  We use the data of tenured and tenure-track faculty at ten public and private
math departments of various tiered rankings in the United States, as a case
study to demonstrate the statistical and mathematical relationships among
several variables, e.g., the number of publications and citations, the rank of
professorship and AMS fellow status. At first we do an exploratory data
analysis of the math departments. Then various statistical tools, including
regression, artificial neural network, and unsupervised learning, are applied
and the results obtained from different methods are compared. We conclude that
with more advanced models, it may be possible to design an automatic promotion
algorithm that has the potential to be fairer, more efficient and more
consistent than human approach.
