The Unparalleled Genius of John von Neumann(cantorsparadise.substack.com)
cantorsparadise.substack.com
The Unparalleled Genius of John von Neumann
https://cantorsparadise.substack.com/p/the-unparalleled-genius-of-john-von-beb
75 comments
recent discussion, https://news.ycombinator.com/item?id=26695502
Huh, I thought it was a new article but turns out they simply republished it on Substack today.
> “There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann” — George Pólya
If you put that scene in a film, people would call it unbelievable.
If you put that scene in a film, people would call it unbelievable.
How much of our global technological progress can be attributed to a handful of geniuses who happened to be at the right time and place?
How much more backward would the world be if the likes of Newton and Von Neumann hadn't existed?
I unironically believe that the government should dig up his body, retrieve DNA samples, and clone him. Populate federal labs and agencies with Von Neumann clones. Sell a few to FAAMNG too for good measure. Let uber geniuses run the nation's courts, monetary policy, tax laws, environmental protection programs, and defense planning and acquisition.
How much more backward would the world be if the likes of Newton and Von Neumann hadn't existed?
I unironically believe that the government should dig up his body, retrieve DNA samples, and clone him. Populate federal labs and agencies with Von Neumann clones. Sell a few to FAAMNG too for good measure. Let uber geniuses run the nation's courts, monetary policy, tax laws, environmental protection programs, and defense planning and acquisition.
Interesting opinion Henry, what did you make of Robert S. McNamara back in the day?
Von Neumann had a uniquely sharp mind. His daughter was very successful and seemingly above average intelligence, but it's not clear that she had his same potential. I do think it's too bad that the brightest minds don't tend to have a lot of offspring.
It is called "regression towards the mean" (https://en.wikipedia.org/wiki/Regression_toward_the_mean). If someone is at a particular extreme, and the trait is hereditary in less than 100% (biologically or cultural), it is likely that their offsprings will be less extreme.
On the contrary - I find it sad that more intelligent and more accomplished people have fewer offsprings on average than others. While the process is not surprising socially, either there is no hereditary factors in intellectual abilities at all (which does not hold water), or step by step, we decline. Let's hope that technological augments to our mental capabilities develop faster than the biological process.
Once I compared the trajectory to "Idiocracy" (from 2006). Yet, a friend said it is an optimistic movie - since they still choose the smartest person as their president.
On the contrary - I find it sad that more intelligent and more accomplished people have fewer offsprings on average than others. While the process is not surprising socially, either there is no hereditary factors in intellectual abilities at all (which does not hold water), or step by step, we decline. Let's hope that technological augments to our mental capabilities develop faster than the biological process.
Once I compared the trajectory to "Idiocracy" (from 2006). Yet, a friend said it is an optimistic movie - since they still choose the smartest person as their president.
twice in a row really, I'd say Camacho was as smart as Joe - he just didn't come from a society that knew to use water for irrigating crops.
This is why it’s vital to identify genius at an early age (it’s mostly genetic, so the parents provide a big clue) and promote those with the ability regardless of their background or circumstances. Trying to lift the masses a few IQ points is largely a waste of time. Pluck the gifted and grow them. This is how our civilisation advances.
> Let uber geniuses run the nation's courts, monetary policy, tax laws, environmental protection programs, and defense planning and acquisition
We literally already let elite school grads do this and where has it gotten us? 40 years of a yawning gap between the cosmopolitan dream-hoarder class and the rest of us fighting for scraps?
We literally already let elite school grads do this and where has it gotten us? 40 years of a yawning gap between the cosmopolitan dream-hoarder class and the rest of us fighting for scraps?
Intelligence only matters to a certain point for good administrators. Morality, courage, and, above all, self-restraint are just as important. These are the people capable of changing the rules in a way that benefits others even if it means a slight drop in personal wealth, power, or prestige. Often we seem to pick those who are constitutionally incapable of doing that, much to our detriment. (One big reason is that egoists can be wealthy, and wealth can manufacture consent, but that's a discussion for another time.)
George Washington could have been a King, and declined. Whatever other skeletons he had in his closet, that decision puts him very high in my book, and is a fantastic example of our American value of both innovation and civic-minded self-restraint.
George Washington could have been a King, and declined. Whatever other skeletons he had in his closet, that decision puts him very high in my book, and is a fantastic example of our American value of both innovation and civic-minded self-restraint.
>civic-minded self-restraint.
Such a well know American characteristic you needed a 22nd amendment.
Such a well know American characteristic you needed a 22nd amendment.
That we have strayed from the virtue of self-restraint is beyond all doubt, root and vine. Our consumerist, ignorant population and our egoist, shameless leadership proves it. That doesn't mean its not a virtue that we once cared deeply about, and or that it wasn't definitional. And it doesn't mean we won't start caring about it again. I'd like to think that its in our DNA, just recessive right now.
The elite schools are populated by smart people who are well on their way to mastering the rules of the game, like their parents did (speaking broadly), but in general they aren't interested at all in changing the rules for the betterment of the broader society. I'm generalizing, but it's basically true. (There may be some idealistic instinct in college; but that quickly evaporates when the hard choices must be made that impact your families income and safety within society.)
How many lawyers build a successful career on mastering the corrupt rules vs how many build a career speaking truth to power and calling out the corruption? Reforming a corrupt system, succeed or fail, will destroy you and everything you love, and these days you won't even get the paltry victory of public esteem. It's worse: half of our public will take the system's side, insofar as they even know about it, because the system can afford great PR and produces endless distraction.)
The elite schools are populated by smart people who are well on their way to mastering the rules of the game, like their parents did (speaking broadly), but in general they aren't interested at all in changing the rules for the betterment of the broader society. I'm generalizing, but it's basically true. (There may be some idealistic instinct in college; but that quickly evaporates when the hard choices must be made that impact your families income and safety within society.)
How many lawyers build a successful career on mastering the corrupt rules vs how many build a career speaking truth to power and calling out the corruption? Reforming a corrupt system, succeed or fail, will destroy you and everything you love, and these days you won't even get the paltry victory of public esteem. It's worse: half of our public will take the system's side, insofar as they even know about it, because the system can afford great PR and produces endless distraction.)
Value != trait
If anything a value is something honored because the breech is more common, valued in part due to scarcity.
If anything a value is something honored because the breech is more common, valued in part due to scarcity.
You mean elite schools with legacy admissions and affirmative action policies? Yeah, it lead the US to a yawning gap. Make college funding conditional on transparent admission based on standardized testing and things will get better.
"I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops." - Stephen Jay Gould
I've always been a bit suspicious of this idea of unrealized potential. You can take anyone and put them in the perfect situation with motivation and there's a good chance they'll succeed. Just as much as a poor child could have the potential to present revolutionary ideas as Einstein did, how many people working in adtech for example could have become revolutionary mathematicians if they put their effort and focus into it? You can apply it to literally anything
> that people of equal talent have lived and died in cotton fields and sweatshops.
Equal potential maybe. But it's nonsense to equate potential with talent. Talent is observed based on demonstrable execution.
A pithy quote is all that is.
Equal potential maybe. But it's nonsense to equate potential with talent. Talent is observed based on demonstrable execution.
A pithy quote is all that is.
Gould is known for placing ideology ahead of science, so it's refreshing that he admits as much.
Stephen F. Blinkhorn, a senior lecturer in psychology at the University of Hertfordshire, wrote that The Mismeasure of Man was "a masterpiece of propaganda" that selectively juxtaposed data to further a political agenda. [..] Jensen also criticized Gould for concentrating on long-disproven arguments (noting that 71% of the book's references preceded 1950), rather than addressing "anything currently regarded as important by scientists in the relevant fields"
https://en.wikipedia.org/wiki/The_Mismeasure_of_Man
Stephen F. Blinkhorn, a senior lecturer in psychology at the University of Hertfordshire, wrote that The Mismeasure of Man was "a masterpiece of propaganda" that selectively juxtaposed data to further a political agenda. [..] Jensen also criticized Gould for concentrating on long-disproven arguments (noting that 71% of the book's references preceded 1950), rather than addressing "anything currently regarded as important by scientists in the relevant fields"
https://en.wikipedia.org/wiki/The_Mismeasure_of_Man
Gould wrote a controversial book attacking whole swathes of science done in the past. The existence of a senior lecturer at the University of Hertfordshire who has written a criticism of it doesn't seem that surprising and certainly doesn't seem sufficient evidence that we should disregard what he has to say.
