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A Practical Guide to Writing an NSF Grant Proposal

Matthew Badger

Your think that your research is going well. You have a shiny new theorem or a novel proof technique or a cool example. You also have some ideas on how to build on your recent research. You want to tell the US mathematics community about your recent successes and share the excitement that you have for your research program. Maybe your faculty advisor, postdoctoral mentor, or colleague suggests that you apply for a grant. Maybe you take the initiative on your own. Whether the reason is to obtain summer salary to support your research, fund travel to conferences, reimburse visitors, pay students, or all of the above, you decide to submit a grant proposal to the National Science Foundation (NSF). This is not something that you have done before—or at least it has been a while since you last prepared a proposal.

What exactly do you have to do?

In this guide, I will outline how to prepare and submit a proposal to the Division of Mathematical Sciences (DMS) at NSF. The goal is to demystify the process and help you with your first proposal from start to finish. There are different types of grants available at the NSF, but I will focus on how to prepare and submit a standard grant proposal to one of the current disciplinary research programs:


Algebra and Number Theory;




Applied Mathematics;




Computational Mathematics;




Geometric Analysis;


Mathematical Biology;







If your research bridges two or more areas, then it is likely that your proposal will be reviewed by experts from multiple fields, but you still have to choose one of the 11 programs for your initial submission.

Grants from the NSF are available to researchers and educators who are employed at US institutions of higher education. There are no citizenship requirements for investigators on most NSF grants. The NSF strongly encourages women, minorities, and persons with disabilities to participate fully in its programs. While a grant proposal is initiated by you, the final proposal will be submitted by your employer on your behalf.

Standard grants are typically awarded for periods of 36 months. When you apply within 10 years of earning your PhD, you are automatically considered an early-career researcher and this may be taken into account during the review process. You do not need to have a permanent position to apply for a grant; postdocs are eligible too and have received awards. (An award is a funded grant.) If you change institutions within the US, then it may be possible to transfer your grant.

Much of the advice to follow also applies for career-stage specific grants such as MSPRF (“Mouse Proof,” for new PhDs) and NSF CAREER (for tenure-track assistant professors). Just be aware that proposals for those awards come with additional restrictions and requirements. More on this near the end.


In NSF jargon, the individual who is responsible for carrying out research and other proposed activities is called the Principal Investigator (PI). Throughout your proposal, you should write in the third person and refer to yourself as “the PI” instead of by your name; this helps reviewers easily identify when you are discussing your past work and what you will do if the grant is funded. As the PI, you will prepare most of the proposal, which is comprised of a series of documents. Financial parts of the proposal may be prepared with assistance from university staff. Once all required documents are uploaded to and reviewed by your university’s Sponsored Projects Office (SPO), your proposal will be submitted to the NSF by an Authorized Organizational Representative (AOR). At some institutions, the SPO is called the Sponsored Research Office.

Each of the research programs is overseen by NSF program officers, who make the final decisions about which grants to fund. If you have technical questions as you prepare your proposal (“Am I allowed to…?,” “Should I…?,”) the best way to get answers is to ask a program officer. Names and email addresses of the current program officers for each program can be found on the NSF DMS website.

After submission, program officers will browse your proposal to determine its topic and group it with similar proposals. Next, your proposal will be sent for review by anonymous experts, who are usually mathematicians who were funded by NSF in the past. Anyone that you may have a conflict of interest with, including colleagues, collaborators, and former mentors, will not be chosen to review your proposal. This means that you should target your proposal at mathematicians who are in the same broad research area (e.g., algebraic geometry, harmonic analysis, logic), but who do not necessarily work on the problems or subfields appearing in your proposal (e.g., positivity, multilinear operators, type theory). After it is reviewed, your proposal will be ranked by a panel of experts. The program officers take this ranking into account when deciding whether or not to fund your proposal. Other considerations such as demographics, geographic diversity, and academic age may also be factored into the decision. You will receive reviews of your proposal at the end of the review process, which takes about 6 months.

Proposals are evaluated using the NSF’s two major review criteria. Intellectual Merit includes the perceived importance of the proposed research within contemporary mathematics or other areas of science; whether the proposed research explores creative, original, or potentially transformative concepts; how well qualified the PI is to carry out the proposed research; and the likelihood that the project can be carried out in the proposed time frame. Broader Impacts are more nebulous, but refer to activities in the proposal or carried out by the PI with the potential to benefit society or to achieve specific, desired societal outcomes. For an in-depth discussion, see Max Lieblich’s article “What is Broader Impact?” in the August 2021 issue of the Notices. There is no official weighting of the review criteria; the most competitive proposals will have excellent Intellectual Merit and excellent Broader Impacts. Expectations for Broader Impacts in a proposal are less for a junior investigator than for a senior investigator.

