From yesterday's New York Times (July 31): In Games, an Insight Into The Rules of Evolution, a profile of Martin Nowak, a mathematical biologist. His interests lie in trying to understand cooperation, which is important in evolution; he has been coming up with mathematical models for it; one example that's given is descendants of the Prisoner's dilemma where various members of a population interact preferentially with certain other members, instead of randomly. (The members that interact with each other more frequently are the ones that are "near" each other, either geographically or in some more abstract sense.) Cooperation turns out to emerge under conditions with are rather simple to identify.
I think that it's important for mathematicians to collaborate with people outside of mathematics, and to be exposed to ideas that at first glance don't necessarily appear mathematical. We're always going on and on to our students about how mathematics can be applied to large parts of everyday life, and I believe that's true. But at the same time, the mathematical community seems to look down on those who actually try to do so, instead lionizing people like Wiles and Perelman who have solved problems that have apparently no relevance to the real world.
The linguist Steven Pinker says that “Martin has a passion for taking informal ideas that people like me find theoretically important and framing them as mathematical models... He allows our intuitions about what leads to what to be put to a test.” I believe that this is one of the most important services we can render to the world. What mathematics is good at is stripping away the parts of a problem that are irrelevant and reducing it to its essence; seeing that that essence has something in common with many other apparently different essences; and finally using that knowledge to solve the problem. (It's like the "applications" exercises in most calculus textbooks, except not stupid. In such textbooks the translation from a real-world problem to mathematics is usually so simple as to just be an annoyance.)
Now, I believe that mathematical research that apparently has no use in the "real world" should be allowed to continue, and be funded with tax dollars, because we don't know what bits of mathematics that we're coming up with now will turn out to be "useful" a couple hundred years from now. (The canonical example here, I think, is that number theory has turned out to be very important for cryptography.) But at the same time, it seems to me that the mathematical community turns its backs on those who dare to actually think about those practical applications.
I hope I'm wrong.