> At the same time, I've noticed that many math folks make no effort to reach out to the other side - recognizing that PDEs are a big deal to some people, intimidating, and not exactly terribly approachable.
Being a mathematician, I don't know any other way than to say: "Read this and this text and understand it. Then you'll grasp what I'm talking about.". I can tell you that even for many math students, say, PDEs are intimedating and not exactly terribly approachable at the beginning. But the difference is that by reading texts, hearing lectures etc. they simply get over it and get quite used to them. So, I believe, the mathematicians you talk about are quite honest in the sense that they are really doing their best, but simply don't know a better way to talk about their topic.
I would suggest starting with "What happened, and why I did it". Having explained my fair share of stochastic simulations of systems of ODEs to clinicians, I think the core of the problem is heading into the mathematical tall grass way to quickly.
> I think the core of the problem is heading into the mathematical tall grass way to quickly.
In my experience non-mathematicians don't like listening to loooong mathematical talks (although those would be necessary for introducing the topic in a more smooth way).
Being a mathematician, I don't know any other way than to say: "Read this and this text and understand it. Then you'll grasp what I'm talking about.". I can tell you that even for many math students, say, PDEs are intimedating and not exactly terribly approachable at the beginning. But the difference is that by reading texts, hearing lectures etc. they simply get over it and get quite used to them. So, I believe, the mathematicians you talk about are quite honest in the sense that they are really doing their best, but simply don't know a better way to talk about their topic.