My thoughts

For me, the most important part of preparing to write my application was carefully reading the entire solicitation for the NSF GRFP that year. In my drafts for my personal statement and research statement, I kept key phrases and directions from the solicitation to make sure I was on track.
When writing the personal statement, the key for me was identifying the story I wanted to tell about my career. How did all of my past experiences move me towards what I wanted to do in graduate school and beyond? This was the question I sought to answer in all sections of this statement.
When writing the research statement, I drew heavily upon the REU I participated in during the summer before my senior year. While I think it is true that the NSF “funds the person, not the project”, it’s important to propose a project that is:

  • appropriate for 5-6 years
  • structured enough to have distinct milestones
  • suited to your background (If this is not clear, write a thorough and convincing background section. Actually, do that regardless.)
  • compelling in both intellectual merit and broader impacts
    • how is this work filling a knowledge gap?
    • what applications/future directions could come from this project?
    • who can be involved in this work besides yourself?

Other NSF GRFP advice

Alex Lang’s website - The specifics were last updated to reflect the 2018 solicitation, so be sure to read the current solicitation carefully, but he has good general advice. He also links to several other pages, and most helpfully, hosts a database of many past winners and honorable mentions.

Mallory Ladd’s website - There is a very nice suggested timeline here, though to be honest, I did not come close to sticking to it. She also provides some past successful applications, though none are in mathematical sciences.

My application materials

Personal statement
Research statement - No, I did not end up working in this area in graduate school.
Reviews - I’ve been told that NSF GRFP reviews are generally helpful, but I did not find mine particularly illuminating. However, they may be helpful to you.