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I’m curious, since I never studied maths past A level. Is there a difference to the way it’s taught now compared to whenever von Neumann was studying. What I

• tekla 3y ago
  Some people just seem to be born with the gift and are simply better. I recommend reading about Srinivasa Ramanujan https://en.wikipedia.org/wiki/Srinivasa_Ramanujan https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
  • jonplackett 3y ago
    This is fascinating. Thanks for sharing.
  • hakdbha 3y ago
    [dead]
  • mycologos 3y ago
    Ramanujan is an interesting comparison. He was an outstanding mathematician, but it feels like his prowess came from a deep love of math and concomitant time spent on it. There's an anecdote somewhere about child Ramanujan working his way through thousands of elementary lemmas for fun, and I wonder if this gave him the almost occult intuitive ability reported by his collaborators. The stories about him have a tone of awe, but not fear. In some contrast, von Neumann seems to have been able to take his enormous fluid intelligence and speed and apply it to pretty much whatever problem he decided, and he did it across many areas, including non-scientific ones. The stories about him are tinged with a little unease, and it's a little harder to see the human underneath his achievements.
    • rowanG077 3y ago
      You are really deluding yourself if you think anyone can reach Ramanujan levels of skill by simply trying hard enough. This takes insane innate talent in addition to trying hard.
      • laichzeit0 3y ago
        Yeah it’s like people thinking anyone can be a Micheal Jordan or Tiger Woods if they just tried hard enough, started young enough, were born in the right place to the right parents enough. Some people just have the gift, it’s like neural networks: some random weight initialisations are just better, some maybe even so close to optimum that almost no training is needed at all.
      • andxor_ 3y ago
        Ramanujan was extra-terrestrial. His note books have produced so many papers and PhD theses. Probably will continue to do so for many more years.
  • nradov 3y ago
    Edward Witten probably falls into that category as well. https://en.wikipedia.org/wiki/Edward_Witten https://en.wikipedia.org/wiki/Edward_Witten
• chpatrick 3y ago
  https://en.wikipedia.org/wiki/The_Martians_(scientists) https://en.wikipedia.org/wiki/The_Martians_(scientists) There was an incredible cadre of scientists from Hungary in the early 20th century. Sadly they were exiled by fascism.
  • javajosh 3y ago
    One wonders what fascism could have done had it not alienated intellectuals. But one also wonders if that alienation is core to fascism, even definitive. Fascism is notoriously hard to define, but "alienates the best thinkers" seems like a good litmus test.
    • deleted 3y ago
      [deleted]
    • tonyarkles 3y ago
      Well... for curiosity-sake I clicked through the list of scientists on the Martians page. Every single one of them has Jewish ancestry. So while fascism more generally (right-wing nationalist authoritarianism) doesn't strictly prohibit intellectuals, World War II fascism alienated these folks because of their heritage. There were still lots of smart people in Nazi Germany, as evidenced by Operation Paperclip which brought ~1,600 Nazi scientists over to the US to work on rockets and help the US fight the USSR in the Cold War and space race.
      • hattmall 3y ago
        >Every single one of them has Jewish ancestry. Well, yes, as that's the defining characteristic of the group and why they moved to the United States and became known as the martians.
      • epolanski 3y ago
        Anti semitism is not a core or a common ingredient of what we historically define as fascist governments. Spain under Franco and Portugal under Salazar did not persecute Jews, in fact allowed them safe passage from Vichy France. Italy really turned antisemitic after more than a decade with the alliance with Germany to appease Hitler mostly. There's a nice book on the topic, in Italian, "Mussolini Razzista Riluttante" by Antonio Spinosa.
• mhh__ 3y ago
  It's hard to imagine von Neumann not being great today (I think some stories are probably made up, but he was obviously in the top 1 minds of his era), but it is probably true that the "easy" stuff has been mined - where I would define easy as things that can stem from an application of brains around the coffee table rather than intense application of years of whittling at the conference stage.
  • titanomachy 3y ago
    > in the top 1 minds of his era Not sure if that’s a typo
    • prerok 3y ago
      Not the author, but probably top 1 percent?
      • kgwgk 3y ago
        More likely top 10 - if it’s indeed a typo.
      • xxs 3y ago
        top 1% would be such way out of range. top 0.0001% would still not make it justice.
        • hiAndrewQuinn 3y ago
          1 out of every million... Yeah, that sounds about right to me as an actual lower bound.
          • alex_smart 3y ago
            Not sure if you’re being facetious? There were not 100 people of the same calibre as JvN in the US or even the world surely.
• empath-nirvana 3y ago
  Eventually you start specializing and learning more and more about a particular topic until you know as much about it as anybody else, and then you just keep going. There's always massive open questions because every question you answer generates more questions.
  • epolanski 3y ago
    This. Which is also why most science published is hard to verify. Pretty much every topic out there is niche enough that the amount of people able to review it (let alone test it) is extremely small and they all know each other.
• Projectiboga 3y ago
  I forget the time frames, but you won't get far out of the 19th century undergrad in math like calculus. Statistics or stuff in Comp Sci you will but not in Calc or Differential Equations.
  • prerok 3y ago
    That's somewhat true, however the way the math is taught has changed. Anecdottally, my father was only introduced to vectors and vector based calculations when at the uni. My generation was taught vectors in primary school already. I think they opted for the different approach to make a more visual representation of the concepts, so younger minds could more easily grasp them.
