## Thoughts About the NSF GRFP Application

Having received a 2021 NSF GRFP Fellowship, I thought it would be useful to share a little about my application process, some methods I used to strengthen my application, and tips that other NSF fellows past down to me. A fellow forewarning to take all of the following with a healthy grain of salt; the competition pool changes year-to-year and there are aspects of my application that may have made me a weaker or stronger applicant if this was a different year. The following statistics should also be taken into account: I received the fellowship as a senior undergraduate from an R1 state school.

#### Overview

The National Science Foundation – Graduate Research Fellowship (NSF-GRFP or NSF) is a STEM fellowship given out every year to students who are pursuing full-time research-based masters and doctoral degrees. The fellowship lasts for the first five years of the student’s respective program and includes three years of financial support with an annual stipend of (roughly) \$34,000 and an educational allowance of (roughly) \$12,000 to the student’s institution (note that if you’re tuition is more than this then the institution you attend agrees to pay the difference). In short, the NSF pays for you to go to graduate school and gives you a yearly stipend. Apart from being one of the most prestigious fellowships in the STEM area, it allows students to circumvent the need for teaching during three years of their program as most institutions require students to teach (or some equivalent) to qualify for their university stipend.

This is a difficult fellowship to receive. The award rate is roughly $15\%$ and in 2020 there were over $13,000$ applications and roughly $2,000$ awards were given out. The award is also field specific, so when you apply you apply under a specific subfield in your field of study. For example, as a mathematics major, I applied for the fellowship in the field Mathematical Sciences – Algebra, Number Theory, and Combinatorics. Your application is competing against the other applications in the subfield you choose, so pick the one that aligns best with your research proposal and academic background (to be discussed). You may apply as an undergraduate senior planning to enter a masters or doctoral program, or within your first two years of graduate study (for all the specific requirements see here). However, current graduate students can only apply once so in total every student has two chances to be awarded the NSF as long as they apply as a graduating senior.

For the application itself, you submit transcripts, reference letters (at least two but three is strongly preferred), and two “essays”: a personal statement and a research statement. The application deadline is in October (the actual date is dependent on your field) and decisions are released around early April of the following year. I have heard that for mathematics, the NSF decision date is post the deadline for graduate programs to send out decision letters since the NSF does not want this in influence acceptances. For the 2021 year this was not the case, and I suspect it was due to COVID-19.

#### Letter Writers and Statements

Both the personal and research statements will be discussed more extensively below, so I only want to make a remark about them here. As with most statements for applications, the $95\%$ rule is a rule I follow religiously: before any application, $95\%$ of it is already done in the work that you have completed prior to starting the application. The remaining $5\%$ is the application itself. A lot of people get caught up in trying to write the best statement they can, but if you have done enough then the application essentially writes itself. If you have a couple of years before you’re applying for the NSF, focus on finding research problems to tackle, ways of enriching your department, or auxiliary things you can do mathematically (like starting a blog!) and start them now. That way you have an extensive amount of material to talk about in your application and writing a draft will be less difficult to begin since you will have a plethora of material to discuss. Editing then becomes the major time suck. If you are reading this and the NSF deadline is nearing, this doesn’t mean you won’t have a strong application. You might have a lot to talk about or you might not. If you fit the latter category, then you will need to be a little more creative about how you display what you have done in your application. I was thinking about applying to the NSF as a second year undergraduate, so I prepared early. Not every NSF supported student fits that category, but they all were able to display themselves as capable STEM researchers who are able to support their respective community.

#### Personal Statement

The personal statement is the first of the two written statements every student must submit for their application. It is also the longer of the two. The personal statement may not exceed three pages and is divided into two sections: intellectual merit and broader impacts. The main goal of the personal statement is two-fold: to paint a picture of yourself as a well-rounded mathematician who is prepared for the work discussed in the research statement, and to demonstrate that you have enriched the mathematics community during this preparation and are capable of working with others during research. The first of these two points is what is primarily displayed in the intellectual merits section and the second in the broader impacts section. However, these two subsections of the personal statement are not disjoint. Your entire personal statement needs to work together as a cohesive unit. The approach I found most useful was describing my mathematical background in the intellectual merit section and then returning to this background in the broader impacts section but from the viewpoint of how it enabled me to become a more adaptive researcher and enrich the mathematical communities and outreach that I was involved in. This way, I was able to display the mathematical background I had but also the social interaction and development that occurred as a result. We never learn alone, and I made a point to emphasize this implicitly in my personal statement.

