It’s not easy to write a good grant proposal. But it can be even harder to write one for the first time, especially if you’re not quite sure who will be reading your proposal. So today, I want to say a little bit about how an NSF mathematics panel is run, and give you some idea of who your target audience should be.

Before I start, I want to include a pseudo-legal disclaimer. For fairly obvious reasons, you are not supposed to reveal that you served on any particular panel. But I am allowed to say that I have served on *some* panels, and there is enough uniformity in the process to make me confident that what I say should resemble your reality if you decide to apply. (Let me also mention that I had some help on this post from a friend [whom I shall refer to as the Hawk] who is much more of an NSF pro than I am. He made various corrections and suggestions on a first draft of this blog, and I even included a few of his remarks verbatim in the text.)

The NSF administers many different types of grants. I’m not just talking about graduate fellowships, postgraduate fellowships and research grants here. There are FRG grants, RTG grants, CAREER NSF grants, REUs, conference grants, and so on. However, for the purpose of this email, I want to concentrate on research grants.

The Mechanics: The panel is comprised of approximately 10 or so mathematicians, who consider approximately 40-50 or so proposals. About six weeks before the panel takes place, each panelist is given the list of proposals and asked to rank the proposals 1,2,3,C based on the following criteria:

1 = I feel comfortable reviewing this proposal

2 = I could review this proposal if necessary

3 = It would be very difficult for me to review this proposal

C = I have a conflict of interest with this proposal

Here “conflict of interest” is defined in a fairly precise way. It includes some obvious things (recent co-authors, people at your institution, family members) and some non-obvious ones (people with whom you serve with on an editorial board, people at institutions that have paid you an honorarium for giving a recent talk). You are also free to declare a conflict of interest which is not on that list. About a month before the panel meets, each panelist is given 12 or so files to read (all the files are online, of course). It is not unusual for a panelist to be given (in their suite of proposals) one or two grants they graded as a “3” above — it depends on how parsimonious they were in their initial grading. For each of these files, the panelist is asked to grade the proposal on both intellectual merit and broader impact. Many panelists also unofficially rank the proposals that they read. In addition to grading the proposals, the panelist writes a brief summary indicating what they feel are the strengths and merits of each proposal. A panelist can, if they wish, also read other proposals.

The next step is that the panel meets at the NSF headquarters in Virginia, sometime between November and March. A typical panel may last 2.5 days. The panel is chaired by the relevant program officer and three or so other NSF employees (usually professional mathematicians who have taken a leave of absence for a two year position at the NSF), so there will typically be 14-15 people in a conference room, each with either their laptop or a supplied computer. The first 1.5 days of the panel consist of going through the files one by one. For each file, the three (or so) panelists who were assigned the proposal read out their review of the proposal. During this time, other panelists (especially those with some expertise) will also offer their opinions. During this period, anyone who is conflicted with the proposal has to leave the room. At the end of each discussion (which takes about 10 minutes), a yellow sticky sheet with the PI’s name has to be placed on a white board with three columns. The columns are officially designated as “strongly recommended for funding,” “recommended for funding if possible,” and “not recommended for funding.” The desired outcome is to have 10% of proposals in the first column, 30% in the second, and 60% in the third. Within the first two columns the names are ordered, although, during the process, certain proposals can float up or down as they are re-evaluated in light of other proposals. During each discussion, a panelist who was not assigned to read the proposal is assigned to be a scribe and record the highlights of each discussion. Each panelist is a scribe on 3-4 proposals.

The final step is for each panelist to write up a summary of the panel discussions for which they were a scribe, highlighting what the panel thought were the strengths and weaknesses of the proposal, indicating “which column” the panel placed the name, and reflecting the extent to which there was uniform agreement or not. Everyone then goes over these summaries to confirm that the summary does reflect the panel discussion. If you ever apply for a grant, you will be able to read this summary, together with the evaluation of the three members who read your proposal in depth. (The panelists assigned to your proposal have an opportunity to modify their evaluations during the meeting if they change their minds in light of the discussion.)

