The prestige and status of research fields within mathematics

While the ``hierarchy of science'' has been widely analysed, there is no
corresponding study of the status of subfields within a given scientific field.
We use bibliometric data to show that subfields of mathematics have a different
``standing'' within the mathematics community. Highly ranked departments tend
to specialize in some subfields more than in others, and the same subfields are
also over-represented in the most selective mathematics journals or among
recipients of top prizes. Moreover this status of subfields evolves markedly
over the period of observation (1984--2016), with some subfields gaining and
others losing in standing. The status of subfields is related to different
publishing habits, but some of those differences are opposite to those observed
when considering the hierarchy of scientific fields.
We examine possible explanations for the ``status'' of different subfields.
Some natural explanations -- availability of funding, importance of
applications -- do not appear to function, suggesting that factors internal to
the discipline are at work. We propose a different type of explanation, based
on a notion of ``focus'' of a subfield, that might or might not be specific to
mathematics.