s family, and it’s well-researched and lengthy (unless otherwise specified, quotes come from there). Macrae opens his thesis agreeing with me:
Johnny had exactly the right parental upbringing and went through the early twentieth-century Hungarian education system that (this book will argue) was the most brilliant the world has seen….
So Johnny had innate talent, gobs of it, but he was also a product of a society and an education system that doesn’t exist anymore. Hungarian society produced geniuses at an astonishing rate.
If you are to beget a genius, a boom era in Belle Époque will serve you best. The booming Budapest of 1903, into which Johnny was born, was about to produce one of the most glittering single generations of scientists, writers, artists, musicians, and useful expatriate millionaires to come from one small community since the city-states of the Italian Renaissance…. Remember, as we do, from what a small constituency of upper-middle-class Budapest males—in one fifty-year period and mainly from three great schools—this tribe of world changers came.
What made Hungary so special? It was not a democracy, but an aristocracy transitioning to a plutocracy. Its inequality meant it could establish an extremely favorable-to-the-elite education system, and it did. However, it was also welcoming to new immigrants and new ideas and new money.
It was the twin city where clever little rich boys… (like Johnny) had a cosmopolitan choice of governesses before age ten, and after age ten (provided they could pass exams and pay) a choice between at least three of the world’s best high schools.
In this milieu of turn-of-the-century Budapest Johnny was aristocratically tutored by a “tribe” of tutors and governesses at his 18-room top-floor downtown home until he turned 10. After that, he went to one of those “world’s best high schools.” There, he was taken under the wing of László Rátz, who was described by Eugene Wigner (winner of the Nobel Prize, who was a year ahead of Johnny under Rátz and one of Johnny’s best friends) as one of the greatest math teachers of all time.
Macrae says it was the “Hungarian tradition with infant prodigies” to find them one-on-one tutoring from university professors. Rátz recognized the boy’s talents shortly after Johnny began formal schooling, and began tutoring him personally. He also arranged for a progression of ever-more impressive math tutors over the next eight years (keep in mind, Johnny had been tutored at home in mathematics previous to meeting Rátz, meaning that he was tutored his entire young life). He and his tutors would, it seems, meet multiple times a week, and later on the revolving door of them contained august mathematicians famous in their own right, like Alfréd Haar, Gábor Szegő, Michael Fekete, and Leopold Fejér. Johnny’s first math paper ever was co-authored with his long-time tutor Fekete, at age 17-18, on Fekete’s area of expertise, and Johnny got his PhD under Fejér (also his tutor and a family friend). Johnny would then go on to study mathematics under Hilbert, one of the most renowned mathematicians of all time.
Johnny’s father Max was an intellectual who had an instinct for education and ran mealtimes like seminars. Regular dinner guests “glittered with especial brilliance,” and included Leopold Fejér, who would become Johnny’s PhD supervisor.
Max’s mealtime seminars were an important feature of all his children’s development almost from the nursery…. Families in those pretelevision and precommuting days met for a relatively full and lengthy late lunch. Then father would go back to the office, but the children would not return to ordinary school. Schooltime afternoons in Hungary were for sports or private tuition or study. The whole family would then have a similar lengthy dinner in the evening. The mealtime habit that Max encouraged was that members of the family, including himself, should each present for family analysis and discussion particular subjects that during the day had interested them….
Max also hired well. German governesses and French governesses (apparently they hated one another), as well as an Italian governess; then, two homeschooling teachers just for English, a Mr. Thompson and a Mr. Blythe (but this started in 1914, so it seems Johnny only began English at the later age of 11). Max sat in on the lessons with Johnny.
Little Johnny had a Fencing Master who came to his home (there was enough room), and a music teacher too, but she apparently did not impart much to Johnny. He had teachers come to his home as well, about whom we know nothing—their contributions have been lost to history.
In their enormous building, their cousins lived on the floor below. Max (the father) bought a summer home that was so nice it is now historically preserved as a place for the local children to play. The entire family was wealthy and well-connected (his mother’s lineage has its own Wikipedia page); indeed, Max was an advisor to the Hungarian Prime Minister Kálmán Széll. For Max’s service—not for a monetary payment—the family was officially ennobled in 1913.
Even if Johnny only became an aristocrat on paper at 10, looking at his young life, any modern person would instantly recognize it as fundamentally aristocratic and elite and his education as, basically, perfect.
How “The Martians” Explained Themselves
The incredible socio-educational environment of Budapest had effects on the entire world and the shape, and ending, of World War II.
Classically, Johnny is grouped with a Jewish-Hungarian group of similar ages called “The Martians” at Los Alamos and beyond (on the Manhattan Project alone were Leo Szilard, Edward Teller, Eugene Wigner, and Johnny himself). All except Wigner appear to have embraced the rumor that they were from another planet, cracking jokes and propagating it themselves.
