Take the tour ×  (Added an epilogue)  I started a job as a TA,
and it requires me to take a five sessions workshop about better
teaching in which we have to present a 10 minutes lecture
(micro-teaching).  In the last session the two people in charge
of the workshop said that we should be able to "explain our
research field to most people, or at least those with some
academic background, in about three minutes". I argued that it
might be possible to give a general idea of a specific field in
psychology, history, maybe some engineering, and other fields
that deal with concepts most people hear on a daily basis.
However, I continued, in mathematics I have to explain to
another mathematician a good 30 minutes explanation what is a
large cardinal.  I don't see how I can just tell someone
"Dealing with very big sizes of infinity that you can't prove
their existence within the usual system". Most people are only
familiar with one notion of infinity, and the very few (usually
physicists and electrical engineering stu