> certainly doesn't seem sufficient evidence that we should disregard what he has to say.
No, we should disregard what he has to say because even his arguments against the century-old studies he attacks (while carefully avoiding modern work) were shown to be faulty. It's like (poorly) debunking phlogiston in the modern day, and expecting to be taken seriously.
No, we should disregard what he has to say because even his arguments against the century-old studies he attacks (while carefully avoiding modern work) were shown to be faulty. It's like (poorly) debunking phlogiston in the modern day, and expecting to be taken seriously.
Stephen F. Blinkhorn, is that you?
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> Let uber geniuses run the nation's courts, monetary policy, tax laws, environmental protection programs, and defense planning and acquisition.
You might want to read up on his political views in general and his role in the creation of the atomic bomb in particular. He wanted to drop the bomb on Kyoto (the historical cultural center of Japan) and actively supported a preventive nuclear strike against Russia.
What's the lesson here? High intelligence doesn't correlate with moral and ethical behavior.
EDIT: just noticed your user name...
You might want to read up on his political views in general and his role in the creation of the atomic bomb in particular. He wanted to drop the bomb on Kyoto (the historical cultural center of Japan) and actively supported a preventive nuclear strike against Russia.
What's the lesson here? High intelligence doesn't correlate with moral and ethical behavior.
EDIT: just noticed your user name...
> actively supported a preventive nuclear strike against Russia.
Well, even Bertrand Russell, who protested against war from WWI to the Vietnam War, advocated a preemptive nuclear strike against the USSR in 1954. The risk of nuclear war killing everyone, once the USSR had nukes, just seemed too great, I guess.
Well, even Bertrand Russell, who protested against war from WWI to the Vietnam War, advocated a preemptive nuclear strike against the USSR in 1954. The risk of nuclear war killing everyone, once the USSR had nukes, just seemed too great, I guess.
So Bertrand Russell wasn't always right, either. Fortunately, the actual politicians in charge were a bit more reasonable.
What if he was right and we live now in a world worse as a result?
What if he wasn’t right and we live now in a world better as a result?
What if he wasn’t right and we live now in a world better as a result?
For the curious, check this essay "Did Russell Advocate Preventive Atomic War against the USSR?": https://mulpress.mcmaster.ca/russelljournal/article/download...
I wonder if their opinions would have changed if they had been aware of the possibility this would result in nuclear winter.
You are assuming the point you are trying to prove: that von Neumann was unjustified in advocating for these things.
Maybe he was just smarter than you (and me) and just had a really good argument for believing those things, given the state of the world at the time and his various priors.
Also, humans have created thousands of different and highly contradictory systems of morality over the past several thousand years. You would probably be better off not believing that you have discovered the Correct Theory of Morality.
Also, humans have created thousands of different and highly contradictory systems of morality over the past several thousand years. You would probably be better off not believing that you have discovered the Correct Theory of Morality.
At least in hindsight I can say with confidence that John von Neumann was wrong in this matter. Or do you really think things could have turned out better if the US had began a nuclear war?
It is one thing to say that in hindsight he held a wrong belief, and another thing entirely (especially without knowing his exact arguments and priors) to say that he held a wrong belief at the time and was not only wrong, but also therefore morally defective.
I would actually argue for the latter. Even if he might have had valid geopolitical reasons to advocate a nuclear strike (althought I highly doubt it), it would have been morally wrong nevertheless. In my opinion, there is never an ethical justification for the usage of atomic weapons. In fact, I firmly believe that the bombing of Hiroshima and Nagasaki was ethically wrong as well, but I know that other people have a different opinion on this matter.
