How to write a postdoc research proposal in mathematics?
I think this might be useful as complementary to the questions mentioned by Suresh. I heard for the first time about Heilmeier Catechism in one of the grant writing workshops. Since then I always think to Heilmeier questions while writing a proposal or paper.

I copy Heilmeier questions from DARPA website, however another version is available from Wikipedia.


What are you trying to do? Articulate your objectives using absolutely no jargon. What is the problem?  Why is it hard?
How is it done today, and what are the limits of current practice?
What's new in your approach and why do you think it will be successful?
Who cares?
If you're successful, what difference will it make?   What impact will success have?  How will it be measured?
What are the risks and the payoffs?
How much will it cost?
How long will it take?
What are the midterm and final "exams" to check for success?  How will progress be measured?