# Soviet Russian mathematical books

The introductory part of this book briefly describes the popularity of mathematics in Soviet Russia. It touches on Russian mathematical circles and generally how society in Russia took to mathematics in a good way. A particular passage caught my eyes:

"The Math Movement had its Grandmasters, who were highly esteemed. Most of them were research mathematicians and university professors who had drawn experience from years spent within the same mathematical circles. Their books, which contained selections of problems with commentaries, or thorough analyses of selected topics from “elementary mathematics,” were in high demand. Many of these books were superb and unparalleled in their quality and depth. Remarkably, they were swept from the bookstore shelves, immediately upon arrival."

So my questions are:

1. Does anyone know of these books?
2. Have there been any popular ones that have been translated?
3. Who were these "grandmasters"?

Any other information would be greatly appreciated.

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somewhat related, you ought to look at Love and Math by Frenkel. I suspect, Gelfand, Krillov, Arnold, but, I'm no Russian so I'll leave it at that. – James S. Cook Jul 6 '14 at 22:07

## 2 Answers

The paragraph you refer to is about probably 50th and 60th, and I am not well aware of the book from that period. However, I would like to point out that starting from 1980 and till 1992 a series of math and physics books was published under the title "Библиотечка Кванта" (Kvant's library). Some of these books are translations of very insightful books, but most are written by big names such as Kolmogorov, Pontryagin, etc. You can find all the issues here. If someone is at school, likes physics and math, and reads Russian, this is a great read.

I would also recommend to check out the magazine Kvant. It has tons of wonderful problems with solutions.

About other books: Probably the series by I.M.Gelfand and co-authors is worth mentioning. These books were initiated and planned by Izrael Moiseevich, but written mostly by the co-authors. You can find some of them in English just going through the books by Gelfand.

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Just to add to this, a publisher going by the name of MIR seems to have been a big player in publishing texts by prominent Soviet mathematicians, however it is very difficult to get hold of those books today, some of them can be found on the site mirtitles.org – seeker Jul 20 '14 at 15:43
@Assad Publisher MIR ("World") is more famous with translations into Russian of many classics in mathematics. It turns out that some books published in Russian in MIR have better quality than the original (due to higher typographic standards and very careful work of editors). They also known as publishing translations of Russian books into English, but I was never fan of this because I think that a translation has to be made by a native speaker, which was not the rule for MIR. – Artem Jul 20 '14 at 16:26
Let me add that a good number of the "elementary" books listed on math.ru, which Artem linked to, have translations into Western languages, most commonly Spanish, French and English. (See math.ru/lib/cat ) So if you want a selection of these books, it's enough to do a search on Worldcat for the authors' names and specify the desired languages. Also, many articles from Kvant were translated into English in Quantum Magazine. – user207349 Jan 14 '15 at 4:10

Extending on Artem's answer:

The website of the MCCME is probably the current "official" go-to place for this kind of books, both classical and new. See their library, their free-books collections and their book series; as far as I understand, (almost?) all of this is freely downloadable (if you only see an HTML, scroll to its very bottom for a DjVU link). I have no idea whether one of these links is contained in the others.

I am particularly fond of the Populyarnye lekzii po matematike (this is also on the MCCME site, but their DjVU links are currently broken) and the Biblioteka matematicheskogo kruzhka series. The names translate as "Popular lectures in mathematics" and "Library of a mathematical circle", and are meant that way: The popular lectures are written for "normal" interested students, and, e.g., Vorobyov's one on Fibonacci numbers spends a page discussing mathematical induction; the one by Skornyakov gives a very basic introduction into linear algebra; Kaluzhnin proves unique factorization for integers before he ventures into $\mathbb Z\left[i\right]$; etc.. The library of a mathematical circle (starting with the famous Shklyarsky-Chentzov-Yaglom problem book whose first tome was translated into English) is more advanced and tends to be written in a problem-book style; it is, I believe, the kind of problem books where the solutions are written for reading, not just as deadweight. I suspect both of these series would fill gaps in Western education if translated (though a few of them have been already -- and a couple of the Library series are actually translations to begin with).

math.ru, again as far as I can tell, combines the above libraries and some more. Of course, you can get even more books from Library Genesis if you know what to search for.

Among the authors you might recognize Eugene B. Dynkin, Igor Shafarevich, Alexander Gelfond. You probably also have heard of the Yaglom brothers if you are into mathematical olympiads; a number of their books has been translated into English (see the linked Wikipedia pages). I don't currently have texts by Arnold and Gelfand staring at me from the screen but I am pretty sure they wrote some.

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Also: mathnet.ru – MattAllegro Mar 30 '15 at 19:30