I am trying to find The number of mortgages that were issued by month
for the last 10 to 25 years.  I am going to graph this against
mortgage rate to see if there is a correlation for a class I am in. I
can find several sites with rates going back to 1971, but I can not
find the number of mortgages.

You can get good data here http://www.mbaa.org/news/weekly_app.asp and
here http://www.mbaa.org/marketdata/mortgage.html. Unfortunately, it's
not in a user-friendly format. That is intentional... they want you to
pay for downloadable data.

If your school provides academic Bloomberg access, you can get the
data. MBARFI <index> (I might have transposed a few letter in the
symbol... it's the mortgage bankers' refinance index). From there,
RELS <go> will get you related securities. One of those should be
absolute data... I'm not sure how far back it goes, though.