It is very difficult to conceive of Japan having turned out any better if Kyoto had been destroyed.
I agree, but I think there are many ways of arguing that the destruction of Kyoto was justified at the time that do not involve arguing that it would make Japan better off. And like I said, there is more than one theory of morality :)
On the contrary:
"Many generations of graduate students who might have been tempted to try to construct hidden-variables theories were beaten into submission by the claim that von Neumann, 1932, had proved that it could not be done. A few years later (see Jammer, 1974,p.273) Grete Hermann, 1935, pointed out a glaring deficiency in the argument, but she seems to have been entirely ignored. Everybody continued to cite the von Neumann proof. A third of a century passed before John Bell, 1966, rediscovered the fact that von Neumann's no-hidden-variables proof was based on an assumption that can only be described as silly." Mermin https://cqi.inf.usi.ch/qic/Mermin1993.pdf
No one is infallible, and this kind of mythical status has problems. Grete was dismissed, and Bell's paper only was admitted because the editor thought it was confirming Von Nuemman even. And even if von Neumman's proof wasn't as "silly" as Bell said, the fact that everyone else ran with it surely harmed quantum theory for a long while, reinforcing the Copenhagen side unjustifiably at the expense of others.
"Many generations of graduate students who might have been tempted to try to construct hidden-variables theories were beaten into submission by the claim that von Neumann, 1932, had proved that it could not be done. A few years later (see Jammer, 1974,p.273) Grete Hermann, 1935, pointed out a glaring deficiency in the argument, but she seems to have been entirely ignored. Everybody continued to cite the von Neumann proof. A third of a century passed before John Bell, 1966, rediscovered the fact that von Neumann's no-hidden-variables proof was based on an assumption that can only be described as silly." Mermin https://cqi.inf.usi.ch/qic/Mermin1993.pdf
No one is infallible, and this kind of mythical status has problems. Grete was dismissed, and Bell's paper only was admitted because the editor thought it was confirming Von Nuemman even. And even if von Neumman's proof wasn't as "silly" as Bell said, the fact that everyone else ran with it surely harmed quantum theory for a long while, reinforcing the Copenhagen side unjustifiably at the expense of others.
Interesting citation, I had heard of John Bell's theorem, which disproves local hidden variable theories.
But I did not know that von Neumann had his own attempt at disproving these theories.
Researching this a little further, I also found people arguing that von Neumanns arguments were misconstrued by Bell.
https://arxiv.org/abs/1006.0499
I wonder how Grete Hermann's arguments compare to the arguments from Bell and what the real truth is.
Ya I am not an expert to judge if Bell, Grete, and Mermin also misunderstood von Neumman, and I see a few papers argue that. But the larger physics community does seem to agree with Bell's take. I do find it a bit weird that paper is using an entire page of what von Neumman would have said in response.
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This is mostly what Plato advocated in The Republic, it inspired quite a few policies over the last few centuries.
The result is not as good as you might expect, this philosophy leads to aristocracy, not the most efficient form of government, by a long shot.
The result is not as good as you might expect, this philosophy leads to aristocracy, not the most efficient form of government, by a long shot.
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Aside from the other issues mentioned by commenters i want to add that this perspective leaves out the whole nature vs nurture debate - so those clones would not automatically become geniuses.
You could essentially just give a bunch of kids a phenomenal education and end up with a similiar, if not better result due to diversification of talents.
You could essentially just give a bunch of kids a phenomenal education and end up with a similiar, if not better result due to diversification of talents.
Although von Neumann was certainly a genius who happened to be in the right place at the right time, he's also an example of how groups of people can create a culture seemingly much more important than the effect of one outstanding individual. Lipót Fejér led a school of analysis at Eötvös Loránd University in Budapest. He ran a seminar, was the centre of a large group of young mathematicians who worked together and was enormously influential.
