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What are some of John von Neumann's ideas "which helped seed the modern world"?

I remember that a philosophy professor called John von Neumann the smartest person who has ever lived. Do you think so too?

When was the decade when JvN was most productive?

Someone said that JvN grew up in Hungary in a trilingual household, learning Hungarian, Hebrew and German- from a very young age on . These languages are different as it gets. Do you think this would be a reinforcing factor boosting his intelligence?

Which areas of science that he invented (or was productive in) did you study so far? Which ones did you have to omit because the field is so different?

Does our numerical system pose any problems in the pursuit of trying to understand the universe when numbers are involved?

JvN is such an interesting person. My favorite anecdote about him is this one:

> “von Neumann would carry on a conversation with my 3-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

This is particularly impressive when you consider that the "rest of us" were the scientists of the Manhattan Project, in other words the greatest collection of genius in one place the world has ever seen.

John seemed special because he was not only one of the greatest intellects in history, but also personable, well adjusted, and the life of the party. His genius didn't come at the cost of social skills. Do you think he was unique in that way?

Reading your book right now and find it truly brilliant (I don’t know much about physics or maths, but still greatly enjoy it). I was particularly impressed by the chapter on the atom bomb, which also had a huge emotional impact on me.

My questions: What will you write about next? Do you have other books to recommend about “people from the future” or about the future in general? If so, which? Which (if any) other people from Europa that moved to the USA because of the Nazis should/could be studied more?

I would love to read your answers to these question if you find the time. Good luck with whatever you are up to, and keep up the great work!

I know that JvN was immensely productive. But is it still worthwhile to read his original works? For comparison, I also like Newton's works, for example, but I still do not read Newtons original works either. Are there any of his works that are particularly original, well witten and understandable for mere mortals?

How legitimate was his conversion to Catholicism?

So I could be cheeky and say you should read the book (well you should) but let's see...

-the 'von Neumann architecture', which is the basis for nearly all stored program computers today, from smartphone to laptop. I'm convinced by historian Thomas Haigh's [work](https://www.tomandmaria.com/Tom/Home) which suggests that JVN was uniquely well placed to come up with the design, manage the various players involved and bring in the cash to do it

-game theory and expected utility theory. JVN didn't live long enough to get the Nobel for it (he'd been dead 40 years by the time Nash, Selten and Harsanyi picked up the first Nobel for game theory. But his proof of the minimax theorem birthed the whole field, and his book with Morgenstern, 'Theory of Games and Economic Behaviour' is the canonical text. Game theory makes Internet firms billions through keyword auctions and other ways. It's also key to thinking about nuclear strategy and expected utility theory is central to behavioural economics

-theory of self-replicating automata. by proving mathematically that machines couldd reproduce, von Neumann inspired the first nanotech pioneers as well as legions of science fiction writers and dreamers (von Neumann probes, self-replicating lunar bases).

-he designed the implosion bomb, Fat Man. He then carried out the first computer simulations ever (sadly, they were to help design better bombs and keep the USA ahead in the arms race). Later, he led the team that carried out the first computerised weather forecast.

(Pushing go now but there's more I will try to add)

Doh! Forgot his deathbed lectures on 'The Computer and the Brain'! This was the first time anyone had compared computers to human brains in a systematic manner, and made the point that while computers were serial machines, the brain was massively parallel. The lectures built a bridge between computer science and cognitive neuroscience for the first time--some would say that's been a pretty useful link!

For more AMAs on this topic, subscribe to r/IAmA_Author, and check out our other topic-specific AMA subreddits here.

I remember that a philosophy professor called John von Neumann the smartest person who has ever lived. Do you think so too?

Yes! Though it depends a bit on what you he meant by 'smart'. In terms of the sheer firepower of his brain, I don't think we know of anyone who was a faster mathematical thinker than von Neumann. His friend, Wigner, claimed that while JVN had the most exceptional brain among any of the incredible geniuses they both knew, Einstein was the the deeper thinker. People thought von Neumann was less of a creative thinker--he tended to bulldoze his way through problems. But I think that was a little unfair on him. I think it's only really now, more than half a century on, we're really beginning to appreciate how prescient his contributions really were.

I focused on his contributions to mathematical logic and the foundational crisis in maths (because that ends up being key to his thinking later), then the science, engineering and maths that is most relevant to us today. So there's a huge swathe of his mathematical contributions I almost completely ignore. There's a whole branch of algebra (https://en.wikipedia.org/wiki/Von_Neumann_algebra) he invented that gets a cursory mention in the book. But Vaughan Jones won the Fields Medal as a result of exploring just a small part of it!

