Many people would like to know where scientific ideas come from and how they arise. In the case of mathematics, new ideas come in the form of new «mathematical objects»: groups, vector spaces, sets, etc. Some people think these new objects are invented-, others that they are discovered. By exploring the birth of descriptive set theory in France and Russia in the period 1890-1930 we show that the leading French mathematicians worked within a rational, secular worldview that made them doubt the legitimacy of infinite sets, particularly non-denumerable ones; on the other hand, the creators of the famous Moscow school of mathematics, particularly those who subscribed to a religious doctrine known as «name-worshipping,» believed that humans has absolute freedom to invent mathematical objects. Partly as a result of their different cultural environments, the French and the Russians took different approaches to the same problem. In the end the Russians created a new field, descriptive set theory, at a time when the French remained hesitant.