Hungary has a disproportionate number of the world class mathematicians of the 20th century. The numbers are even more extreme when you consider that those mathematicians are all from Budapest, all from Eötvös, and the vast majority of them Fejér's supervisees. It's totally plausible that Fejér created an environment where people who might otherwise have been middling mathematicians, decent engineers, or never have found their niche, were transformed, by collaboration and inspiration, into the likes of von Neumann, Erdős, Pólya.
Even today the Eötvös school of analysis and combinatorics is a significant powerhouse, with most members direct mathematical descendants from Fejér. And there are other branches such as Cambridge combinatorialists where the influence of Fejér's students and grand-students has been key in the formation of world class mathematicians.
Hungary has a disproportionate number of the world class mathematicians of the 20th century. The numbers are even more extreme when you consider that those mathematicians are all from Budapest, all from Eötvös, and the vast majority of them Fejér's supervisees. It's totally plausible that Fejér created an environment where people who might otherwise have been middling mathematicians, decent engineers, or never have found their niche, were transformed, by collaboration and inspiration, into the likes of von Neumann, Erdős, Pólya.
Even today the Eötvös school of analysis and combinatorics is a significant powerhouse, with most members direct mathematical descendants from Fejér. And there are other branches such as Cambridge combinatorialists where the influence of Fejér's students and grand-students has been key in the formation of world class mathematicians.
> In fact, von Neumann claimed to do some of his best work in noisy, chaotic environments such as in the living room of his house with the television blaring.
I often think of this when people claim it is impossible to conceive of any advanced thought in an open office or noisy environment. In fact, it is just a personal preference and one environment isn't necessarily any better than another.
I often think of this when people claim it is impossible to conceive of any advanced thought in an open office or noisy environment. In fact, it is just a personal preference and one environment isn't necessarily any better than another.
Not impossible, just impossible for them.
First, the difference between the television blaring and my office talking is that in office chatter I'm constantly picking up bits of sound that make my brain think I should be paying attention to them. The sounds of a Simpsons rerun I've seen 90 times don't distract my brain in the same way.
Second, we're talking about what works for MOST people, Peopleware has actual data to back this up, the majority of people need quiet private space to do deep work.
First, the difference between the television blaring and my office talking is that in office chatter I'm constantly picking up bits of sound that make my brain think I should be paying attention to them. The sounds of a Simpsons rerun I've seen 90 times don't distract my brain in the same way.
Second, we're talking about what works for MOST people, Peopleware has actual data to back this up, the majority of people need quiet private space to do deep work.
> in office chatter I'm constantly picking up bits of sound that make my brain think I should be paying attention to them
Agree. I found that hearing my boss on one side of a phone call where they referenced me or my work in some way was very distracting. What had happened? What was going to happen? What was I potentially being committed to?
Agree. I found that hearing my boss on one side of a phone call where they referenced me or my work in some way was very distracting. What had happened? What was going to happen? What was I potentially being committed to?
I find it the opposite. To work in a noicy environment is obviously so remarkable that its worth writing about.
Something that greatly surprised me when I worked in my first open plan office was that I didn't prefer any headphones or earbuds of any kind. I kind of melted into my work and sometimes looking up at people walking by or various smells, sounds, etc. would keep my mind active.
Actually it is not just personal preference. I remember reading studies that show that school children perform worse when there is background noise. Here's one article: https://www.psychologytoday.com/us/blog/ulterior-motives/201...
I’m not trying to single you out but I think you are making an incredibly common mistake that I see everyone make all the time, and it almost never gets called out, so I’m going to do it here now:
Just because a study finds that some cause, on average, has some effect, I don’t think it is correct to start believing that that cause and effect will hold for you or any else in particular.
I’m convinced that for you noise is distracting, and that it is probably the case for most people, but I also totally believe that for some people it can work the other way around. I don’t think you can use the aggregate result of a study to argue against somebody else’s personal experience.
Just because a study finds that some cause, on average, has some effect, I don’t think it is correct to start believing that that cause and effect will hold for you or any else in particular.
I’m convinced that for you noise is distracting, and that it is probably the case for most people, but I also totally believe that for some people it can work the other way around. I don’t think you can use the aggregate result of a study to argue against somebody else’s personal experience.