However, this clustering of genius probably isn’t as historically mysterious as it’s been made out to be. Nor was it solely a Jewish phenomenon, e.g., there were plenty of non-Jewish Hungarian geniuses produced by that period, like Albert Szent-Györgyi or György Békésy (both won Nobel Prizes). Macrae cites that Johnny’s Lutheran school self-identified as 52% Jewish, and speculates that over 70% of Johnny’s school may have been ethnically Jewish, with many having converted. Other elite high schools were probably somewhat similar.
Additionally, many of those kids were second-generation immigrants (including Wigner and Johnny), which we know can be a huge boon to academic success. Indeed, we see the exact same effects here in America today, coupled with the advantages of cultures that emphasize academic achievement. Johnny’s school was ~70% Jewish-Hungarian (at ~20% of the population), for probably pretty similar reasons that MIT right now is 47% Asian American (at ~7% of the population).
From Russian’s steppes, from Bismarck’s Germany, from Dreyfus’s France, and from Hungary’s own mountain villages they came: a cultured and upwardly mobile group, intent on giving their sons (sadly, more than their daughters) the education that some of them had never had.
According to Macrae, Jewish immigrants chose to go to Budapest, rather than New York, because of its culture and sophistication, its (somewhat) meritocratic aspects, its quality of life, such as its extremely plentiful domestic servants, its education system, and there was no long and dangerous sea voyage—all this attracted the upper-class specifically to Budapest.
In fact, Budapest of that era may have been one of the few places and times in all of history where you could hire a bevy of top-notch professional private tutors and governesses without being obscenely wealthy (just well-off), and also where it was standard to do so (which is why formal school started so late).2
What did they themselves think? Eugene Wigner wrote in his memoirs:
Many people have asked me: Why was this generation of Jewish Hungarians so brilliant? Let me begin by making it clear it was not a matter of genetic superiority. Let us leave such ideas to Adolf Hitler.
Instead, he suggests that credit is due to “the superb high schools in Budapest, which gave us a wonderful start,” but that most impactful was “our forced emigration." And indeed, Johnny agreed that it was the situations into which they were thrown, historically, and had to succeed in to survive.
Therefore, we see that Budapest operated like a reservoir-release model, drawing in via immigration a bunch of talent, educating it incredibly well due to rare historic and economic circumstances, and then exploding in a forced diaspora via antisemitic persecution and world war.
John von Neumann Didn’t Invent the “von Neumann” Architecture
He was afraid on his deathbed that history would forget his name. That now seems unlikely. No one can argue that John von Neumann wasn’t one of the greatest contributors to human understanding in the 20th century. His relevancy only continues to grow into the 21st century, as the topics he touched on (like computers) have become more central (see, e.g., The Man from the Future).
As an adult, probably owing at least partly to his lengthy aristocratic tutoring, Johnny was incredible at formal frameworks, calculations, and taking an idea to its conclusion before anybody else. He simply knew, crystallized, so much more than others. However, there’s an uncomfortable corollary:
Johnny borrowed (we must not say plagiarize) anything from anybody, with great courtesy and aplomb. His mind was not as original as Leibniz’s or Newton’s or Einstein’s, but he sees other people’s original, though fluffy, ideas and quickly changed them in expanded detail into a form where they could be useful for scholarship and for mankind.
Let us consider a perfect example of this, which is always high on the list of Johnny’s contributions: the “von Neumann architecture” of modern computers.
ENIAC was one of the earliest uses of vacuum tubes as a general-purpose computer. It was developed at the Moore School of Electrical Engineering of the University of Pennsylvania. A fellow early computer scientist who was also in the military, Herman Goldstine, secured von Neumann a tour of it (and involved him with the funders). Johnny, as usual, instantly understand what was central and important about the numerous planned potential improvements to ENIAC, which John Mauchly and J. Presper Eckert had been working out. The two men had built ENIAC and had been off-and-on designing a follow-up for a while, and all this they openly shared with Johnny.
Not long after Johnny’s visit, inspired by McCulloch and Pitts’ famous early work on artificial neurons, Johnny wrote up a report on Mauchly and Eckert’s planned design of EDVAC, but first he chose to finalize some of the existing ideas they’d proposed (likely adding in some on the programming side) and then he slapped on a bunch of abstract formal math to redescribe it in his terms (a critic might say “jargon,” but it is very cool jargon).
But then Herman Goldstine sent out the report with only Johnny’s name on it, and voilà! The “von Neumann architecture.”
Here is an excerpt from “A Letter to the Editor of DATAMATION” by John W. Mauchly.
