A while ago I got a job as a theoretical interdisciplinary modeler in a purely experimental lab of a different field from my own. It was an experiment for the lab and a big change for myself. It was risky for both, but also potentially a great opportunity.
Unfortunately I ended up feeling professionally isolated. Most people here know little math, some very little. There isn't anyone I can discuss the details of my work with, only the "big picture" and results. It turns out that I am the kind of person for whom discussions and interaction is essential. Without them my thought seem to gradually slow down and stop. When trying to solve a mathematical problem, I find myself unable to see obvious things and can barely make any progress. Yet when I get the opportunity to discuss it with others, suddenly everything becomes obvious. It's often not even necessary to get feedback from someone, it's sufficient to explain what I am doing, to put it into clear terms, and the solution just pops out.
The big question: How can I work efficiently and maintain my creativity and productivity when working in isolation?
I have tried several things. I tried to maintain contact with former colleagues through VOIP, though this is not too practical. Then I noticed that sometimes it is sufficient to just think about how to explain a question to someone, and the solution comes to me before even calling them. Purely imaginary discussions help too. I think this is where the solution to my difficulties should lie, but after realizing this, I am still struggling. I also tried writing down the problem to force myself to articulate it better, but this turned out to be ineffective and extremely time consuming.
Has anyone else encountered similar difficulties? Is it a common problem? There are famous scientists like Ramanujan who are said to have worked as hermits and still made great leaps. I imagine that what works best differs from individual to individual. I suspect that I am particularly susceptible to grinding to a halt once I find myself in isolation, despite being an introvert. But I do believe that there should be a way to improve the situation.
I have already decided that in the future I must avoid such situations. But until then I must find a way to be more productive while working alone.
Maybe you can find one of your new coworkers is interested in your work. Even if they don't know the high-level math, they might understand or at least be interested in the process, the outcomes, or just be looking for conversation.
Maybe some or one of the people who don't know the math just don't remember or are into that level or type. E.g. an Engineer (or any STEM person) may have done 40 hours of Calc and higher, 20 years ago, and wouldn't know how to do some, but would be happy to talk about it in words.
You can also post questions to stackexchange. Just formulating the question might help as you stated.
What about your supervisor? Maybe talk to them.
Maybe hire another person in the lab.