Comments on the paper “Two letters by N. N. Luzin to M. Ya. Vygodskiῐ”

Some passages in the paper "Two letters ... " in the January issue of this MoNTHLY may be difficult to understand without a background knowledge of historical traditions that were well known to Luzin and Vygodskil. After a brief biographical note on Luzin I provide some background information on actual and potential infinity; on the French textbooks used by Luzin when he was a student in Moscow; on the (non)differentiability of continuous functions; and on Weierstrass and his influence.