Curious about math and Soviet Union Why were so many very good books written by authors with Russian surnames?
 A: 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. 


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*There's a history of government support for Mathematics going back at least as far as the invitation to Euler in the mid-1700s. 

*A lot of what one might think of as Russian surnames are actually Jewish surnames. Russia had (and still has) a large Jewish population, and Jews have been well-represented among the ranks of the world's top mathematicians. 

*The Soviets decided they needed science to beat the West, especially after World War 2, so they put a lot of money and effort into science and math. One consequence was the Sputnik; another was a lot of math books written by people with Russian surnames. 
Well, there you go. Probably worth roughly what you are paying for it, but, there you go. 
A: 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:


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*Backgorund - good mathematics in school: in Soviet Union school education was starting for kids of 6-7 years and was lasting for 10 years. After that people could enter university to pursue the Specialist degree (5 years, middle between BSc and MSc). For the last 3 years at school they learnt trigonometry, basic calculus in $\mathbb C$, integrals and derivatives, solid geometry/stereometry (when I was studying, calculus in $\mathbb C$ was not given).  

*Motivation and support - during the WW II and the Cold War, mathematicians were necessary to reach the desired results. There are some Russian surnames known especially in the control society like L. Pontryagin and N. Krylov. Due to the same reason, Russian physics were also strong that time. 
Other areas of applied sciences and applied maths were not popular and also had strong  influence from the side of authorities. That can be said about biology and, of course, economy. That may be one of the reasons there are not known names e.g. in Game Theory.
Here you can also think about the facilities which were available for Soviet scientists. That time you can either did fundamental research in pure maths or physics or control which were supported. Even Computer Sciences, I would say, were badly developed due to the lack of facilities. There were a lot of people going to West especially in 80s-90s to do Computer Science because it can be done there.

*Strong traditions in scientific society about the education. A. Kolmogorov is known to be one of the greatest Russian mathematicians but he also participated a lot in the school program for mathematics. Also among his students there are V. Arnold, A. Shiryaev and E. Dynkin. Especially Arnold was known to be a perfect at his lectures (I managed to attend some of them 5 years ago and they were very impressive) 
It was very important for the mathematician in Russia to be able to know how to teach - and in my opinion it relates quite much with how do you write the book.

*Note also that a lot of such reasons are true for the Western mathematicians as well - just Russian surnames are more 'exotic' so that's why you more often notice that the book is written by authors with such surnames.