Aside from the intellectual merit and broader impacts sections working together within the personal statement, the personal statement needs to foreshadow the research proposal. Both the personal statement and research statement work together to describe you mathematically. If your personal statement describes your mathematical background in a way that doesn’t show you are prepared to tackle your research proposal, then you have not convinced anyone that you are capable of tackling the problem. This was the essential issue I had to resolve to make sure that both of my statements worked together. The intellectual merits section of my personal statement initially discussed my entire mathematical background, and I found that much of it was either surperflous or could be drastically condensed. I ended up primarily focusing on two points: the prior research and paper I co-authored with my advisor and the REU that I participated in. Both of these experiences involved work closely related to my research proposal so I was able to communicate that I was well-equipped for tackling the problem in my research statement.

#### Research Statement

The research statement is shorter than the personal statement; you are allowed at most two pages including references. The research statement can better be thought of as a research proposal (however people might not tell you that). The idea is that you are proposing a research project, giving good heuristic reasoning for why you can complete it, and why it is important for the larger STEM community. Like the research statement, the personal statement is also divided into two subsections: intellectual merit, and broader impacts. In every NSF supported student’s research proposal that I have seen, there is also a third section: background (more on this later). Before we discuss the research statement in depth, I want to make the important point of choosing a good research project. In my case, a good research project was one that belonged to my field of study, one I had a sufficient amount of background in, and one that I had some heuristic reasoning about. The third point here is the one that I think is the most subtle. I could have picked a problem in my field that I knew a lot of background for, but if I had not run any examples and had absolutely no idea about how to solve it, there is no way I could have convinced a committee that the project was well-suited for me. On the other hand, picking a problem you have completely resolved is also not good because then you aren’t really proposing a project at all. You need to hit a nice middle ground. Aim for something that you have run plenty of examples for, understand why it is difficult, and understand enough to make an educated guess about how to solve it. One of the comments on my application said I could have given more details about why my problem was difficult, so I could have done more to this second point. If you have a project in mind, but have not spent time to understand it a little, then I strongly recommend you sit down with it first for a week or two. You will find that the research statement becomes much easier to write once you have done this.

#### My Application Stragety

Having all of this prepared, this was my weekly breakdown:

• (Week $1$): Dissect other student’s NSF applications. Use this information to help write first drafts of personal and research statements. First peer review session (focus on both statements).
• (Week $2$): Total of $10$ hours editing outside of the peer review session across both statements. Second peer review session (focus on personal statement).
• (Week $3$): Total of $12$ hours editing outside of the peer review session across both statements. Third peer review session (focus on personal statement).
• (Week $4$): Total of $14$ hours editing outside of the peer review session across both statements. Fourth peer review session (focus on research statement).
• (Week $5$): Total of $16$ hours editing outside of the peer review session across both statements. Fifth peer review session (focus on both statements).
• (Week $6$): Total of $10$ hours editing outside of the peer review session across both statements. Sixth peer review session (focus on the application holistically). Ask any other people you feel comfortable with to review your application.

In Week $1$ the primary goal was to look at the general structure of an NSF supported mathematics student’s application. For example, this is where I discovered that these applications have a background section in their research statements. You will likely find other successful devices that I overlooked so make sure not to skip this during your first week. Personally, I spent around two hours on every student’s application but you might complete this faster or slower than I did. The important part is to look at how the applications work together holistically; don’t get stuck on the details. I ended up spending less time writing first drafts of my personal and research statement than I did on dissecting other NSF applications. This is where the $95\%$ rule came in very handy since my “draft” was more just getting everything I had done down on paper in a somewhat-cohesive way.

Weeks $2-5$ were the bulk of the editing process. The idea was to increase the amount of time I spent editing each week outside of peer review sessions. If I had finished making all of the edits from the previous review session before my total editing time was reached (which was often); I would re-read my entire application while checking for how the application worked holistically. The key here was re-reading not just the part I edited, but the rest of the application too. I was making sure at every stage that the entire application worked together. While in my peer review sessions I tended to get more out of the comments on my personal statement than the research statement since the latter is pretty specific and you can’t expect everyone to understand your problem as well as you do. To combat this, I was editing my research statement every week but waited until I had a very solid draft of my research statement before I let that be the center of the peer review session. This approach worked well since I had plenty of time to streamline how I approached the background section.

Week $6$ was slightly different. The bulk of the peer review session was spent looking at how both the personal statement and research statements worked together to form a holistic application. I also sent my near-final drafts off to NSF supported students for comments and to other peers. I purposely spent less time editing this week since I didn’t want to focus on nitty-gritty details and potentially conflicting comments from peers. Your application is not going to be perfect, and that’s ok.