Naturally, “architecture” or “logical organization” was the first thing to attend to. Eckert and I spent a great deal of thought on that, combining a serial delay line storage with the idea of a single storage for data and program…. The EDVAC was the outcome of lengthy planning….
But [Johnny] chose to refer to the modules we had described as ‘organs’ and to substitute hypothetical ‘neurons’ for hypothetical vacuum tubes or other devices which could perform logical functions. It was clear that Johnny was rephrasing our logic, but it was still the SAME logic….
He must have spent considerable time at Los Alamos writing up a report on our design for an EDVAC... But Goldstine mimeographed it with a title page naming only one author—von Neumann. There was nothing to suggest that ANY of the major ideas had come from the Moore School Project! Without our knowledge, Goldstine then distributed the ‘design for the EDVAC’ outside the project and even to persons in other countries.
Don’t misread this as my saying that Johnny was a plagiarist or unoriginal. Johnny contributed to the computer revolution in later ways as well, and that specific incident is almost certainly just Herman Goldstine’s fault, although Johnny did silently benefit. Johnny was fond of saying some version of “It takes a Hungarian to walk into a revolving door behind you and come out ahead” and that’s precisely what happened.
My point is merely that, while Johnny was absolutely one of the greats in the pantheon of science and math, one of is how we should see John von Neumann. His first major work on axioms had “run aground” on Gödel. His second major work on formalizing quantum theory had been upstaged by Dirac’s notation, which became the standard, and his major proof that hidden variable interpretations of quantum mechanics were supposedly impossible turned out to be flawed, due to what John Stewart Bell called a “silly” error.
Johnny’s long-time assistant and fellow great Hungarian mathematician, Paul Halmos, wrote about him that:
As a writer of mathematics von Neumann was clear, but not clean; he was powerful but not elegant. He seemed to love fussy detail, needless repetition, and notation so explicit as to be confusing…. quite a few times, it gave lesser men an opportunity to publish “improvements” of von Neumann.
Johnny even suspected that Norbert Wiener had a mind “intrinsically better than his own.” Who was Norbert Wiener? Another famous early computer scientist and cyberneticist that people like to tell stories about.3 He was also another child prodigy shaped by his father, but much more intently and viciously than Max; e.g., when Norbert was born, his father held a press conference saying he would raise a genius—and, well, he did. Johnny also envied the dreamy Einstein’s deep and intuitive leaps of genius.
Nobel Prize winner Eugene Wigner, Johnny’s best and longest friend, had plenty of high praise for Johnny, but firmly gives his opinion on whether John von Neumann was the Greatest Scientific Mind of All Time. The answer was no.
Einstein’s understanding was deeper than even John von Neumann’s. His mind was more penetrating and more original than von Neumann’s.
Johnny’s friend, Stanisław Ulam, who suggested the idea of automata growing on cells that Johnny then formalized into cellular automata (note again the pattern), wrote of Johnny that:
In spite of his great powers and his full consciousness of them, he lacked a certain self-confidence, admiring greatly a few mathematicians and physicists who possessed qualities which he did not believe he himself had in the highest possible degree. The qualities which evoked this feeling on his part were, I felt, relatively simple-minded powers of intuition of new truths, or the gift for a seemingly irrational perception of proofs or formulation of new theorems.
Absolutely none of this means that John von Neumann wasn’t a genius, nor contributed far more than all but a few others. Certainly, plenty of other geniuses thought he was smarter than them (just as he suspected Einstein and Wiener might have something he didn’t). His output attests to it. As Halmos, his assistant, summarized:
Brains, speed, and hard work produced results. In von Neumann’s Collected Works there is a list of over 150 papers. About 60 of them are on pure mathematics (set theory, logic, topological groups, measure theory, ergodic theory, operator theory, and continuous geometry), about 20 on physics, about 60 on applied mathematics (including statistics, game theory, and computer theory), and a small handful on some special mathematical subjects and general non-mathematical ones.
But even in his incredible output and the legends around him, Johnny’s overall academic oeuvre seems closer to what one would expect from someone whose talents were due to his perfect education vs. his supposedly-superhuman brain itself. His work is a triumph of formalizing things beautifully and quickly, being in the right rooms, flat-out knowing more than other people, and competitively beating them to the punch (he described himself in a letter to his daughter as “an ambitious bastard”).
I personally can’t help but feel that Johnny’s most original work was his development of game theory. Games have existed for a pretty long time, but here’s Johnny in 1928 with “Theory of Parlor Games” which grows into his famous 1944 book Theory of Games and Economic Behavior.
