Upvote:1
You are probably thinking of the "Martians from Hungary" — a group of prominent and very successful scientists, mostly physicists and mathematicians who emigrated to the United States in the early half of the 20th century. Quite some of them attended even the same school in Budapest.
There are several theories about the cause, but one of the most interesting notes that they were all Ashkenazi Jews, a(n ethnic) group with a remarkably high average IQ. Combined with a relative acceptance of educated Jews in Austrian-Hungarian society, availability of excellent education and good contacts with the rest of European science then lead to this phenomenon.
Upvote:2
I don't know enough about Austria's history from that period, so I'll leave that part of the question alone and concentrate on the Hungarian side.
Marx György (a Hungarian physicist) wrote A Marslakók Legendája (Legend of the Martians), which is an excellent read about this subject. There is a semi-translation (some sentences are left out for no reason), but it's better than Google translate, so if you don't speak Hungarian I suggest reading this. His theory is - in a tl;dr version - conflicts are good for creativity, and this period was full of them here. He also held a lecture in Sweden, Conflicts and creativity - the Hungarian lesson, with huge overlaps.
What I think he was missing - probably because most people here know about it anyway - is Klebelsberg Kuno's reform. After WWI Hungary lost about 70% of the land area and 50% of the population with it, and - due to the peace treaty and end of the war - military spending had to be cut down dramatically. The money freed up was mostly spent on education, so the talents had a good environment to learn.
Upvote:4
There is ample evidence for the positive answer to your question 1. This phenomenon is well-known and is often mentioned.
On question 2, my answer is "it is not completely clear". And on question 3, I think it has not been investigated in full generality. As an example, let me cite the first few lines of the preface to the book by Janos Horwath, Panorama of Hungarian mathematics in the 20th century (Springer, 2006):
I am often asked about the reason why mathematical research exploded in Hungary at the beginning of the twentieth century. My usual answer is, only half in jest: the two reasons are the personality of Lipot (Leopold) Fejer and the High School Mathematics Journal (Kozepiskolai Matematikai Lapok, abbreviat ed KaMaL). This book will not answer the question because it would take a team of historians and sociologists to establish the causes of the scientific revolution that took place in Hungary during the first half of the twentieth century
Apparently no "team of historians and sociologists" has tried to do this so far. Explanations involving Leopold Fejer, unique high school, mathematical journal for children, and mathematical competitions are probably not sufficient, because this intellectual explosion happened in many areas, not only in mathematics and exact sciences.
See also answers to the related question: What made early 20th-century Vienna such an incubator for various intellectual activities?