> Just because a study finds that some cause, on average, has some effect, I don’t think it is correct to start believing that that cause and effect will hold for you or any else in particular.
Where did I say this at all? This is a straw man. The original comment stated, without any evidence at all, that noisy, chaotic environments aren't necessarily worse. I stated, with evidence, that it has been shown to have a negative effect on average. No where does this preclude that it may help some people or have no effect on some people.
Where did I say this at all? This is a straw man. The original comment stated, without any evidence at all, that noisy, chaotic environments aren't necessarily worse. I stated, with evidence, that it has been shown to have a negative effect on average. No where does this preclude that it may help some people or have no effect on some people.
On the other hand, there is evidence that a certain amount of noise helps creativity: [1], [2]
[1] - https://medium.com/s/how-to-design-creative-workspaces/how-n...
[2] - http://www.jstor.org/stable/10.1086/665048
[1] - https://medium.com/s/how-to-design-creative-workspaces/how-n...
[2] - http://www.jstor.org/stable/10.1086/665048
I find noise distracting when things are not working, and I believe they should be working, and this process has been going on for a while. Otherwise I find noise sort of calming.
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> such as in the living room of his house with the television blaring.
The environment is still under his control. Not at all like an open office.
The environment is still under his control. Not at all like an open office.
In my opinion one of the great contributions of Von Neumann was the fact his "First Draft of a Report on the EDVAC" report was spread so quickly in academic circles. When Eckert and Mauchly attempted to apply to patent their ideas for the ENIAC, the courts decided that the report constituted prior publication, and their patent application failed, meaning the key ideas and concepts from the ENIAC, many which define modern computers, were now in public domain and could be used freely
Great people are warranted discussion, but as someone who was once in the academic math world, I had to quit reading after a few sentences.
Genius is a very real thing, but I don't need to read adulation after adulation in a series of anecdotes and quotes that will only make me feel inadequate.
The mathematics itself is greater than the mathematician, who himself craps on the toilet like anyone else. Focus on the math, not the mathematician. It will make you happier.
Genius is a very real thing, but I don't need to read adulation after adulation in a series of anecdotes and quotes that will only make me feel inadequate.
The mathematics itself is greater than the mathematician, who himself craps on the toilet like anyone else. Focus on the math, not the mathematician. It will make you happier.
> Focus on the math, not the mathematician. It will make you happier.
Personally I don't feel inadequate when reading about someone like von Neumann, as I'm not really tempted to compare myself to him in the first place. Colleagues are peers, people I graduated with are peers, but von Neumann is almost like another species.
I forget who it was who pointed out that Silicon Valley billionaires tend to dress like 'normal people', in sharp contrast to aristocrats. People don't tend to feel poor for comparing themselves against the Queen, as they perceive too much distance to make a personal comparison.
Personally I don't feel inadequate when reading about someone like von Neumann, as I'm not really tempted to compare myself to him in the first place. Colleagues are peers, people I graduated with are peers, but von Neumann is almost like another species.
I forget who it was who pointed out that Silicon Valley billionaires tend to dress like 'normal people', in sharp contrast to aristocrats. People don't tend to feel poor for comparing themselves against the Queen, as they perceive too much distance to make a personal comparison.
>Colleagues are peers, people I graduated with are peers, but von Neumann is almost like another species.
Von Neumann's contemporaries agreed, which is why he and other Ashkenazi Jews from Hungary were nicknamed Martians https://en.wikipedia.org/wiki/The_Martians_(scientists) . Societal and genetic pressures over centuries produced unusually high IQs (and some associated genetic problems).
Von Neumann's contemporaries agreed, which is why he and other Ashkenazi Jews from Hungary were nicknamed Martians https://en.wikipedia.org/wiki/The_Martians_(scientists) . Societal and genetic pressures over centuries produced unusually high IQs (and some associated genetic problems).
> Personally I don't feel inadequate when reading about someone like von Neumann, as I'm not really tempted to compare myself to him in the first place. Colleagues are peers, people I graduated with are peers, but von Neumann is almost like another species.
