I care a lot about improving the world around me. On this page, I describe some thoughts and activities in this realm (at least the ones related to mathematics), organized by the various problems that they attempt to address: underrepresentation, environmental impact, public relations, and mathematics education.

underrepresentation: Though mathematics is a pursuit which is in theory equally available to all, in practice our community suffers from underrepresentation of a number of different groups, based on a wide range of factors including race, class, gender, etc. While there are certainly broader and well-documented reasons to be unsatisfied with the current state of affairs, I also think it's just plain unfortunate that the community surrounding something so beautiful remains so insular (see also "public relations").
environmental impact: Mathematicians -- and academics more generally -- tend to travel quite a bit for conferences. This has serious negative impacts on the environment. A complicating issue here is that it'd unfortunately be pretty detrimental to a young academic's career to refuse to travel, since conferences are a primary means of interacting with one's research community and making one's name, face, and work known.
public relations: The field of mathematics serves as a means of probing the outermost reaches of human understanding. For this reason (and many others), I think it's important that we share our art with society at large. But we do a really, really bad job of this, and the average person not only has little idea of what we do and why we think it's beautiful, but also harbors some residual fear and distaste for the field. For contrast, consider astronomy. The average's person's day-to-day life is probably roughly equally affected by astronomy and theoretical math, and yet the general public attitudes towards these two fields differ dramatically. In particular, people tend to feel like they have some basic understanding of advanced astronomical concepts such as black holes, whereas there is essentially no analogous general sense of familiarity with advanced mathematical concepts. It's a long-term goal of mine to change this. I hope that someday we can instill in the general public the same sense of awe wonder for the collective human endeavor of mathematical thought and inquiry that programs such as NASA and CERN already inspire.
mathematics education: Mathematics can be an extremely effective vehicle for teaching students how to think. But at all levels, mathematics education is in dire need of improvement. Part of this is that we don't seem to do a very good job of educating our educators. Once, in middle school, I "proved" that 1=-1 through some tricky (and incorrect) applications of square roots of complex numbers; when I showed this to my teachers, not only were they unable to point out what was wrong with my argument, but they didn't even care that I had broken the entire system! Of course, part of the issue here is the general public idea of what mathematics even is (see "public relations").