Then the panel ends; the panel has given the program officer a (roughly) ordered set of names, and it is up to the NSF to decide whom to fund. I’m not sure the extent to which the recommendations of the panel exactly mirror the actual results, although I suspect that it is quite close. I can imagine, however, that a programme officer feels that a certain proposal suffered because nobody on the particular panel was an expert in that area, and they may decide to send that proposal off for further review. The Hawk says: The actual results can deviate significantly from the advice of the panel. I think it’s safe to say that the ‘highly recommended’ proposals always get funded. After that, there are various other objectives that the program officers are trying to achieve — gender diversity, racial diversity, support for young PIs, support for worthy PIs at undergraduate-only institutions. The panel list is typically the default in cases where none of those other objectives apply, though you can imagine reasons to deviate from it (e.g. you might not let the same person suffer the bad luck of being the first person after the cutoff two years running, you might support a proposal in a subdiscipline that has otherwise been shut out, etc). So in the ‘recommended’ zone there are certainly some inversions. It’s also not unheard of for a ‘not recommended’ proposal to end up being funded. One way this can happen is for the proposal to be looked at by a second (perhaps more appropriate) panel that likes the proposal much better. But also, the program officers can simply decide that the panel’s conclusions about a proposal were unjust for some reason, and raise the proposal up in the rankings.

How narrow is the focus of each panel? As I mentioned, there are approximately 40-50 proposals for each panel, of which maybe 15 are funded. So take the 80 or so people who are research active and applying for grants who are closest to you mathematically, and that gives you a rough idea. If you study Galois representations and modular forms, or Iwasawa theory, or the arithmetic of Shimura varieties, or arithmetic geometry of some kind, your proposal may well end up in the same panel as mine was (it can happen — as it did to me last year — that your proposal ends up being evaluated by *two* panels — this is possibly done in order to normalize the orderings in some way. Because I wasn’t there, I can’t quite tell what the difference was between the two panels). The Hawk says: This is the first time I’ve heard a suggestion that normalization is the reason that some proposals are looked at by two panels. I think this happens either because the program officers feel that the proposal straddles two panels to such an extent that they feel both opinions could be useful; or because the proposal has two very different parts that genuinely fit in separate panels; or because the assigned panel decided that there were parts of a proposal that they didn’t have the expertise to comment on, and so they suggest getting the input of another panel. On the other hand, I’m pretty sure that my proposal would not be on the same panel as someone like Ken Ono or Soundararajan. Could my proposal be on the same panel as Akshay’s? I’m not sure. I probably would have said no if my proposal didn’t end up on two panels last time. And Akshay is a collaborator of mine! So it’s pretty focused. On the other hand, there are certainly areas in each field which are smaller than others, and if you work in such a sub-field, then it’s more likely that the panelists will not be experts in your area.

Who serves on the panel? First, there are a few NSF rules which apply to panels . (update: this information was wrong — it turns out there are no formal NSF requirements for the constitution of any panel.) Beyond this formal requirement, who is a typical member of the panel? Well, of course, one goal of the program officer is to make the panel is not *too* uniform. But, for example, I would expect that there would always be at least one person on the committee who knows as much (say) about modular forms and Galois representations as I do. So if that is what you do, then you can be pretty sure that whomever that person is will be reading your file. But you can also be sure that someone who is *not* an expert will also be reading your file, perhaps someone in Iwasawa theory, say. And this already should give you a pretty good idea of your target audience. In other words, you have to do two things:

You have to explain to Iwasawa theory person why the modularity theorems you are going to prove are interesting. When is math interesting? Well, there are plenty of ways it can be interesting. You may have an idea of how to apply previous machinery in a novel way. You may have an interesting application in mind. You may have a completely new approach to an old theorem. You may have a completely new idea on how to solve an open problem. This is what you want to get across when you are talking to Iwasawa theory person — to give a sense of why the general problem you are studying is interesting, and how you are going to make a contribution to that field.

are going to prove are interesting. When is math interesting? Well, there are plenty of ways it can be interesting. You may have an idea of how to apply previous machinery in a novel way. You may have an interesting application in mind. You may have a completely new approach to an old theorem. You may have a completely new idea on how to solve an open problem. This is what you want to get across when you are talking to Iwasawa theory person — to give a sense of why the general problem you are studying is interesting, and how you are going to make a contribution to that field. You have an easier job convincing me (or equivalent) why your modularity theorems are broadly interesting, but you still have to conveince me that you particular proposal is interesting. More importantly, you have to convince me that you can carry out your proposal successfully, or at least to the point of producing interesting mathematics. The Hawk says: I think it would be worth mentioning here the fine line between saying enough about how you intend to carry out your plans that the panel is convinced you can do it, and saying so much that they think you’ve done it already. I think new proposers often struggle on this point.

Of course, if you do something other than what I do, then replace “Iwasawa theory person” above by me or equivalent and “me” by someone with expertise in your field.

