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Math is much more than what I was taught in school. I discovered that as a child when stumbling upon this Hungarian math book at the local library: https://www.amazon.com/Playing-Infinity-Dover-Books-Mathemat...
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It's difficult to generalize, but by pretty much any metric you choose Hungary produced a massively disproportionate share of the outstanding mathematicians of the twentieth century.
can you give couple examples that are most prominent?
George Pólya (1887−1985). Look at those dates—another immortal. Pólya was Hungarian. Even more striking than the rise of the Germans in the early nineteenth century was the rise of Hungarians in the early twentieth. While the German states (excluding Austria and Switzerland) in 1800 had about 24 million people, the Hungarian-speaking population of Hungary was around 8.7 million in 1900, and I believe never rose above 10 million. This small and obscure nation produced an astonishing proportion of the world’s finest mathematicians: Bollobás, Erdélyi, Erdős, Fejér, Haar, Kerékjártó, two Kőnigs, Kürschák, Lakatos, Radó, Rényi, two Rieszes, Szász, Szegő, Szokefalvi-Nagy, Turán, von Neumann, and I have probably missed a few. There is a modest literature attempting to explain this phenomenon. Pólya himself thought that the major factor was Fejér (1880−1959), an inspiring teacher and gifted administrator, who attracted and encouraged mathematical talent. A high proportion of the great Hungarian mathematicians (including Fejér) were Jewish—or, like Pólya’s parents, “social” converts to Christianity, of originally Jewish stock.
Source: Personal experience. I am a Fazekas alumni and have a Hungarian maths teachers masters as well. I am bankrolling a very small reform school in Hungary so I am in contact with current Hungarian teachers every day and also I am obviously very interested in what's going on so I read a lot.
The experimental school produced the highest proportion of students to go on to receive college degrees (not just attend college, but finish) every seen in the country. The results were absolutely amazing and tremendously good. But... it's harder for teachers to teach that way. They can't plan ahead. They have to know their subjects inside and out, not just read off of a lesson plan. If a student asks a question that the teacher can't answer, the teacher has to admit it and try to figure it out with them, which many teachers are not emotionally mature enough to participate in alongside an adolescent. It gives a great deal of power and agency to adolescents, and our society is obsessed with stripping adolescents of every iota of control over their own life and denigrating them as much as possible. So widespread adoption of such schooling cannot gain much support at all.
The documentaries also did a good job showing how the "traditional" schooling methods broke the 'spirit' of adolescents and sucked the love of learning and figuring things out right out of them, turning them into disinterested husks of human beings, while the experimental school left them as vibrantly full of a love of life and learning as they entered it. Such things are of course difficult to measure and generally distrusted by our "pleasure is a sure sign of hidden dangers" mentality.
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When you use this approach, you generally cover less material, but cover it better. For most classes, this seems like a good tradeoff. 4 classes isn't really that much. You can essentially replace the time students would normally spend "studying" with them spending that time working on the problems. Further, in my experience, this type of work is far more engaging than traditional studying, so it is easier for studen…
Moreover, as people practice, they can get generically better at meta-skills such as (in no particular order) skimming, close reading, constructing mental outlines of arguments, drawing diagrams and pictures, inventing examples to match given specifications, testing concrete examples against abstract statements, generalizing specific relationships discovered in the examples to abstract laws and proving them generical…
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Why is Hungarian math so forward looking but not the other subjects? Is Hungary especially good at math?
This question is not just worth understanding in itself but it would be essential to ask at many levels, as science education is becoming the key to the survival of humanity. As a Hungarian who left the country 20 years ago I have been fascinated by this surprising success of the country, partly because I did not personally get a good science education there. Actually, it was very unbalanced, with most of it barely m…
Interesting comment overall, and also the part I excerpted above. I had read Akio Morita's (Sony co-founder) book, Made in Japan, some years ago. Wonder if that (what you said about science education in Japan) was part of the reason for Sony's success.
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Moreover, as people practice, they can get generically better at meta-skills such as (in no particular order) skimming, close reading, constructing mental outlines of arguments, drawing diagrams and pictures, inventing examples to match given specifications, testing concrete examples against abstract statements, generalizing specific relationships discovered in the examples to abstract laws and proving them generical…
That's a nice list of meta-skills. Do you have any further reading to recommend on identifying/teaching meta-skills?
