I am a faculty member in a department that is not mathematics, but is highly-ranked in my field. I greatly enjoy working with mathematicians, and have had a number of successful collaborations.
Sadly, when I first meet a new mathematician I am often met with skepticism because I do not have the right pedigree, i.e., neither my bachelor's degree nor my PhD come from a math department. Often I find myself in a situation where, rather than exploring fun an interesting ideas together, I get things "explained" to me as though I am an outside amateur with pie-in-the-sky ideas.
Ironically, I almost completed a double-major in math as an undergrad, but rather than fulfilling the last few course requirements, I was advised to take the upper-elective math electives that I found most interesting unless I "really needed the math diploma for a job or something." In grad school, I didn't do math quals of course, but did take plenty of courses in the math department (and from the best of them!). And did a thesis co-advised by a mathematician. Not to mention the enormous amount of time I've spent learning on my own, and the perspectives that I've been so fortunate to absorb from my collaborators in math, and from the numerous conferences and workshops I've participated in. I don't regret the path I've taken (it's been exciting and fulfilling), but I still find myself wishing I had the damn pedigree.
So, question: what's the easiest way to convince a new mathematician that I belong to his/her tribe? (So that we can just get on to the important business of exploring fun and interesting ideas...)