How many papers does a mathematician publish (on average) in a year?
This varies on a lot of things (e.g., by field and what kind of institution someone is at), however, there have been various studies.  For instance Figure VII (p70) of this study (which seems a bit strange to me) graphs the annual number of papers per mathematician and their most recent data (2005-2008) appears to put the average just under 0.7 for "high-exposure mathematicians" and 0.2 for "low-exposure mathematicians."

That said, things vary a lot by area and what one considers as "research active."  I would guess that it rather pure, theoretical areas (which I am most familiar with), among people I consider professors research active 1-2 papers/year is pretty typical.  For postdocs I imagine the average is &lt; 1/year (including those who are not "research successful") and for US PhD students &lt; 0.2/year (most PhD students probably don't have anything published by the time they graduate, though they may have 1-2 preprints).