How to get started

A grant proposal is a complex document with many components. Start early! The more time that you give yourself to write and revise, the better chance you have to submit a competitive proposal. I recommend beginning work at least two months before the submission deadline. If your proposal is due in September, then you should ideally start no later than early July. (Life is not always ideal.)

At the start of a new proposal, you should:

1. Identify the NSF submission deadline. Current information about grant programs is always available on the NSF DMS website. With the exception of Mathematical Biology, which now accepts proposals year round, each of the other 10 programs has a single submission window per year, usually in the fall. For example, the next round of proposals in Probability are due between September 10 and September 25, 2023. But the next proposals in Topology are not due until November 7, 2023. Before you do anything else, look up the deadline for the program that you want to apply to. Make sure that you have time to complete a proposal.

2. Identify any internal deadlines and reach out to university staff. It is common for a university’s SPO to require an internal submission deadline anywhere between 5 days to 14 days before the NSF deadline. This is needed so that they can audit your proposal and leave time for you to fix any issues before submitting the proposal to the NSF. If you have not applied for external funding at your institution before, ask your mentor or supervisor about the local procedure and any department or university resources that are available to assist you.

3. Create a folder. Download the PAPPG. Make a separate folder for each proposal that you work on. Download a copy of the current Proposal & Award Policies & Procedures Guide (PAPPG). This is a very long document that specifies the rules for all grant proposals to the NSF. Ignore the temptation to use the version of the PAPPG from last year, since it has probably been updated. Refer to the PAPPG as you work on each part of the proposal.

4. Get an NSF ID. Login to Start a new proposal. If you do not already have an NSF ID, you can request one on After logging in, find the link to create a new Full Proposal. You will be prompted to fill out basic information, starting with your organization (university). On the next page, use the search box to find the code for the program that you are applying to (Geometric Analysis, Foundations, etc.) For a standard grant, you should select Research Proposal for the proposal type and Single Proposal for the collaborative status. Finally, enter a short title for your proposal—for examples, look up recently funded awards on the NSF DMS website. If everything went right, you will be assigned a temporary proposal number and see a screen with the list of required and optional documents that make up the proposal.

5. Begin working on the proposal. Most required documents may be prepared in LaTeX, Google Docs, or Microsoft Word, and uploaded to as PDFs. Exceptions are the Budget and Cover Sheet, which are entered directly on, and a trio of Senior Personnel Documents, which are filled in using NSF-supplied templates. It is time to work on these documents.

Cover Sheet (1% effort)

Most of the Cover Sheet is auto-filled with information that you entered when creating the proposal. In addition, you must enter the country codes for any planned foreign collaboration or travel. You must also specify the award period (36 months) and pick a requested start date (1st or 15th of a month). For applications made in Fall 2023, a typical start date would be 6/1/2024. This will let you be paid summer salary starting in summer 2024.

Project Description and References Cited (75% effort)

This is the most important part of your proposal. In the Project Description (PD), you have up to 15 pages to say what you want to do, how you will try do it, why it is reasonable, why you are qualified to do it, and what its broader impacts are. The PAPPG specifies -inch page size, at least 1-inch margins on all sides, either Times New Roman or Computer Modern (default LaTeX) fonts of size 11pts or higher, and no more than 6 lines of text per 1 inch of vertical space. Smaller fonts in mathematical expressions are okay. Plan to use all 15 pages as anything shorter may convey a lack of seriousness to reviewers. Figures are allowed and can be effective, but should be used sparingly, because they quickly reduce the amount of space you have to write. You may not include hyperlinks to external documents or do anything else to get around the 15-page limit.

You should use citations in the PD like in a research paper, but References Cited do not count against the 15-page limit and must be uploaded separately. The easiest way to do this is to prepare the PD with references at the end like you would for a journal article. Then, once the document is in its final form, use a free web app to split the PDF into two files and upload them separately on I encourage you to use author-year citation labels like [Bad11] or [BG22] instead of numerical labels like [23], [42], because the names and dates help create a better narrative.

I think of the body of the PD as being organized into three differently sized “blocks.”

Block #1 Prior NSF Support (0–5 pages). If you have received support on one or more NSF grants with an end date in the last five years (e.g., you were an RA on your advisor’s NSF grant), then you must have a separate section labeled Results from Prior NSF Support. The PAPPG specifies a hard limit of 5 pages for discussing prior support. Start by listing the number of each grant, the PI of the grant, the dates of the grant (e.g. 6/2020–5/2023), and the total dollar amount of the grant. Next, under a required subsection labeled Intellectual Merit of Prior NSF Support, cite any papers or preprints from prior support. Then describe in short, titled, minimally technical paragraphs the major outcomes and scientific impact of prior support. Finally, under a required subsection labeled Broader Impacts of Prior NSF Support, summarize any broader impacts from the period of the award. It is okay if portions of this block are duplicated in other parts of the proposal. If you have not received any prior NSF support, start your PD with the second block.

