Research statement for a fellowship application: should I introduce my area?

Question

I'm applying for a research postdoc fellowship in mathematics (I just finished my PhD) at a prestigious UK university. I've been told to write a research plan for what I intend to do with the fellowship. Unfortunately I have no idea who is going to be reading my plan.

Should I start off by introducing them to my area? My area is in evolutionary PDEs and professors in eg. number theory may not know anything about it. I was going to define a PDE and then quickly talk about my previous work and then my intended research work. Overall it's 3 pages at the moment.

Answer 1

You have to convince readers of two things:

1. The problem is important
2. You are qualified to tackle it

To that end, you should make the problem and likely outcome accessible to anyone, but your proposed approach can assume more skill.

Answer 2

You don't need to aim this at the number theory people. They may not be experts about PDEs, but they will be smart enough to show your proposal to somebody in the department who is.