• sublinear 3y ago
  Contrary to all the fawning in this thread I can only say the somewhat obvious that if you were alive then you'd too think that was a reasonable thing for you to do.
• j7ake 3y ago
  I guess the issue is that being able to articulate what is the frontier problems of any field requires a certain amount of jargon and technical knowledge. I think one can learn math and physics without being at the frontier. One can appreciate the beauty of solutions of classical problems by discussing the problem in a historical context.
• dukeofdoom 3y ago
  Not really an answer to your question. But here's a picture of math entrance exam from 1869 to Harvard. https://imgur.com/a/bDGRU https://imgur.com/a/bDGRU
• somat 3y ago
  Often, I feel things are taught poorly. Most just want to sort things out, then teach it systematically from bottom to top. I understand this, it is a lot simpler, but that is not how we figure things out. there are false starts, things that did not work The best teachers, guide you in this process of discovery.
  • rowanG077 3y ago
    It's not only simpler. It's also faster. We don't want people exiting high school and they just learned of the concept 0.
  • 0xEF 3y ago
    Sagan's old quote about making an apple pie applies, here, I think. Building on your sentiment, I have always felt that schools (in the US, at least) tend to teach students what to think rather than how to think. There is a huge emphasis on "here is the answer, now go find the questions" where I posit more focus should be placed on guiding a student to problem solve, think critically, and discover a few things for themselves, especially at the younger ages
• keithalewis 3y ago
  There are still massive open questions. The current educational system does not providing the tools you need to address them. Maybe you should look into Laslo Polgar. Another Hungarian who taught his daughters how to beat chess grandmasters.
• kqr 3y ago
  I strongly recognise this sentiment. It's why it was so refreshing to read The War Trap[1]. Granted, it's 40 years old at this point, but the author took data I have access to, used maths I know, and derived new results on a complicated topic. It's incredibly inspiring. What other complicated fields are just waiting for the right person to come along and discover their fundamental laws? I have a vague suspicion that partial differential equations are criminally underused in modeling for software developmemt and system design. [1]: I wrote a short review at https://two-wrongs.com/war-what-is-it-good-for.html https://two-wrongs.com/war-what-is-it-good-for.html if anyone is curious.
• k1t 3y ago
  My memory of school at that age was they'd teach you one thing as though it was the absolute truth, then the following year tell you it was all a lie (or over-simplification) and actually it works like this. Then the next year they'd do it again. We'd occasionally catch them at it when in Chemistry they'd tell us electrons worked one way and in Physics they'd say they worked another. Anyway, I can definitely see how an enquiring mind might want to move past all this and find out The Truth.
  • _glass 3y ago
    I hated this. I started school in Saxony (state in Germany), and then my family relocated to Bavaria. The curriculum switched from a science to a language focus, so I already knew all the next-level Chemistry, and was really annoyed by the style of teaching it wrongly.
  • mkl 3y ago
    I (in NZ) remember that happening in physics and chemistry, but not maths. Maths has unambiguously and provably correct answers, so while more general methods and topics are introduced, old results don't change. (Maybe this is why I became a mathematician!)
    • mrWiz 3y ago
      This pattern appeared in my math math education in the USA as well, but not as pronounced as in physics or chem. The biggest example is that we were initially taught that you cannot take the square root of a negative number. I also have vague memories of learning that a larger number cannot be subtracted from a smaller number (sometime early in grade school).
• lordnacho 3y ago
  It's like that all the way through undergrad, you're just learning things that have been known for a long time. You need to know the basics before you can contribute anything new, and there's a lot of basics nowadays. Once you get to the edge, the game changes a fair bit. You'll need to know the actual experts, rather than just watching YouTube lectures or reading textbooks. In terms of difference at the level you're talking about, the one big difference is that von Neumann's parents recognized how smart he was, and could afford to hire appropriate tutors to accelerate his learning. There's this thing called Bloom's Two Sigma, though I'm no expert on the area it would appear that having a tutor improves results considerably. Now imagine one of the smartest kids ever born having parents who got him tutors.
• randomcarbloke 3y ago
  Actually yes, the gymnasium at which he studied in Hungary during the turn of the C20 had a very fast and formulated approach to mathematical learning, it churned out a handful of truly exceptional minds, there is literature but it is sparse.
• jhbadger 3y ago
  >What I mean is, the way I was taught maths and science in general was with a feeling of “look we basically know everything just learn this and you’ll be fine”. That's pretty much how anything is taught in high school (and even most undergraduate programs). It's considered confusing to teach students that a lot of what we "know" is known to be incomplete and will change. I've kept some of my textbooks on immunology and other biomedical topics from the 1990s and parts of them are basically unrecognizable to what we are working on today. Sure, the basics haven't changed but the details certainly have.
• xLaszlo 3y ago
  Hungary had and still has a state sponsored "elite" education for gifted children. From a relatively early age kids are regularly tested (both materially and curiosity wise) if they are interested in "better" Maths. So they are prepared to a STEM trajectory. You don't need to be a genius just reasonably good and interested. I would think 10% of all kids take part. Check out UKMT for the equivalent in the UK or Kangaroo competitions. Secondary schools has a 130! year old journal (KOMAL) for competition Maths (again various difficulties) but those who go on to become mathematicians (an extremely selective subject in Hungary) pass the hardest tests as well. So Hungary has various levels of gifted children support programs and has it for the last 100+ years (across 3-4 different government structures)