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.
I am curious if it's because they are hungarian, or because they are jewish. Jews pay particular attention to science and arts, from what I gather from my jewish friends. Nobel laureates, for example, have disproportionate amount of jewish among them (compared to jewish population as a percentage of world population).
You don't have to be curious for more than five minutes. Several of those mentioned are Jewish, but most of them are not. There are not disproportionately more Jewish Hungarian mathematicians, compared to the proportion of say, Jewish people in Budapest before WWII, or the proportion of Jewish people in the Austro-Hungarian Empire.
Looking only at the first half of the twentieth century, there at least as many world-ranking mathematicians from Hungary as from Poland, a country with a strong mathematical tradition, a much larger population, and a massively larger Jewish population (around a quarter of the Jewish people in the world in the 1930s).
It's worth adding that comparing the proportion of Jewish Nobel prize winners to Jewish people in the world might not be a fair comparison. Much of this can probably be explained by the strong correlation between being European (including Russian/Soviet) or American, and being a Nobel prize winner.
You don’t have to be very curious to find out that about 22% of Nobel Prize winners have been Jewish [1], which leaves your controversial Western population at under 100 million even stretching the worldwide Jewish population to 20 million.
Except for Bolyai, all mentioned above are indeed Jewish. Also all mentioned in your other comment (Fejér etc.) except Bollobás. Also Wigner, mentioned in another comment.
I stand corrected. I wrongly believed that many of these including Fejer and von Neumann were not Jewish.
I think the comparison with other populations such as Poland still seems to point out that something about Hungary in the 20th century was special, other than the presence of many Jewish people.
Ashkenazi Jews have an average IQ of 108-112 compared to a European average of ~100. This shifted mean means they have a much higher percentage of very smart people (~6 times per capita rate of >140iq which is the norm for Nobel prize winners)
This over representation of high IQ is similar to the historical over representation in Nobel prizes for hard sciences.
You can't make conclusions about the number >140 based on a shift of the mean. IQ is scaled so that the general population has a normal distribution. That doesn't necessarily mean some subpopulation has a normal distribution. Even if that was the case, the subpopulation distribution would still have a different standard deviation. (It would partly depend on the level of assortative mating within that population.)
What an odd statement. Nobody said it's because they're Hungarian. It's because of the educational system at the time, which affected everyone in said system, regardless of ethnicity or "average IQ".
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!
Interesting list since they received quite heterogeneous and many times mixed education, home vs. institution, Hungarian vs. foreign, also their adult achievements were many times reached/mastered in other than the educating country.
As long as the measure is the production of little children inside one of the historic borders of Hungary (or maybe elsewhere by at least one Hungarian-born parent) who later contributed to mathematics notably, this or that way, here and there, then Hungary is really good at math!
Here's a footnote about Hungarian mathematicians in the 20th century from Prime Obsession. Amazing book by the way, highly recommended.
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.