Why so many very good books were written by authors with Russian surnames?
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The title mentions the Soviet Union, but the body asks about Russian surnames. These are not the same. A lot of good mathematics was done by Russians before there was a Soviet Union. A lot of good mathematics has been done by people with Russian surnames who never lived in Russia, Soviet or otherwise. So it's hard to know what to make of your question.
But I'll make a few suggestions, if you promise to keep in mind that I have no training, expertise, or experience as a historian and am therefore uniquely unqualified to write an answer.
Well, there you go. Probably worth roughly what you are paying for it, but, there you go.
I am not a historian as well, but I know a bit of Russian math from the inside. I liked the article @JM cited very much. As you may already learn from comments by Henry and answer by Gerry, Mathematics in Russia has been started seriously in XVIII cent. and is known mostly thanks to Euler how came to St. Petersburg, the capital of Russia that time.
There are more well-known names from XIX century like Chebyshev, Markov, Lyapunov, Lobachevsky and S. Kovalevskaya but I would say that the most fruitful period is XX century. I cannot say that I know all the reasons, but maybe some of them: