What is Mathematics? Passages....

So I was asked during the break between the semesters to take part in an Intersession course designed to bridge the void between the sciences and the humanities (mind the gap!) by having professors from all stripes discuss common topics to a diverse audience.  The idea is that each professor sees the topic from the perspective of their chosen field and the same topic often looks quite different to different people.  It is a wonderful idea hatched and developed by Dr. Kristin Cook-Gailloud, the Director of the Program in French Language and Culture here at Hopkins.  This is the second year running this course and I thoroughly endorse it.  Alas, due to scheduling issues, I did not participate this year.  But a topic in this year's course, Passages, stuck in my head.  The idea of movement from one state to another is something innate to a mathematician, if regarded as movement from a state of ignorance and confusion to clarity and enlightenment. 

So I wrote an essay to clarify my idea of passage in mathematics.  It is here:

Passages in Mathematics

Enjoy and do let me know what you think....