It’s also the most him. As a child, Johnny would dress up and have his brothers move sheets of paper around, enacting battles. Probably it was Kriegsspiel, a Prussian military war game that had strong influences on later gaming systems like Dungeons & Dragons and Warhammer. It didn’t seem to matter who won or who lost to Johnny, instead his question was: Is there an optimal strategy? We can see how this evolved into: Is there a provable optimal strategy? Even there we can see how his environment influenced his work as much as his genetics.
Just Because It’s on Wikipedia Doesn’t Make It Real
Now that we have sketched the man, and his many, many impressive contributions (but also noted their occasional overhyped nature), we have the capacity to look honestly at the legends and myths around Johnny’s raw mental abilities.
Unfortunately, these myths have propagated to the point where even Wikipedia is wrong. E.g., on Wikipedia it’s stated that Johnny could divide 8-digit numbers in his head at the age of 6.
The actual link takes you to a 2007 pop-sci book titled Mathematics: Powerful Patterns In Nature and Society by one Harry Henderson. Here’s what Henderson’s, and thus Wikipedia’s, child prodigy feat is based on: an incredibly brief section about Johnny’s childhood (because this book is not a biography).
No specific source, unfortunately! Yet Henderson, via Wikipedia, is cited by so many others for the same claim.
Indeed, we can debunk this entirely. For I tracked down another “eight-digit” number story about Johnny that the author Harry Henderson (who had no connection to Johnny) almost certainly misremembered. His Further Reading section contains Macrae’s biography, and, yup, there it is written by way of introduction that:
Three usual descriptions are that Johnny exuded self-confidence, had the world’s best memory, and could multiply eight-figure numbers by other eight-figure numbers in his head. All these descriptions are half wrong.
Henderson almost certainly just misremembered that part of Macrae’s biography. And so not only is Wikipedia, by way of Henderson’s mistake, reporting an ability that’s “half wrong,” the situation is even worse, because from the surrounding context Macrae is clearly talking about the adult Johnny, not Johnny as a 6-year-old! And Macrae’s quote is about multiplication. So it is thrice wrong.
Other rumors have similar origins. Enter, once again, Herman Goldstine. That’s right, the same guy who gave Johnny all the credit for the von Neumann architecture.
In 1972, Herman Goldstine published The Computer from Pascal to von Neumann, in which he makes a number of much-cited wild claims about Johnny, including about his early life, things that Goldstine could not possibly have known for sure. First, he says that “He and his father joked together in Classical Greek.” However, Macrae specifically notes that Johnny’s family denies any memory of this (and there goes Greek from the list of languages he was fluent in as a young child).
Second, Goldstine gives us what seems to be the original “perfect recall” story:
One of his most remarkable capabilities was his power of absolute recall. As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover, he could do it years later without hesitation…. On one occasion I tested his ability by asking him to tell me how A Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes.
Macrae also mentions this story, but gives some pretty critical context that deflates the whole thing from superhuman to merely incredibly impressive: Johnny had specifically memorized the beginning of Dickens’ A Tale of Two Cities prior to coming to America to improve his English.
Through this practice, he was able at age 50 to baffle Herman Goldstine by quoting the first dozen pages of Dickens’ Tale of Two Cities word for word.
Macrae also mentions that:
In English he had chosen to browse through encyclopedias and pick out interesting subjects to learn by heart. That is why he had such extraordinarily precise knowledge of the Masonic movement, the early history of philosophy, the trial of Joan of Arc, and the battles in the American civil war. In German in [his] youth he had done the same thing with Oncken’s [history].
That’s obviously impressive, to remember a long passage so many years later. But Goldstine makes it sound like he “tested” Johnny on the opening of a random book—except it couldn’t have been a random book, as it was the exact same passage Macrae reports Johnny purposefully memorized years before to practice his English. Likely, either that book came up in conversation naturally and the demonstration actually occurred, but then Goldstine misunderstood or misremembered (or worse) and portrays his effort as “testing” him (and perhaps exaggerated the length of the passage too).4
Consciously choosing passages to learn by heart to improve one’s feel for a language is incredibly astute, but also wildly different from being able to remember every book you’ve ever read. Indeed, the same titles (the history he read when he was young, the Dickens, and entries in an encyclopedia) crop up again and again in the stories of recitations. If it wasn’t purposeful memorization, it wouldn’t be listable like that. It would really be just any random book. Like a telephone book!
Incredibly, that’s also another (false) claim.
This claim is from Prisoner’s Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb, yet another pop-sci semi-biography more focused on the science than Johnny himself, published in 1993 by William Poundstone. And surely we can trust the esteemed author of other books like How Do You Fight a Horse-Sized Duck?
