The author raises an interesting question as to how the Soviets produced so much scientific talent, but his discussion of math circles strikes me as more of a tangent than a convincing answer. Were these math circles really so widespread, and were they a big part of producing mathematical and scientific question? He doesn't address this. However, the book he is reviewing is available online [1] and I see from skimming it that Zvonkin says only one of his students ultimately chose math as a profession. My hunch is that the structure of the formal education system in the USSR played a larger role.
The real answer is that we (I speak as a Russian) didn’t have such advanced computers in the USSR. What was routinely solved numerically in the US, had to be painstakingly traced analytically, and new methods had to be developed for such approaches, and mathematical education had to be boosted so enough people could work in the field (mostly developing new weapons, sadly).
Another girl, not his daughter, from the girl's circle also became a mathematician (whereas the daughter is a professor of film studies). So, yes, genetic, family culture (most of the parents of the kids from the math circles were teachers or academics), interests...
If you study much of 20th century mathematics and physics, you'll certainly find Soviet mathematicians showing up everywhere. Control theory, probability, nonlinear differential equations, etc.
Just from the names of theorems alone, it's pretty hard to miss.
The Soviets produced a lot of outstanding mathematicians.
It's remarkable in absolute terms and it's even more remarkable considering that Soviet education was generally anti-science for much of its existence (e.g. see [0]).
IIRC Stalin eventually left a group of mathematicians and physicists alone because it was clear that if they were suppressed the Soviet Union couldn't win wars or plan the economy.
My initial hypothesis would be that creating this kind of playground in the otherwise dismal intellectual atmosphere, combined with the ability to select the best people from all over the empire, and the urgency and funding that came with the wars and cold war, played a major role in their ability to do important work.
Russian was a scientific power in the 19th Century before Soviet Union, and continued during the Soviet era. The west had limited access to it, due to the Cold War.
Soviet Union wasn't called a superpower for nothing. USSR had many world class achievements in scientific and applied areas, and some organizational achievements in social and manufacturing areas. There are examples and counterexamples, but the result is what we have, and while at some areas ex-Soviets were seen as backwards people in early 1990-s, in some others they really brought some positive advancements to the West - or First World - when the borders became open.
Case in point: The reason why the US heavily relied on Soviet rocket engines for their launches for ~15 years (before SpaceX dominance) was because they were simply more advanced and cost effective. Material science apparently was a step above - Soviet scientists were able to create an alloy for use in oxygen-rich engines which was unbelievable to Western counterparts till they visited and had it demonstrated.
This is one example, and there could be many - both where USSR had an edge and where it was behind. I believe here we want to have the overall picture - and that picture was that there actually were some novelties which were interesting on the West, even though in overall quality of life and some associated parameters USSR was notably losing. Or, saying it from another end, USSR wasn't advanced enough to avoid dissolution after - not necessarily caused by - the Cold war, even though it had some achievements unavailable on the West.
Yes, that was what I also wanted to point out here. As in, the set of novelties Soviets had over the West was at least non-zero. And that rocketry happened to be one may be surprising to some of those less informed about space technology.
Quantify in my opinion requires qualify because, how many is "a lot?" But broad strokes, the USSR was an intellectual powerhouse. Add as many "in spite of"'s as you like, but in my opinion the "a lot" target is achieved. You mention science and I'll get to that, but I want to first target what I feel is a general misconception of the Soviet Union as like, a bleak concrete-ridden, muddy backwater of labor camps (it kinda was of course) with nothing to contribute to the world.
Post revolutionary periods always produce fantastic art, literature, and social experiments. See post-revolutionary American religious scene for an example. In the Soviet Union, there's a clumping of great literature around 1917. Summary: https://en.wikipedia.org/wiki/Russian_literature#Early_post-...
> The Imaginists were post-Revolution poetic movement, similar to English-language Imagists, that created poetry based on sequences of arresting and uncommon images. The major figures include Sergei Yesenin, Anatoly Marienhof, and Rurik Ivnev.[65] Another important movement was the Oberiu (1927–1930s), which included the most famous Russian absurdist Daniil Kharms (1905–1942), Konstantin Vaginov (1899–1934), Alexander Vvedensky (1904–1941) and Nikolay Zabolotsky (1903–1958).[66][67] Other famous authors experimenting with language included the novelists Boris Pilnyak (1894–1938), Yuri Olesha (1899–1960), Andrei Platonov (1899–1951) and Artyom Vesyoly (1899–1938), the short-story writers Isaak Babel (1894–1940) and Mikhail Zoshchenko (1894–1958).
Sorry for the big copy paste, but, there's just so many of them, and to literature nerds, what they did was "groundbreaking." I know it sounds silly but let us literature nerds have our thing.
Then there's a bunch of fun leftist / communist poetry, from Vladimir Mayakovsky and Nikolai Tikhonov (the "Could nails from such people be fashioned" guy).
And on and on. Art had some interesting characters as well, "in spite of" the Socialist Realism thing. Isaak Brodsky, for example.
Re: science, as someone else linked, efforts were hampered slightly by the repression of science that was perceived as in opposition to dialectical materialism, but in general the Soviet Union seemed very determined to create a lot of engineers.
You have Fields medal winners: Grigory Margulis (interestingly he suffered from the Soviet antisemitism mentioned in this article), Vladimir Drinfeld, and Sergei Novikov. And you have nobel prize winners such as Nikolay Semenov, Nikolay Basov + Alexander Prokhorov, Pavel Cherenkov (the Cherenkov radiation guy) + Ilya Frank + Igor Tamm, Leonid Kantorovich (basically invented linear programming), Pyotr Kapitsa, and Lev Landau.
Then there's the obvious such as the fact that the Soviets were first to put a satellite in orbit, first to put a human in orbit (arguably far more useful than putting a human on the moon, though putting a human on the moon is probably more inspiring).
What is interesting is how during the time these may not be "contributions to science" due to the USA and the Soviet Union often not sharing advancements in science with eachother because of the Cold War. Imagine if the two nations had been cooperating with eachother. Then again maybe there wouldn't have been a "Space Race."
> Imagine if the two nations had been cooperating with eachother.
I think Kennedy and Khrushchev, having defused the Cuban Missile Crisis, might have started on a path leading in this direction — but both of them got cancelled.
[1] https://sites.icmc.usp.br/sasha_a/zvonkin-e.pdf