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János Bolyai [1], Theodore von Kármán [2], Leo Szilard [3], Dennis Gabor [4], Edward Teller [5], Paul Erdős [6], John von Neumann [7]. [1] https://en.wikipedia.org/wiki/J%C3%A1nos_Bolyai [2] https://en.wikipedia.org/wiki/Theodore_von_Kármán [3] https://en.wikipedia.org/wiki/Leo_Szilard [4] https://en.wikipedia.org/wiki/Dennis_Gabor [5] https://en.wikipedia.org/wiki/Edward_Teller [6] https://en.wikipedia.org/wiki/Paul…
With the exception of Bolyai, those are all Jewish. AFAIK Hungary did push above its weight for some time, but that was thanks to its Jewish population. Ironically Hungarians are extremely antisemitic, although nearly all known Hungarians were/are Jewish. Good riddance!
One should not make irresponsible comments like this. Yes, I'm Hungarian but claims like these are just plain stupid.
As a hungarian, I'm pretty surprised by this article, since the quality of hungarian education is getting worse and worse, thanks to the "reforms", which basically means they are spending less and less on education on all level. And however in the past, math education was world class, now the "old school" teachers are retiring and other than a handful of elite schools (Fazekas, Eötvös, Radnóti etc) most of the school…
> since the quality of hungarian education is getting worse and worse, thanks to the "reforms", which basically means they are spending less and less on education on all level I always wondered what good metrics are to measure the quality of education. Since you say “worse and worse” can you share any insight to that? I mean you could potentially refer to the OECD world rankings but somehow I don’t trust those lists,…
My experience was pretty much exactly as described in the article as well and I am forever grateful for the school and my teachers for giving me a foundation I could build on later in life. I'd like to point out a few things though, others have already touched upon some of these:
First, similar to why it's hard to replicate the Silicon Valley startup model elsewhere (or at least why it takes such a long time), the issue is somewhat similar here. The method of teaching is just one part of the equation. It was a whole "ecosystem" of fantastically knowledgable and respected teachers who could anywhere else be university professors or researchers, publications (such as KoMaL), camps, competitions and other extracurricular activities aimed at elementary and high school students, and a culture of math and science being interesting and fun vs. the stereotypical hard and boring.
The way of teaching feels a little bit more of a consequence of this culture rather than the source. You can pick your own preferred origin story for how that culture emerged: a booming industrial economy in the age of the Austro-Hungarian empire, a multi-ethnic, liberal (in the original sense of the word and given the context) country, the migration and resulting concentration of Jews in Budapest, or a series of exceptional teachers and mentors. The highly visible world-wide successes in the first half of the 20th century then later provided an on-going narrative that benefited the national ethos and hence made plenty of funding available in the second half (conveniently forgetting the austro-hungarian, the economic boom, the liberal or the jewish part of the story). But in any case the culture and the support system is (or at least was) there and that one is very hard to replicate at a broad scale, although certainly easier within specific communities. As someone mentioned, even in Hungary it is not broadly present and is limited to a certain set of top schools.
Also, there is a flip side to this story. Personally, I really liked math before going to high school and completely lost interest by the time I finished. Partly because a lot of kids around me were much better so I felt like a failure, partly because I was more interested in computers and programming and also in finance, all of which was looked down upon. The prestige of winning a programming competition was nowhere near the same as placing well in math or physics. Working as a developer on the side was considered a distraction. I think this was for the better for me personally. A decent number of my classmates got burnt out and had severe depressions due to the pressure. You were almost expected to win a gold medal at the International Olympiad and eventually become a world-wide math celebrity. I can't shake the feeling that a lot of them "peaked" at the end of high school, although perhaps that's partly the result of the rapidly declining university system.
Again, I'm very grateful for what I got but it's more in terms creative thinking and problem solving than specific math skills. In fact, I got to learn other subjects, such as history and literature through the same method which I now realize is very unusual in a country where those subjects are usually heavily biased toward insitilling a national identity as opposed to fostering independent thinking.