Nope, it’s almost certainly another misremembering of a different source. Specifically, this time from a 1973 source: “The Legend of John von Neumann,” by Paul Halmos (a great mathematician in his own right, but also, importantly, Johnny’s assistant for many years). Halmos writes a tongue-in-cheek accounting of the stories and legends about Johnny’s intelligence. Early on, Halmos says there’s a story in circulation that Johnny (as an adult) could “memorize the names, addresses, and telephone numbers in a column of the telephone book on sight,” but Halmos makes perfectly clear that it’s just a story, and is, like many others, “undocumented” and “unverifiable.” Halmos may even be implying it was Johnny’s own joking that originated it:5
Speaking of the Manhattan telephone book he said once that he knew all the numbers in it—the only other thing he needed, to be able to dispense with the book altogether, was to know the names that the numbers belonged to.
So that joke (he knows the numbers, get it?) may have started the rumor about Johnny memorizing phone books as an adult (or they originated elsewhere, but certainly Halmos himself never witnessed anything like that in his many years of working closely with Johnny or he’d say so). However, somehow Halmos’ wry recounting of tall tales makes it into Prisoner’s Dilemma, and there it is mistaken to be (a) about Johnny as a child, and (b) true.
What’s interesting is that Halmos, who would be in one of the best positions to judge the adult Johnny as his assistant, does give actual examples of Johnny’s calculating brilliance. Some are as impressive as the legend suggests—e.g., Johnny solving difficult math puzzles, or once beating a computer at a calculation. But others are, frankly, not so impressive. Kind of disappointing, really. Johnny arrived at a solution in two seconds while his students took 10 seconds? Okay. He once gave a presentation on his area of expertise without any notes? Okay, now we’re just reaching for stuff.
Halmos even makes us question how many languages Johnny knew. Apparently:
At home the von Neumanns spoke Hungarian, but he was perfectly at ease in German, and in French, and, of course, in English.
So that’s “only” four fluent languages as an adult, and his biographer Macrae implies that Johnny’s English spelling was bad. Stanisław Ulam does say an adult Johnny remembered his Latin and Greek from school (implying he learned it in the formal system) and could kind of speak Spanish by adding “el” to things (again, this seems like clear reaching?). So we have four fluent languages, his ability to add “el” to words, and at least some unclear amount of Latin and Greek from school as an adult—deeply impressive, except for the Spanish!
But that impressiveness was, yet again, transformed via the rumor mill into him knowing all those (and more) languages fluently as a young child, while it’s quite clear that he started learning English only at 10 or 11. The Italian governess apparently never had much of an impact on Johnny—odd for someone who could learn everything effortlessly!
The “Nothing Ever Happens” Explanation
While hopefully giving Johnny his incredible due, we have so far debunked that child Johnny had the preposterous powers assigned to him, and we’ve also shown how even his adult legend has been exaggerated. There’s so little original scholarship too that pretty much everything links back to the same few mistakes I’ve identified.
Johnny died before writing his autobiography, a huge blow to history. To make matters worse, some Johnny biographies contain numerous errors. Even Macrae’s biography isn’t perfect (see this footnote6 for a historical error I identified, and other minor criticisms). My long-standing policy is not to try to hurt people via gotcha mistakes, and I believe that most people are doing their best, and so I’ve tried to not single out any individual author too much (other than the long-dead Goldstine, but perhaps it was a series of errors on his part too).7
Johnny undeniably was a child prodigy. Wigner’s memoirs attest to that.8 But Wigner only met Johnny when Johnny was 12, already having been tutored by Rátz privately for two years, and simultaneously likely Fekete as well. A preteen can indeed be incredibly mathematically impressive, especially when they are being tutored by those two!
Personally, after all my reading, I do believe Johnny had a mind like a steel trap. I just also believe he was mortal. And the boring explanation is that he simply had a habit of memorizing certain passages and pulling them out to show off.
There is suggestive evidence of this. One of the best first-hand accounts of Johnny’s mental powers comes from Johnny’s brother himself. While it’s unfinished, his brother does mention young Johnny’s memory as being “amazing” and “powerful” and at one high point, “almost unlimited.” But he was 8 years younger than Johnny, and really the only concrete examples he gives of these powers are things like Johnny explaining scientific concepts at the dinner table really well, impressively deducing the answer to a prize question, and the older Johnny finishing his homework quickly. And his younger brother also explicitly says that many of the rumors swirling around Johnny are false, and implies that a real biography will one day correct them. Nowhere does he deny that Johnny engaged in explicit memorization and study, of which there was a family habit; tellingly, in the middle of the unfinished recollections, Johnny’s brother begins to lapse into old poetry in other languages, and admits these are poems that he explicitly memorized back then, in that glittering cognitive Belle Époque of his brain—writing about Johnny was surfacing them.
Given his family’s practice of memorizing, Johnny likely had both an innately good memory for the things he read but also studied and practiced them. And most families also don’t expect recitations at the dinner table to begin with. Even his grandfather used to come over and perform arithmetic tricks, abilities that Johnny had a jolly time exaggerating later in life.
