Experimental Blog #56

Comments on "Naming Infinity" - A True Story of Religious Mysticism and Mathematical Creativity by Loren Graham and Jean-Michel Kantor

For someone whose mathematical understanding is limited this small book is not very easy to describe. Nonetheless, the story of these late 19th and early 20th century mostly French and Russian mathematicians is quite illuminating. Although the first modern mathematician who "discovered", or "invented", the mathematical theory of sets was a German, the French soon took over its further developement and elaboration.
The authors say, however, that since the French mathematicians were limited by Rene' Descartes' rationalism and Auguste Comte's positivism, they eventually came to an "intellectual abyss."
On the other hand, there existed in Russia centuries of tradition of "mysticism", that, although sometimes condemned as heretical "Name Worshipping," did not prevent the Russian mathematicians from mixing mathematics and religion.
How do these mathematical ideas exist? Are they imagined? Or are they real? Have they always been there to be discovered? Or do they become real, or come into existence, only after they are named?
The usually religious and sometimes even "Name Worshipping" Russian mathematicians naturally came under fierce attack and persecution by the materialist Marxists who eventually came into power everywhere in Russia. Many, maybe most, were imprisoned. Some were executed, or died violently, and others "converted" and promoted the aggressive, intolerant, and totalitarian ideas of the new Soviet Union.
However, in spite of these events, the Moscow School of Mathematics grew and became world famous.