Some physicists blame JvN for the blind faith in the Copenhagen Interpretation of Quantum Mechanics due to his no hidden variables proof that was later shown to be invalid. Is this criticism valid?

Thank you so much. You're very kind! Writing this book really pushed me to my intellectual limits. And a lot of it was written during lockdown, when I was also trying to homeschool. So my brain was kind of fried. I'm writing a kids' science fiction novel at the moment but I'm also the primary homemaker right now so that's proving... distracting. Needless to say, writing about (relatively) obscure mathematical geniuses doesn't make you rich. I have another non-fiction book in mind but not sure if I can justify it financially. I won't say too much about it but in some ways it would be similar to 'The Man from the Future'--it follows the birth and influence of a scientific idea, and looks at the stories of all those involved and dissects how it came to be. Let's see...

Former professor and historian of computing here. I used to make the case to students that John von Neumann was the father of the computer: not just because of the von Neumann architecture, but also because he was a well-respected public figure who proselytized for investment in computer technology: often to people in the upper echelons of power. Any anecdotes you could share that might make that case to the people of Reddit?

Yes! This is what struck me about him too! When you think about other mathematical geniuses they were often quite strange characters (Paul Erdős springs effortlessly to mind). Some said that this was a facade and I suppose to an extent it was--with a brain like that, von Neumann was often quite isolated from other humans. But he genuinely did seem to enjoy parties and loud music, bad jokes and naughty limericks. I think his upbringing had a hand in this--but it's also key to his interest in applying maths to problems in the real world. He wasn't ever going to be happy in an ivory tower.

Well I guess you mean his deathbed return to Catholicism? In fact, he and his brothers all converted to Catholicism after their father's death in 1928. There isn't much evidence he took religion seriously at all through his life and when he returned to the faith on his deathbed, his brother, Nicholas, couldn't bring himself to believe that it was genuine. He claimed it was because the hospital's Catholic priest was the only person fluent in ancient Greek and von Neumann wanted to chat!

Von Neumann was certainly terrified of his own death (he was only 54 years old when he died) . His daughter, Marina, says her father was thinking of Pascal’s wager and had always believed that in the face of even a small possibility of suffering eternal damnation the only logical course is to be a believer before the end: ‘My father told
me, in so many words, once, that Catholicism was a very rough religion
to live in but it was the only one to die in .’

So take your pick.

Thank you, I think I'll read your book soon.

Wow! How much time do you have? Some of the work is surprisingly accessible. I can verify that I am mortal but read large chunks of 'Theory of Games' and (just about) understood it. This was really important to do for the book because actually most people stopped reading the book and relied on textbooks written afterwards that were based on it. His game theoretic treatment of poker is a classic and I was charmed by how 'bluffing' magically appeared as a strategy when he did the maths.

Mathematical foundations of QM is still important today but it depends how deep you want to get into that. 'The Computer and the Brain' is very readable--and astonishing when you think that it was written in 1956. It feels very contemporary in some ways.

Whoo! Now I look at this in some detail in the QM chapter of the book. You may be aware that there's a dispute over that proof that it still going today! Jeffrey Bub and, separately, Dennis Dieks have argued that von Neumann never meant to rule out all possible hidden variables– only a subset of them. They claim what he was actually arguing was that a hidden variables theory couldn't have the same mathematical structure as his own ie they cannot be Hilbert space theories. And that's true: Bohmian mechanics isn't a Hilbert space theory.

To answer your question though...it's complicated (sorry). Von Neumann seems to have been open to the idea of hidden variable theories ie he didn't think they were mathematically suspect. But my gut feeling was that he didn't see the point of them!

However, he wasn't dismissive of Bohm as other physicists were. From my book:

>While Heisenberg and Pauli branded Bohm’s theory as ‘metaphysical’

or ‘ideological’, von Neumann was not dismissive, as Bohm

himself notes with some pride and more than a little relief. ‘It appears

that von Neumann has agreed that my interpretation is logically consistent

and leads to all results of the usual interpretation. (This I am

told by some people.)’ Bohm wrote to Pauli shortly before his theory

was published. ‘Also, he came to a talk of mine and did not raise any

objections.’

Bohm might have hoped for Einstein to embrace his ideas, which

restored both realism (particles exist at all times in Bohmian mechanics)

and determinism. Einstein was, however, less kind than von

Neumann. Disappointed that Bohm had not rid quantum mechanics

of ‘spooky action at a distance’ (which he could not abide) he privately

called Bohm’s theory ‘too cheap’.

