But Tell Us How You Really Feel, Dr. Z

Communicating math… aye, there's the rub:

Rutgers professor Doron Zeilberger has a bit of a gadfly/curmudgeon reputation in the mathematical community… which is what (in part) makes him so interesting to hear out! He has an opinion piece about math communication in the latest "Notices of the AMS" which is getting some buzz, including inspiring a blog post from Jason Rosenhouse. The Zeilberger letter (pdf) is here:

http://www.ams.org/notices/201311/rnoti-p1431.pdf

In it, he criticizes "pure mathematics" for its 'fanatical' focus on "rigorous proofs," and urges greater emphasis on "experimental mathematics" noting:

"Mathematics is so useful because physical scientists and engineers have the good sense to largely ignore the 'religious' fanaticism of professional mathematicians and
their insistence on so-called rigor, which in many cases is misplaced and hypocritical, since it is based on 'axioms' that are completely fictional, i.e., those that involve the
so-called infinity.
"The purpose of mathematical research should be the increase of mathematical knowledge, broadly defined. We should not be tied up with the antiquated notions of
alleged 'rigor'."

It is an interesting (recommended) read and not very long, and his criticism of higher-level math communication as "highly dysfunctional" (only comprehensible to the few specialists who share a given area of work), spurred Jason Rosenhouse to write his own interesting blog post, largely in agreement:

http://scienceblogs.com/evolutionblog/2013/12/03/communicating-mathematics/

Rosenhouse's piece would be worthwhile alone for his own illustrative account of a math conference presentation as a nervous grad student; but there are many other good points in the post as well.

I recommend you read both these pieces, and you may want to also check out some of Dr. Zeilberger's other (wishy-washy, NOT!)  opinions here:

http://www.math.rutgers.edu/~zeilberg/OPINIONS.html