We don’t hear any specific anecdotes about Johnny’s supposed ability to remember literally anything he wants in his daughter’s memoir, The Martian’s Daughter, and I feel like that might crop up if you lived together for years. And we know from Macrae that Johnny “could rarely remember a name” and:
His memory and feel for words, plus unsurpassed feel for mathematical symbols, had not extended to memory for faces. All his life he was embarrassed by not knowing people who clearly knew him. He had no sort of photographic memory. This imposed some limitations on his mathematics (he was not good at envisaging shapes) but probably also added to some of his strengths.
We also have this story about Mandelbrot and Johnny both forgetting a proof they worked on together.
[Mandelbrot] told me that one long afternoon he and von Neumann were working together trying to prove a difficult theorem. As their conversation advanced, von Neumann asked Mandelbrot several times to take notes on their progress. Each time Mandelbrot grandly replied that he would remember everything and write it up the next day. But the next morning he woke up and could not remember any of the key steps in the proof they had been developing. He said that when he confessed this to von Neumann he had never before seen a man so angry and he himself remembered the incident as the ultimate embarrassment of his professional career.
Meanwhile, Johnny’s daughter offers the observation that Johnny’s first wife (her mother) complained he was always taking an encyclopedia to the bathroom.
My mother used to say, only half jokingly, that one of the reasons she divorced him was his penchant for spending hours reading one of the tomes of an enormous German encyclopedia in the bathroom.
So maybe he just read and re-read books on the toilet? There’s an answer as mundane as possible!
Of course, the further part of the “nothing ever happens” explanation is that people tell stories about other geniuses too. E.g., Norbert Wiener had an “encyclopedic memory” according to Steve Heims, but only Johnny’s has been transmuted via internet lore.
What we do know for sure is that Johnny’s huge amount of crystallized knowledge was:
… the explanation of his extraordinary powers of mental calculation. He was not actually better than many other mathematicians—or indeed than some vaudeville freaks—at multiplying one eight-digit figure by another. But he used his accumulations of mathematical constants and equations to become a startling problem-solver and extraordinary concept-expander.
The Something Happened Explanation: Johnny Had OCD
I couldn’t help being struck, in my reading, by how Johnny’s second wife’s personal account strongly suggests he had OCD:
A drawer could not be opened unless it was pushed in and out seven times, the same with a light switch, which also had to be flipped seven times before you could let it stay.
This conflicts with another legend, that Johnny was 100% normal, despite his intelligence. He liked parties, yes, but he wasn’t normal—just normal compared to people like Dirac, who crept along next to walls. The details of Johnny’s wife’s account have only emerged somewhat recently, and there hasn’t been much time for scholars to digest it.
And, interestingly enough, there’s a phenomenon where OCD sometimes manifests as “memory hoarding.” It’s not well-studied, but it’s common enough for the term to be used. Here’s from the OCD Center of LA:
Memory hoarding is a mental compulsion to over-attend to the details of an event, person, or object in an attempt to mentally store it for safekeeping. This is generally done under the belief that the event, person, or object carries a special significance and will be important to recall exactly as-is at a later date. The memory serves the same function for the mental hoarder that the old newspaper serves for the physical hoarder.
Maybe Johnny’s version of OCD manifested within his studying habits and he became a “mental hoarder.” Johnny certainly could have disguised this, just as he pragmatically accepted his daughter hiding her Jewish ethnicity later in life to keep appearances copacetic. Maybe he kept his own mental issues as private as possible too.9 Like, say, in the bathroom? Perhaps he sat on the toilet for hours and hours going over encyclopedias, not in raw intellectual pleasure, but in tormented neurosis. There are stories of him abruptly leaving parties to go do something mysterious, only to return as if everything was fine hours later. Everyone’s always assumed he was jotting down brilliant notes for new mathematics. Maybe he was just living out his OCD in the bathroom again.
Again, there’s no strong need for the OCD hypothesis. But if you are going to give full credit to the remaining anecdotes (which are less preposterous than the ones I’ve debunked), the OCD hypothesis is more likely than that he genetically had a memory so beyond even his genius peers. And there’s a funny corollary. It might mean that out of a million embryos, maybe Johnny’s brain specifically wouldn’t be the one picked by genetic scoring! If you cloned Johnny today into a different family environment, you might not get a genius, but merely a smart person with OCD focused on stuff that’s not memorizing equations and hobby history.
My overall thoughts on pop-hereditarianism
I actually hate writing about hereditarianism, even obliquely.
All the pivots are predictable and exhausting: “What about Study A, or Person B, or example C, or observation D!” Or “What about some other dug-up 80-year-old claim about Johnny—you can’t disprove them all!”