What should I take away from this? First up, I think that an NSF grant proposal is probably the most technical audience you will write for in a context that is not one of your research papers. So you don’t need (beyond a cursory mention) to say how modular forms played a role in the proof of Fermat’s Last Theorem which you might do (say) in a job application. Nor do you need to define the class group of a number field, or explain what a modular curve is. But, at the same time, and this is very important, it can still be incredibly useful to place your work in a broader context. For example, on my last NSF proposal, I started out by reminding the reader briefly how there are very general conjectures linking Galois representations coming from geometry to automorphic L-functions. I reminded the reader that special degenerate cases of this conjecture correspond to very classical objects like the Riemann zeta function. I then mention how the work of Wiles addresses the case when the representation comes from the cohomology of an elliptic curve over \(\mathbf{Q}.\) Then I explain how all the generalizations of Wiles’ theorem share a common assumption, namely, that the Galois representations over \(\mathbf{Q}\) that one can study by this method have the property that they are, up to a twist, self-dual. So already, in perhaps not much more than a half a page, I have given the context to explain how proving that a non-self-dual Galois representation is modular is “interesting.” Of course, then I have to go on an explain *how* I am going to say anything interesting about non-self-dual representations.

Do fat cats just get their grants without trying? Every proposal is evaluated on its merits, but of course “prior success” is taken into account when judging future chances of success, and so it should be. But if Peter Scholze (say, to take someone who is not in the US so I can use his name) sends in an application consisting solely of “I am working on several projects that I decline to disclose but that I expect to be of the same importance as my prior results,” he would not be funded. More realistically, I have heard that it has been the case that fields medalists have been turned down for grants, but because all grants that are turned down are never officially acknowledged, this is just hearsay. My feeling is that, on the whole, the panels do a pretty good job, and (apart from the occasional controversial case) there is more of a uniform agreement than you might guess. The Hawk brings up the key point that this opinion only concerns number theory panels. It may be the case (and I occasionally here rumours to this effect) that other areas are not run as well. I would also say that the fat cats (on the whole) seem to put as much effort into writing their NSF proposals as everyone else.

How can I compete with the fat cats given I’m only just starting out? This is taken into account. If you are at most 6 years from your PhD, your proposal is evaluated in that context; an effort is made to fund promising young people, and also people who have never received prior NSF support. That said, it’s not easy to get a grant the first time you apply coming straight out of a postdoctoral position.

What about broader impact? This is hard for younger people. But everyone on the panel realizes this and so the expectations are lower. You probably don’t have any grad students yet, so what can you say? Perhaps you have given expository talks at a workshop? Perhaps you have written up detailed notes on otherwise hard to access topics? Perhaps you have gone into the public schools in some hardscrabble inner surburban neighbourhood and and taught calculus? (Not the last one? Then don’t suggest that you might if there’s no reason to suspect that you have any previous inclination to do so.)

Don’t Imagine that you are going to be held account for what you say you are going to prove in future proposals. Future proposals will be evaluated on their own merits (as well as prior research), and nobody is going to know or remember what you said in your previous NSF grants. It’s expected that some of problems you are working on might not work out, and that you will have new ideas while working on the proposal.

Two further suggestions from the Hawk:

When will I hear back? Answer: who the hell knows. Usually within six months from the deadline, but not always, especially these days when the federal government is funded from continuing resolution to continuing resolution. If you hear in January, either you are Peter Scholze or it’s bad news. By May, no news is good news: you probably weren’t in the ‘not recommended’ pile, and they’re waiting to see how far they can stretch the money in the ‘recommended’ pile.

If I get the grant, how much money will I get? Answer: probably less than what you asked for in your budget, and if not, you probably didn’t budget enough. Less glib answer: the program officers do adjust the award sizes in order to hit their target funding rates. You shouldn’t fret that if you ask for too much and the person who’s next on the list asks for a lower number, that could hurt your chances. The natural followup: “If program officers have that kind of discretion, wouldn’t it be better if they gave smaller awards to more people?” You can certainly argue that in theory that might be better, but in practice the answer is emphatically no. DMS’s (DMS = division of mathematical sciences at the NSF) funding rate is already much higher than that of other divisions, as high as can politically be sustained within NSF. If the funding rate went up, DMS’s budget would be cut, and the rate would go back down again.

Do you have any other thoughts? The fact that approximately 30% percent of proposals get accepted is a fairly immutable law of nature. It is no doubt depressing to be continually rejected by the NSF, and good people simply stop applying, in some sense making it then harder for everyone else. If, for some reason, the number of applications suddenly doubled, it wouldn’t be the case that the success rate would halve, but more proposals would be awarded. So, there is a real sense in which the more people who apply the more grants are awarded.