Thank you for the detailed answer! It is a little sad that Grete Hermann rebuttal was ignored (possibly because of sexism?) until John Bell came along.

I just purchased the book and I’m looking forward to reading it!

I remember an anecdote about John Von Neumann that a Professor of Byzantine History had said he had greater expertise on Byzantine History than he had. I wonder how and why he was so interested in history? And were there any other random areas where he was far more knowledgeable than you would expect?

Yes I totally agree. I must say that on this point, I lean heavily in my book on 'ENIAC in Action' by Haigh and colleagues. But as I was writing it became clear to me that von Neumann was uniquely well positioned to help birth the modern computer. So you have his work on mathematical logic during the foundational crisis, the fact that he nearly anticipated Godel, he wrote a reference for Turing then worked down the hall from him and read 'On Computable Numbers'-and understood it!

But then he was practical minded enough to care about programming and engineering and the messy stuff. And enough of a visionary to understand the computer's potential (for science at least, don't think he predicted Facebook):

>I think it is soberly true to say that the existence of such a computer would open up to mathematicians, physicists, and other scholars areas of knowledge in the same remarkable way that the two- hundred- inch telescope promises to bring under observation universes which are at present entirely outside the range of any instrument now existing.

-von Neumann

And yes, he was apparently a brilliant manager. He kept the chief engineer of the IAS computer, Julian Bigelow, and Herman Goldstine, the director of the project, from falling out.

>He kept Herman and I from fighting by some marvellous technique,’ Bigelow remembered. ‘We got along like oil and water, or cat and dog; and von Neumann would keep this here, and this there, and smooth things over.’

Finally, von Neumann had proved his usefulness to the US government and military-a role he embraced. By the end of WWII, he was taken seriously enough that the military was willing to pay most of the costs for building his computer at the IAS--AND he managed to convince them that everything - all details of the project- should be in the public domain! This to me is remarkable--I argue that makes him the sort of godfather of the open source movement.

Then he got the rest of the money from the IAS--because they didn't want to lose their academic superstar!

So he combined all these incredible traits in a way that no one else I know of really did.

There are anecdotes that JvN liked to party, have a few drinks and maybe he a was a smoker (all protagonists smoke in these old black-and-white movies from the 50s). Did he ever utter a remark about what alcohol or nicotine did to his brain? I for one rarely drink, and when I did I need a couple of days to fully recover or to recharge my mental capacity. (Top athletes are not supposed to drink during competitions either.)

Is it known how drink-proof JvN was?

Hermann was a remarkable person. Heisenberg devoted a full chapter of his autobiography to Hermann's arguments about causality in quantum mechanics! Thanks and hope you enjoy the book.

He did like a drink and could hold his alcohol. There was a lot of drinking in the Mitteleuropa circles he hung around in and he and both is first and second wives enjoyed hosting boozy parties. But he never smoked! He apparently reached the conclusion it was unhealthy!

Norm Mcdonald is no genius of the caliber of this convo, but he was a smart guy and when he's being genuine about his friendship and people he loves, I think it shows a sign of what true appreciation can be. It's easy to become nihilistic if you are even slightly above average...

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I've seen it recently argued that it was more likely due to being published in philosophy journals and physicists never refer to philosophy journals.

Do you think he was smarter than Gauss? Why?

Odd example but I miss Norm.

Great question, I'd wondered the same.

Have you ever seen impractical jokers?

Richard Feynman was also a smooth operator

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>When was the decade when JvN was most productive?

This one's really difficult. Unlike Einstein, von Neumann remained productive throughout his whole life--even writing an influential lecture series on his deathbed! But the 1930s were incredible. During that decade, he published his book establishing the rigorous mathematical foundations of quantum mechanis (still definitive), explored the non-linear dynamics of explosions (which would later lead him to his decisive contribution to the Manhattan Project), proved his version of the ergodic theorem, began exploring rings of operators (now known as von Neumann algebras) with 3 monumental papers... (he also bribed a driving test examiner in Princeton to get a license)

His rings of operators are probably his most profound contribution to pure maths. As Freeman Dyson wrote: ‘Exploring the ocean of rings of operators, he found new continents that he had no time to survey in detail. He intended one day to publish a grand synthesis of his work on rings of operators. The grand synthesis remains an unwritten masterpiece, like
the eighth symphony of Sibelius.’

Still von Neumann managed to write 7 papers totalling 500 pages on them! The mathematician Vaughan Jones was awarded the Fields Medal for his work on the mathematics of knots, which emerged from his study of Type II von Neumann algebras. And Carlo Rovelli and Alain Connes used Type III factors in their effort to solve the ‘problem of time’: that though we feel time to flow ‘forwards’, there is no single
unified explanation for why this is so (quantum theory and general relativity, for example, have radically different concepts of time).