It’s also a fraught subject, and I don’t like confrontation. I’m much like Johnny that way—always smoothing things over (our similarities, unfortunately for me, end there). There are just far more interesting things to do, and I want to get along with most individuals.
The problem is, despite not actually being a blank slatist, I’m interested in what makes for a great education and this stuff pops up in my way when I want to talk about it. The philosophy also attracts immoral and dangerous political ideologues who use it as a way to accumulate power. That’s not to say everyone who disagrees with me is evil or bad! Plenty of others do honestly approach the question of Nature vs. Nurture and come down more on the hereditarian side than I. That’s perfectly fine and reasonable, of course. But when it comes to the pop-hereditarian movement as a whole, the loudest voices on social media will take over, if they haven’t already, as the project of pop-hereditarianism has obviously become a political one.
Since this small but symbolically-important slice of the pop-hereditarian movement—all their legends about an individual with a genetically-perfect brain called John von Neumann—has turned out to be built on absurdly selective credulity, and on shallow intellectualism in general, I hope readers can reach their own conclusions about how much of the rest is not lightning coming out of arses, but something else.
Johnny was unlikely to be a strong hereditarian. First, there was his hatred of Hitler, and he would have likely drawn the analogy just as Wigner did. But more relevantly, it is evidenced in his own explanation of why he and his peers from Budapest were so brilliant (all we know is that he gave cultural reasons), as well as practically in his life, like his unusual arrangement (after the divorce) for how his daughter was to switch to living with him during her most intellectually formative years (she became Vice President of General Motors). Also, his own ethnicity did not appear particularly important to him. As Macrae writes:
There is a danger in overemphasizing Johnny’s Jewish origins. Except for a Jewish sense of humor—which he kept all his life—Jewishness never meant much to him. His daughter says she did not know of her Jewish heritage until her teens.
To render “The Martians” even less mysterious, there were likely significant peer effects. In Eugene Wigner’s memoir, he recounts constantly bumping into and befriending other Hungarians abroad, and there was probably a bit of favoritism too. Princeton originally hires Wigner mainly because they wanted to entice Johnny, and, e.g., his mentor, the famous Michael Polanyi, was from Budapest as well, and even in Berlin that informs their relationship:
Polanyi took an interest in all of his assistants, but I felt that he liked me especially…. Because Polanyi was a decade my senior and held a far higher position, it was not quite proper for him to befriend me as he did.
People love to tell obviously exaggerated stories about famous mathematicians. A story about Norbert Wiener goes like this: His family moves to a new address, and his wife, knowing he would forget the new address, writes it down on a sheet of paper. Wiener uses the paper for notes that day, then throws it away. He goes back to the old address and realizes he’s lost. So he asks a little girl nearby “I’m the famous Norbert Wiener, and I’m lost. Do you know where I live?” And the little girl replies: “Yes, father.”
It’s also worth mentioning that Goldstine’s second anecdote beyond the Dickens story is far far less impressive.
Another time, I watched him lecture on some material written in German about twenty years earlier. In this performance von Neumann even used exactly the same letters and symbols he had in the original.
But it isn’t that surprising that a (great) research would remember their own work 20 years ago and use the same symbols!
In the same “Legends of John von Neumann,” while talking about the telephone-memorizing being a rumor Halmos cracks a joke that, unfortunately, was probably misread by many. He says that “some of the von Neumann stories in circulation” are that:
At the age of 6 he could divide two eight digit numbers in his head; by 8 he had mastered the calculus; by 12 he had read and understood Borel’s Théorie des Fonctions.
Halmos is using these as specific examples of rumors that are “undocumented” and “unverifiable,” but the progression is so punchy he could just as well been wryly making them up himself, i.e., mastering calculus at age 8 and understanding Borel’s Théorie des Fonctions by 12 is the mathematician’s way of saying “fireballs from his eyes” and “lightning from his arse.” But since mastering calculus at 8 does seem kind of like a possibility for Johnny (understandably) at least a few authors thought “Wow, lightning!” even though Halmos had just said that these were stories.
Here’s one error I identified in the Macrae biography: Macrae implies that the very first tutor Rátz arranges was Szegő (this is where the story of Szegő having “tears in his eyes” from meeting young Johnny comes from—the tears were reported by Szegő’s wife).
However, this is provably false. Macrae writes that Szegő had “done the initial coaching in 1915-16” of Johnny, and that Johnny’s tutoring was then taken over by others. But I discovered that Szegő was not even in Budapest in 1915-1916; he’d already entered the World War as a cavalier! He only returns to Budapest after the war. So the story of “tears in his eyes” probably came from then. I speculated that Fekete, a tutor by trade, and Johnny’s first co-author, was actually his paid tutor for the entire 8 years, introducing Johnny to his notable associates over time. I found that this is supported by John von Neumann and the Origins of Modern Computing by William Aspray.
