Why are women are less likely to enter professions in math and
science, especially teaching? How strong is the evidence that
discrimination is the cause of the gap?

"She [Hopkins] doesn't argue that there can't be any differences
between the abilities of men and women, but she said there is vast
evidence that social factors do affect women's performance. For
example, she mentioned studies that indicate that women score higher
on math tests if there are fewer men in the room while they are taking
the test.
The five other women who were offended by Summers' speech also argued
that their objections were based on research that indicates women do
perform at the highest levels when given the same opportunities and
encouragement as men."
http://www.boston.com/news/education/higher/articles/2005/01/17/summers_remarks_on_women_draw_fire?mode=PF

It seems clear to me that a large part of the difference is nurture,
however the offended women would have shown the proof that men and
women are naturally equal in math if there was proof available.

30 years ago discrimination against women would have definately made a
good case.  But today the difference seems to take on more of a
societal norm (the fact that far fewer women than men are interested
in math and science for whatever reasons... be it that their parents
more likely pushed them in another direction or they saw it as
masculine to like math).  All the women I knew well in college that
were math or science majors easily got into positions in their desired
fields (more easily than the men in fact).