But I'd have to choose the 40s for their incredible impact: the von Neumann architecture, the conversion of the ENIAC into the first modern stored program computer, the work on the Manhattan project, his work to aid the US and the secret mission to help the British Navy, the first ever computer simulations, Monte Carlo method with Ulam, the first modern computer program with his wife Klara Dan, the IAS computer project--which with its widely circulated progress reports spawned the first generation of modern computers including IBM's first commercial computer, and, as a hobby, he invented modern game theory with Morgenstern.

Incidentally, for more on Klara Dan von Neumann, might I humbly recommend:

https://engelsbergideas.com/portraits/klara-dan-esoteric-intellect-who-wrote-the-first-modern-computer-code/

and

https://www.lostwomenofscience.org/season-2

Von Neumann's contributions are incredible. But much like Turinf, died relatively young in his early 50s. If he had lived as long as, say, Einstein, would he of kept up such an incredible pace of contributions to humanity?

The guy was still writing incredible lectures on his deathbed! He would have been unstoppable. He was taking an interest in molecular biology too in the '50s. It was a huge loss that cancer took him so early.

You might like this photo https://twitter.com/Ananyo/status/1438483690640785413?s=20&t=g2IGfKeMrZCUTOYum6IpWg

the one thing i will always remember about von neumann is that von neumann architecture means "programs stored in memory". my computer hardware prof verbally beat this idea into us and said that if we don't remember it on graduation day he'd take away our diploma.

question: what's the most unexpected thing someone could learn about von neumann?

Well he was blessed with a photographic memory. So he read a 10 volume history of the world in German when he was a kid and could recite pages verbatim in his 40s! I think he enjoyed military history a fair bit (he read the history of the Peloponnesian Wars) and war games. This probably played into his later interest in games and explains partly why he formulated game theory. Like a lot of mathematicians at the time, they wondered whether maths could help bring peace. They hoped they could use maths to resolve conflicts. Emanuel Lasker, chess grandmaster and a pupil of Hilbert, said the institutes dedicated to the 'science of contest' would ‘breed teachers capable of elevating the multitude from its terrible dilettantism’ in matters of negotiation, transforming politics completely, and ‘aid the progress and the happiness of all humankind’.

He also loved reading novels-Dickens, for example-he was able to recite huge chunks of A Tale of Two Cities. But really he seemed to live and breathe maths, outside the time he spent driving badly at speed and partying.

One of his main blind spots was...himself. He didn't keep a diary though you get some glimpes of the man through his copious letters (his love letters to Klara Dan are remarkable!). But even here, he'll be talking about current affairs, then veer off into a 6 page maths proof! I don't think he was given to analysing his own feelings much...

I definitely think there's something in that. But the physicists of the 20s and 30s were far more interested in 'philosophical' issues and interpretation of QM than physicists now, though it's making a bit of a come back in certain circles.

Hermann did prepare the way with an essay which she sent to Bohr, heisenberg and others--and we know that Heisenberg and
von Weizsäcker read it, and met with her to discuss the essay. but her criticism of the 'no hidden variables' proof was just a small part of that essay and the resulting paper. She didn't seem to attach that much importance to it herself. There was a lot of sexism obviously but it's a mark of Hermann's intellect that she overcame even that and was taken very seriously.

But yes, she first published her thoughts in Abhandlugen der Fries’schen Schule, which was philosophy. When she was asked to send an edited version to Die Naturwissenschaften, which would certainly have been read widely by scientits, she left her criticism of von Neumann out....

Von Neumann in a suit and tie. Feynman in a t-shirt. Classic.

Shout out to julian Bigelow late of 3 hornor lane Princeton nj!!!

Yes I wish she was encouraged to publish her von Neumann work in a physics journal. In any case, I was quite impressed to see her show up in Heisenberg's Physics and Beyond (I think that was the book) as a someone Heisenberg found worthy to write about, and discuss her ideas seriously.