Rátz contacted a mathematics professor… at the University of Budapest, and arranged for a young mathematician on the faculty, Michael Fekete, to tutor John regularly in mathematics at home, an arrangement that continued throughout the eight years that John attended the Lutheran Gymnasium.
Johnny’s tutoring progression now makes more sense, and speaks, yet again, against Johnny being a superhuman child prodigy (just, you know, one of those “normal” child prodigies). Johnny wasn’t taken immediately to the most famous mathematicians around and given their time, he had to work his way up, and he’s provoking tears when he’s 15-16 years old, not 11-12.
So too when it comes to talking about Johnny’s mental abilities, I found Macrae frustrating. His carefully-chosen language occasionally plays up Johnny’s memory, but his fanciful descriptions could equally apply to Johnny just studying things, simply faster and better than most other people. If I were a biographer, and there was a rumor my subject could memorize any book he wanted to instantly, I wouldn’t lean into the legend by writing vaguely that he learned something by “reading very quickly but with enormous concentration” without mentioning the pretty critical information about whether he read it exactly once and whether the resultant knowledge was truly verbatim. Same with describing a study session as “one concentrated gulp.” What is “one gulp,” exactly? One read? One hour? A whole day? I’ll tell you what it is: it’s poetic license for “He memorized it fast but I don’t know the details.”
Speaking of mistakes, I wrote all this, my own mini-biography of Johnny, over just a few days. I’m sure there’s a mistake or two of my own hiding somewhere, given the huge number of sources and names and dates! I’ll try to correct anything major I missed [See the new “Errata” comment for changes and additions].
Obviously, something about Johnny originally attracted the attention of Rátz. Wigner does hype up Johnny as a 10-year-old as knowing a bunch of mathematics, but he makes this comment while clearly speculating about Rátz’s motivations, which he didn’t know (and of course, Wigner only meets Johnny himself at 12, so he’s basically just trying to explain why Rátz did what he did and doesn’t himself know).
Incidentally, the OCD hypothesis might also explain why Johnny’s first wife left him (which is somewhat mysterious, given how well-matched they were and their good relationship afterward). Perhaps her many complaints about him being more attentive to his “work” than her were actually just as much about his OCD behaviors.
Could someone edit the Wikipedia, please? To remove the faulty citations in that screenshot? I'd suggest starting the Child Prodigy section instead with:
John von Neumann was a child prodigy who by the age of 12 "already had an astonishing grasp of advanced mathematics." source: The Recollections of Eugene Wigner.
Rather than the current incorrect "8 figure" claim.
I've heard sometimes it's better to ask for an editor or someone with experience, since there are lots of rules, and first-time accounts editing a big page like Johnny's might be distrusted. But I really don't know anything about Wikipedia's details.
Errata:
There was much discussion of this piece. I’m thankful to everyone who replied. As I said in a footnote, I expected a few changes given the size and length of this piece. I've added in two new pieces of supporting evidence: the Mandlebrot story of Johnny forgetting a proof (someone on social media mentioned this, but I can't find the account to credit them), and also that Goldstine's second anecdote about Johnny's perfect memory is far less impressive. Additionally, I’ve made four changes to maximize accuracy and fairness: all minor, and none affecting the thesis.
1. Due to the recent scholarly evidence that Johnny likely added variable addresses to the “von Neumann” architecture, which is at least one novel part of the full whole he’s credited with, the sentence describing him as just “mixing and matching” was expanded to imply inclusions of at least some original contributions, although I don’t get into the details.
2. Eugene Wigner’s quote about Einstein vs. Johnny is no longer described as him judging the “Smartest Man” but the “Greatest Scientific Mind.” This is because it was pointed out Wigner could be read as distinguishing the two types of intelligence at another point of his recollections and specifically saying the scientific greatness is not based on speed, but on the overall qualities closer to what he assigns to Einstein (but he never gives a description of “smart”).
3. The “He did not have a photographic memory” quote is expanded to provide more context from Macrae, since there’s ambiguity around it, as Macrae says it in the context of remembering faces, but also suggests it impacts how Johnny visualized things and did math. Its original truncated version was in a paragraph merely arguing that he "couldn't remember literally everything" (a high bar) and Macrae's statement supports that. However, it could be read as the decider of all the other debates and anecdotes, being so strong, so I included more context.
4. I no longer describe some unspecified past biographies as “pop-sci slop,” I just point out some contain errors (I’m fine with books containing mistakes, it’s inevitable, although I think some of these tall tales did need more checking).