Block #2 Research Problems (9–14 pages). The bulk of the PD should revolve around a series of clearly labeled problems that you propose to work on. Group related problems into their own sections. Start each section with general background and describe any major advances in the last 5–10 years. While there is no exact rule, I recommend stating between 8 and 12 problems—some easier, some harder, none out of reach. Problems can take a variety of forms, including questions, conjectures, and statements like “Prove …or find a counterexample.” Number your problems so that you may refer to them throughout the proposal and your reviewers can refer to them in their reviews. Before and/or after each problem statement make sure to describe both the context for the problem and one or more strategies to attack the problem. Discuss how difficult each problem is and your estimation of the likelihood it will be solved. If you forget to discuss a strategy for one or more problems, it will be called out as a weakness in the reviews. Novelty or variety of problems may be viewed as a strength. Relating your narrative back to your past work can be seen as evidence that you are qualified to work on the proposed problems. It is okay to report on work in progress.

Block #3 Broader Impacts (1/2–2 pages). You are required to have a separate section labeled Broader Impacts, in which you describe any broader impacts of the project or being carried out by the PI parallel to the project. The length of this section should scale with the number of years past your PhD.

As a final remark, although I have seen it done, there is currently no requirement in the PAPPG to have a separate section in the PD labeled Intellectual Merit. Your exposition in Block #2 already discussed Intellectual Merit at length.

Project Summary (5% effort)

This is a specialized abstract of your project, which is comprised of exactly 3 paragraphs. It is used to help program officers categorize your proposal and is useful for reviewers when they are writing their reviews. Do not include any mathematical notation, equations, or references. The Project Summary (PS) must be entirely self-contained. Delay writing the PS until after you have a solid draft of the PD.

Paragraph #1. Overview. (The PAPPG says that you actually have to label this paragraph “Overview.” A similar rule applies for paragraphs #2 and #3.) Write in a few sentences—seriously, the overview should be short—about the major topics and themes of the proposal. After reading the overview for a proposal to the Analysis Program, for example, a program officer should be able to decide whether the proposal focuses on complex analysis, geometric function theory, harmonic analysis, etc.

Paragraph #2. Intellectual Merit. This paragraph should set the context for the proposed research and give a high-level description of different clusters of problems tackled in the proposal. Discuss the novelty of proposed problems and methodology, connections with other areas of mathematics or science (if any), and the potential impact of the research. This paragraph should take around 50% of the PS.

Paragraph #3. Broader Impacts. Highlight past, present, and future broader impacts in the proposal and carried out by the PI. This paragraph need not be exhaustive, since you described broader impacts in more detail in the PD.

Budget and Budget Justification (10% effort)

The Budget is a line-item accounting of the money requested for proposed activities, broken up into categories that are specified in the PAPPG (Salaries, Equipment, Travel, etc.). Pay close attention to the section on Allowable and Unallowable Costs. Rates for certain expenses (Overhead, Fringe Benefits) are determined by your university in negotiation with a federal agency. The Budget is entered using a form on the website. You must also upload a Budget Justification, which is a companion document of 5 pages or less that details your planned expenditures in plain sentences. There are no simple instructions for this part of the proposal. You should ask for help from department or university staff or senior colleagues to prepare the budget. Even so, do not neglect these documents. Your university may not allow you to spend money that you receive from the NSF unless you described the expense in advance in the Budget Justification.

To start work on the budget, list everything that you might want to spend money on. You are allowed to and should ask for 2 months of summer salary per year (based on your 9 month university salary). Other common things that you might want to ask for are money for travel for collaboration or to attend conferences, money to reimburse research and seminar visitors, money for publication costs, money to purchase books or an office computer, laptop, or tablet. Be imaginative. You may request academic year and summer salary for graduate RAs. The likelihood of receiving this increases if you name the students in the justification and discuss which problems are appropriate for graduate students in the Project Description. Although your budget requests should be reasonable, do not worry too much about the total dollar amount. When your grant is awarded, NSF program officers may ask you to revise your budget downward, if necessary.

Senior personnel docs (5% effort)

For an individual proposal, the only senior personnel is the PI. You must complete three documents.