Perhaps I am more prone to egoism than you! I had a "promising" start to my career and a lot of ambition. I've fallen off that track and had time to reflect on what matters, but I still feel twinges of ego-driven ambition.
Perhaps I am more prone to egoism than you! I had a "promising" start to my career and a lot of ambition. I've fallen off that track and had time to reflect on what matters, but I still feel twinges of ego-driven ambition.
The queen does not have much personal money anyway. it belongs to the family.
I think it is understandable to feel inadequate. that is motivation to be better.
I think it is understandable to feel inadequate. that is motivation to be better.
> I think it is understandable to feel inadequate. that is motivation to be better.
I don't see the sense in this. No amount of work would turn the average mind into the next von Neumann.
I don't see the sense in this. No amount of work would turn the average mind into the next von Neumann.
being better does mean being a copy of the guy
You can work as much as you like, you're still going to be nowhere near as smart as von Neumann. Why should that be motivating? I'm not convinced there's an upside to feeling inadequate by comparison.
Thank you for sharing your perspective on this. I think other people probably feel similarly.
I am old enough now that I accept my limitations, and have decided to apply my talents to areas that I find interesting and valuable.
Just because I will never be a Leibnitz, I’m still confident that I can help teach people what I know and help them on their own paths to reach their individual potential.
But still, I marvel at geniuses like Feynman who made things seem so effortless.
I am old enough now that I accept my limitations, and have decided to apply my talents to areas that I find interesting and valuable.
Just because I will never be a Leibnitz, I’m still confident that I can help teach people what I know and help them on their own paths to reach their individual potential.
But still, I marvel at geniuses like Feynman who made things seem so effortless.
As a counter, I absolutely love reading about these extraordinary individuals. To be sure their intellectual standing and productivity is almost overwhelming, such that I have to study hard just to appreciate the foothills of the mountains they sprang among like heavenly goats, but their humanity, their joi-de-vivre, and most especially their historical context is hugely worthwhile knowing.
Reading of the achievements of others doesn't make me feel inadequate, rather it fills me with hope and real joy.
Yes, Mathematics is greater than mathematicians, but never forget our mathematics is still profoundly and inescapably human, and none the worse for it. Read more Mathematics!
Reading of the achievements of others doesn't make me feel inadequate, rather it fills me with hope and real joy.
Yes, Mathematics is greater than mathematicians, but never forget our mathematics is still profoundly and inescapably human, and none the worse for it. Read more Mathematics!
"Focus on the math, not the mathematician."
Do you think von Neumann's education might have had anything to do with what he was able to achieve?
How about how he was raised by his parents?
Or how about his work ethic, motivation, and attitude towards discovery?
How about the people that he admired and that influenced him?
Learning these things might help us to raise future extraordinary achievers, or might even help us with our own lives/work.
You will not find any of these things in his mathematics, but you might learn about them by studying his life.
Do you think von Neumann's education might have had anything to do with what he was able to achieve?
How about how he was raised by his parents?
Or how about his work ethic, motivation, and attitude towards discovery?
How about the people that he admired and that influenced him?
Learning these things might help us to raise future extraordinary achievers, or might even help us with our own lives/work.
You will not find any of these things in his mathematics, but you might learn about them by studying his life.
99.9% genes in his case. Look how hard parents push their kids these days, yet few even come close to his genius.
"99.9% genes in his case"
You think if he was raised in a third-world country without access to education he would have achieved just as much?
He was raised in the intellectual hothouse of turn of the century Hungary, which also produced many other eminent mathematicians.
His parents were wealthy nobility, who could afford the best education for their children, and believed strongly in its value.
"When they were young, governesses taught von Neumann, his brothers and his cousins. Max believed that knowledge of languages in addition to Hungarian was essential, so the children were tutored in English, French, German and Italian."
He attended "one of the best schools in Budapest and was part of a brilliant education system designed for the elite."
"The Hungarian school system produced a generation noted for intellectual achievement, which included Theodore von Kármán (born 1881), George de Hevesy (born 1885), Michael Polanyi (born 1891), Leó Szilárd (born 1898), Dennis Gabor (born 1900), Eugene Wigner (born 1902), Edward Teller (born 1908), and Paul Erdős (born 1913)."
