I am finishing my Master's degree in Mathematics and will be enrolled in a PhD program in the U.S. starting from fall. In my country (Russia) we have thesis as a mandatory requirement for all degrees (including BSc and MSc, not just PhD). I hoped that my Master's thesis would be good enough to be published, but my advisor says it is not (I derived some new results, but they aren't very generic and groundbreaking). My Bachelor's thesis was not published too.
My question -- is it bad to have no publications prior to PhD or is it normal to begin publishing only during PhD years? In my view no publications is understandable for BSc students, but I'm not sure about MSc. The question is not about admission (I was admitted to a couple of decent programs this year), but about general timeline and expectations from students in sciences, especially from Master's degree holders.