When should I begin publishing? 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.
My experience on this (Europe, physics department): I started my PhD last year, up to that point I had coauthorship on one publication (This dates back to my bachelors degree, I was a research assistant on a project that lead to a publication). Fellow PhDs in my current group have either one or no publicatiion as coauthors from their masters programme. 

To cut it short: In my field it would be quite uncommon to have your 'own' papers (as in first author, not sure if a journal would even accept such a submission) before you finished your masters, coauthorship depends on how keen the supervisor is on publishing results (and how well the overall research on that topic is progressing, my thesis was connected to a PhD's research, as those results could be published I got coauthorship).