"At the age of 15, he began to study advanced calculus under the renowned analyst Gábor Szegő... He then went to the University of Göttingen on a grant from the Rockefeller Foundation to study mathematics under David Hilbert."
Most people don't get opportunities to study at one of the most elite educational institutions in the world, with world-class academics.
That is not genetics, that's opportunity.
"Look how hard parents push their kids these days, yet few even come close to his genius."
Maybe they're "pushing" in the wrong way. And is pushing what needs to be done?
What was von Neumann's parents' approach exactly? How did they interact with him and what values about learning did they instill in him when he was young?
These questions are important to answer.
You think if he was raised in a third-world country without access to education he would have achieved just as much?
He was raised in the intellectual hothouse of turn of the century Hungary, which also produced many other eminent mathematicians.
His parents were wealthy nobility, who could afford the best education for their children, and believed strongly in its value.
"When they were young, governesses taught von Neumann, his brothers and his cousins. Max believed that knowledge of languages in addition to Hungarian was essential, so the children were tutored in English, French, German and Italian."
He attended "one of the best schools in Budapest and was part of a brilliant education system designed for the elite."
"The Hungarian school system produced a generation noted for intellectual achievement, which included Theodore von Kármán (born 1881), George de Hevesy (born 1885), Michael Polanyi (born 1891), Leó Szilárd (born 1898), Dennis Gabor (born 1900), Eugene Wigner (born 1902), Edward Teller (born 1908), and Paul Erdős (born 1913)."
"At the age of 15, he began to study advanced calculus under the renowned analyst Gábor Szegő... He then went to the University of Göttingen on a grant from the Rockefeller Foundation to study mathematics under David Hilbert."
Most people don't get opportunities to study at one of the most elite educational institutions in the world, with world-class academics.
That is not genetics, that's opportunity.
"Look how hard parents push their kids these days, yet few even come close to his genius."
Maybe they're "pushing" in the wrong way. And is pushing what needs to be done?
What was von Neumann's parents' approach exactly? How did they interact with him and what values about learning did they instill in him when he was young?
These questions are important to answer.
> Most people don't get opportunities to study at one of the most elite educational institutions in the world, with world-class academics
Most don't. Many do. And Vom Neumann was still massively ahead of them, and the rest of the world.
Trying to write off his raw brain power as mostly a consequence of his socio-economic standing and upbringing is intellectually bankrupt but populist-pandering poppycock.
Most don't. Many do. And Vom Neumann was still massively ahead of them, and the rest of the world.
Trying to write off his raw brain power as mostly a consequence of his socio-economic standing and upbringing is intellectually bankrupt but populist-pandering poppycock.
Of course some of it genetics, twin studies show significant correlations.
We should not discard the importance of pedagogy and mentorship.
Polgar chess prodigies is an interesting experiment on upbringing and crystallizing genius abilities in gifted children though.
We should not discard the importance of pedagogy and mentorship.
Polgar chess prodigies is an interesting experiment on upbringing and crystallizing genius abilities in gifted children though.
Then again you need all three for genius, confluence of raw material of talent, opportunity to train under great teachers and means to follow through with it.
Where the latter two are available, it is easier to find genius, which is why it often occurs in clusters.
Where the latter two are available, it is easier to find genius, which is why it often occurs in clusters.
>The mathematics itself is greater than the mathematician, who himself craps on the toilet like anyone else. Focus on the math, not the mathematician. It will make you happier.
The mathematician reveals the math. The math won't reveal itself
The mathematician reveals the math. The math won't reveal itself
> The mathematics itself is greater than the mathematician, who himself craps on the toilet like anyone else. Focus on the math, not the mathematician. It will make you happier.
To each his own I guess, but personally I don’t want to waste my time on something I’m not good at nor do I have the capability to be good at.
To each his own I guess, but personally I don’t want to waste my time on something I’m not good at nor do I have the capability to be good at.