I learned that he was a romantic. Don’t believe me? You can hear his letter to his second wife, Klara Dan, during the second season of the Lost Women of Science podcast. I don’t have it to hand but the intensity of it is something else Take a listen (the series is great) https://www.lostwomenofscience.org/season-2

Gosh. Again I have to say ‘define smart’. But it’s a great comparison. Gauss was a brilliant mathematician who made important fundamental contributions to physics so it’s very apt. I’m biased of course but.., In terms of sheer brain power, von Neumann. In the breadth of his contributions-von Neumann. Von Neumann’s problem was he left so much unfinished-he’d just innovate and move on. So Gauss superior. Not qualified to compare their contributions to pure maths

I heard Gauss could add and multiply 20 digits in his head, could solve equations in his head no different from writing on the board, whereas neumann at best could multiply/add 8 to 10 digits. Although just working memory(can't gauge the rest abilities as they are a bit abstract), that's a pretty huge difference tho?

Yes that’s right. He spends a chapter talking about her ideas

It is. I didn’t know that I must admit. So perhaps Gauss could outdo von Neumann in feats of mental gymnastics… one thing I meant to say, comparing the two -it’s von Neumann’s impact on our modern lives I find so amazing. By formalising utility theory -giving us a way to compare and measure human happiness-that’s shaped the way we think about ourself today for better or worse. Neoliberalism sprung directly from that idea. And I think there’s a tendency to view ourselves as these happiness optimising machines. Or maybe that’s just me…

Oh. Here’s something else I learned that surprised me to an extent. An economics prof pointed this out to me (sadly) after he read the book. Princeton was incredibly racist in von Neumann’s day but von Neumann championed David Blackwell, when most others would not. This raised von Neumann, the man as opposed to the mathematician, to new heights for me when I was told about it. There’s a nice blog post on Blackwell which mentions the impact of this on him: https://stat.illinois.edu/news/2020-07-17/david-h-blackwell-profile-inspiration-and-perseverance

And of course there’s a lot more to higher maths than doing big sums in your head! But still-impressive.

What made you want to write about him?

Was hoping someone would ask this so thanks. As I mentioned in the post, I came across the name first in high school. Then again at university. I was studying physics but an old friend, who was studying economics, was besotted with game theory. In the 15 years or so I was in science journalism, his name kept popping up more and more often but in wildly different contexts… interpretations of quantum mechanics (more interest in that because of quantum computing), nuclear strategy, internet commerce, AI etc So one day I just pulled a bunch of random pop science books off my shelf at home (eg Chaos, Consciousness Explained etc) and I found he was in the index of about half. I read the biography by Macrae but it doesn’t really engage with the science so I thought there must be some book that tells me what von Neumann did that means he’s getting talked about so much. It was fascinating to me that a mathematician could have so much impact outside maths. Most popular maths books and bios tell you about how great maths is for its own sake, but here was a mathematician taking on really big real world questions. I don’t read scientific biography much though I liked A Beautiful Mind (the book NOT the film) and American Prometheus so I deliberately set out to write about von Neumann ideas, lacing bits of his life story through that and adding historical context, and a bit about von Neumann’s interactions with others when relevant (like John Nash). So, for the record, it was never meant to be a standard biography. Some people felt cheated by that, some love it. I wrote a book about a mathematical genius that I’d want to read, which takes his ideas seriously. I’ve wanted to write a book since I was like 5 and I’d had ideas before. Many years ago I pitched a book about the hygiene hypothesis to a respected agent and was snubbed. Several years later Ed Yong wrote a book along the lines of the one I pitched (though he did a much better job of it than I could have). So with the von Neumann book, when publishers were interested I thought—it’s now or never…

nice, for a second i thought you were going to say von neumann was racist but thankfully it was the opposite. also i'll check out the later

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How do you feel about posting the most Bengali thing I've ever seen on reddit?

Are you seriously comparing a comedian to actual geniuses? Norm was above average in entertainment value but not in intelligence. Not really a legitimate comparison.

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Lol. Pretty good actually. But its about a Hungarian/American/Jewish/Catholic mathematician it’s not like AMA about macher johl and Satyajit Ray… that would be true bong. BTW I’ll be in Hyderabad for the India Science Festival in January then in Bangalore and Delhi for talks so if you’re in the neighbourhood… (you’re probably in the States though I guess)

Actually in Delhi. I'm a psychotherapist and neuroscience student. Have a passing interest in mathematics and science things though. I'd love to come by even if i can't engage in depth.

And somehow being an expert on a prolific yet understated mathematical genius makes it more Bengali than macher jhol. Lol.

Seems unlikely that a genius would fall for Pascal's wager...

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When my dad met Edward Teller, he said the saddest day in his life was when he went to visit John in the hospital when he had late onset dementia and he couldn't remember how to do basic math

He was def above average in intellect :p

Your optimism/ expectation of how intelligent the average person is, is too high, but ya I did kinda say he's not of that caliber but hey understanding things is through context and he was my context.