1. Biosketch (1–2 pages). A biosketch is a very short CV with a specific structure and 2-page limit. To enforce compliance, the NSF now requires you to use a website called SciENcv: Science Experts Network Curriculum Vitae to produce the biosketch. The website will walk you through required elements and build a PDF that you can save and upload to

2. Current and Pending Support. Using the NSF supplied template, describe the project goals and list the dollar amounts of any current or requested research funding from the NSF, other government agency (US or foreign), or private foundation. Also list the proposal that you are preparing as pending support. This document helps the NSF avoid double-funding the same research.

3. Collaborators and Other Affiliations. To help NSF identify potential conflicts-of-interest between you and reviewers of your proposal, fill out the NSF supplied template. Follow the instructions and list your PhD advisor(s), PhD students, postdoctoral mentors and mentees, collaborators, as well as their current affiliations (university or employer).

Miscellaneous docs (4% effort)

1. Facilities, Equipment, and Other Resources (1–2 pages). For mathematics, this document is rather anodyne. You should convey that you have adequate resources to carry out proposed activities. Items that you may wish to describe are office space, computing resources, journal and library access, staff support, and availability of local lodging (for visitors).

2. Data Management Plan (1/2–1 page). State whether or not you expect your project will produce any data sets. Describe how you will preserve and disseminate any research products (papers) produced by the project (PI website, arXiv, etc.) Your DMP does not need to be long, but take it seriously.

3. Postdoctoral Mentoring Plan (conditional). If you request any salary for a postdoc on the budget, then you must upload a comprehensive single page mentoring plan. Otherwise, leave this section blank.

4. Letters of Collaboration (optional). If parts of the project are joint work, then you may upload a signed letter from each collaborator attesting to their willingness to support the project. The letter must use the specific language described in the PAPPG and does not function as a letter of recommendation. These letters are optional.

5. List of Suggested Reviewers / List of Reviewers Not to Include (optional). Barring exceptional circumstances, it is customary to leave these blank.

Submitting your proposal

When all required and any optional documents that you want to submit have been finished and uploaded to, click the link to Share Proposal with SPO/AOR. This will alert the office at your university in charge of proposals to review your documents. Depending on local procedure, it is possible that you should also contact the SPO directly. Remember that you must send your proposal for review in advance of the NSF deadline. This is often the most stressful part of the process, because you will now wait on someone else to “click submit” on something that you have spent many hours working on. Stay calm, monitor your email, and be prepared to make any last minute changes to the proposal requested by the SPO. After everything is reviewed, the AOR can submit the proposal to NSF.

Congratulations! You did it!!

General advice

Your proposal will be judged based only on what you put in the proposal. Reviewers are not required to read your papers or preprints or look at references. Unlike when you are applying for a job, there are no letters of recommendation. This means that in your proposal, you need to be your own advocate! It is up to you to explain the importance of your past work and your proposed research and say why you can succeed (but not in a boastful way). By taking time to write a better exposition, you can make it easier for reviewers to write a quality review of your proposal and improve the chances of getting funded. The reality is that not every quality grant can be funded. If your grant proposal is not funded, do not be discouraged from applying the following year.

Advice for MSPRF

The Mathematical Sciences Postdoctoral Research Fellowship (commonly called the NSF postdoc) is an award that is available for US citizens and permanent residents who have held the PhD for less than 2 years. Typically you apply in October of the year that you expect to graduate. If you do not receive the award after your first attempt, it is a good idea to apply again the following year. The Project Description for the MSPRF application is limited to 5 pages and you must discuss the choice of institution and sponsoring scientist. This does not leave much space to talk about mathematics! An effective proposal will convey several interesting mathematical ideas in a concise way. You must request confidential letters of recommendation from your PhD advisor and 2 other researchers. If at all possible, secure a letter from a notable mathematician in your field that is at a different university than where you earned your PhD. In addition, you will upload a supporting letter from the sponsoring scientist that you can read. Does this letter of support indicate that they know what you are about or does it sound generic?

Advice for CAREER

The NSF CAREER award is for untenured assistant professors who are on the tenure-track. Applications are due in July. It can be observed that most recent CAREER recipients previously received the MSPRF or a standard grant, but this is not a requirement. One challenge is that this is a 5-year grant and in addition to research you must propose educational projects—that means you need to describe more activity in the Project Description within the same 15-page limit. If possible, tie in your educational projects with prior broader impacts. An effective proposal will devote at least one-third of the PD to the educational component and also explicitly discuss Integration of Research and Education. It is reasonable to expect reviewers on CAREER panels to be mathematicians who are farther from your speciality than reviewers for standard grants. You may apply for the CAREER award at most three times. Do not feel pressured to apply before you are ready.


Photo of Matthew Badger is courtesy of Matthew Badger.