How much do math professors get paid in the United States?
There are several sources for this data. There are general salary surveys, such as the one done by the Chronicle of Higher Education.  These often classify only by rank and type of institution, not by discipline. 

There is a more informative discipline-specific survey done by the American Mathematical Society: their Faculty Salary Report. This lags behind by a year or two while they process the data; the most recently released report when I write this is from 2013. The AMS divides mathematics departments into several groups depending on specialty and whether the department offers a doctorate, master's, or bachelors degree as its highest degree. 

For future reference, here are the mean (average) reported salaries for new hire Assistant Professors in the 2013 AMS report. The meaning of each category is described in the report, which has much more detailed information. 


Public, PhD-granting Large: $83,242
Public, PhD-granting Medium: $72,284
Public, PhD-granting Small: $67,043
Private, PhD-granting Large: $88,080
Private, PhD-granting Small: $75,722
Applied Math Department, PhD-granting: $81,234
Statistics Department, PhD-granting: $77,759
Biostatistics Department, PhD-granting: $88,362
Master's degree granting: $60,355
Bachelor's only: $56,217


There is also data available from CUPA-HR (e.g. 2014 Executive Summary). This organization has much more detailed data, but most of the data is not publicly released (university administrations pay for the data, so they can compare themselves to peers). They do release a summary by field, including mathematics, applied mathematics, and statistics.