Graduate Fellowships in Math

How to Win a Fellowship for
Graduate Study in Mathematics

Evans M. Harrell and Michael Lacey

Note: This article appeared in Math Horizons in December, 2004. A hyperlinked version with a related FAQ list will be maintained at

So you're going to become a mathematician! You told your parents you plan to get a Ph.D. and solve the Poincaré conjecture, or prove the Riemann hypothesis, or, well, maybe just discover your own beautiful, deep fact about the universe that nobody ever knew before. Your parents smiled indulgently and tried to be supportive, but there were some pertinent remarks about making a living and that little matter of the college loan that needs to be paid off. How can you follow your dream without going broke?

The most reassuring thing to tell your parents is that an enormous number of college students take basic mathematics like calculus, so universities need to employ graduate students as teaching assistants. Not every graduate student gets a stipend as a teaching assistant, but a large portion of them do, and you can usually make financial support a contingency of your application for graduate school. Teaching assistants usually get excused from tuition and receive a magnificent wage which is quite sufficient for you to lodge with your computer and your cat in one of those hovels behind the coffee shops at the low-rent end of the campus. You probably even get benefits.

But wouldn't it be great if you could get paid just as much for sitting around and thinking, which for a mathematician is a synonym for fun? This is not a fantasy - it is called a fellowship. The Federal Government and several private foundations have decided in their wisdom that every year a few hundred graduate students in mathematics should live this fantasy life. It's a wonderful country!

It is not hard to find out about the major fellowships that are available. They are listed near the beginning of the academic year in the Notices of the American Mathematical Society, which you should obtain in time for some of the important deadlines in early November. (The AMS is a partner organization to the MAA, which publishes Math Horizons .) The AMS web site,, will also lead you to information about fellowships available to aspiring mathematicians going to graduate school.

There is no getting around the fact that these fellowships are highly competitive. Who are the winners, and how can you be one?

In 2002 the National Science Foundation awarded nearly 100 Graduate Research Fellowships. This is the best known fellowship for graduate students in mathematics, but our advice other national fellowships is similar. These include:

and many more. If you are in an interdisciplinary program or applied mathematics, you may have access to fellowship programs targeted at the sciences or engineering. And don't neglect the prestigious fellowships for study abroad, such as the Fulbright, Gates, Marshall, and Rhodes, which are not usually thought of as available for mathematicians, but they are.

For many, a fellowship application is a central part of applying to graduate school. After all, the items you have to put together, test scores, transcript, personal statement, and letters of recommendation, are pretty much the same, so it is not much extra effort.

We will describe the NSF Graduate Fellowship, which is representative of other national fellowships. This is a large, stable program of the Federal Government, but some details can change from year to year. The applicant must be a US citizen or permanent resident alien. The Graduate Fellowship provides three years of support that can be taken over a five year period, so an awardee can take one full year of support for the first year of graduate school, saving the last two years for when the thesis research is being done. An NSF Fellow intent on an academic career might alternate getting teaching experience with full-time study and research.

The level of support for the 2003 competition was $27,500 stipend for a 12-month tenure plus $10,500 cost-of-education allowance per tenure year. Applications are accepted from college seniors and from graduate students in their first year. Seniors are especially encouraged to apply. Frequently, the hardest fellowship to apply for is the first one. Since you will have eligibility in your first year of graduate school, the application that you make then will likely be stronger, and will certainly easier to prepare.

In preparing the application, it is helpful to keep the review process in mind. The selection of Fellows is made by a panel of mathematicians that meets in February of each year in Washington. Oak Ridge coordinates and oversees the selection of the panel, which will be a diverse mix of faculty coming from colleges and universities, both public and private, from around the country. Over a two-day period the panel ranks a large number of applicants in mathematics (694 in 2002). A great deal of care is taken to make the ranking fair and consistent. Then the ranked applicants are aggregated into substantially comparable groups, and only the groups which are reported to the NSF staff.

Afterwards, the NSF uses a range of other criteria to select the awardees, taking into account such things as geographical region and other factors determined to be consistent with policy and legislative intent of the program. The applicants in the top category always get the awards, while the other criteria come into play for applicants who rank well but not quite so high.

GREs and GPAs. One component of the NSF application is GRE scores from both the general and subject tests. The general test is a test of one's general undergraduate education and ability, and is similar to the SAT test, with verbal and analytic portion. There is in addition an essay portion.

The general test is given electronically, and so there is a lot of flexibility about when and where to take it. The subject test is still paper based, and so must be taken at a fixed time and place. In order to have your scores reported in time for the NSF graduate competition, the last possible day to take the test is the December date, usually the first Saturday in December. This is the test date for which the NSF can have the test fee waived. (But there are some restrictions on the waiver, such as the score only being reported to the NSF competition.) See the application materials for complete details.

We advise you to take the GRE subject and general tests in the spring of your junior year. These scores can be used in the NSF competition, as well as admission to graduate schools, which commonly require them. Many students will have already had the course work that is required for the GRE subject test by this time, and the scores taken in the spring can be used for both the NSF competition and graduate school. Taking the GRE early will permit you the option of retaking it, if you desire.

Most applicants for the NSF Fellowship have excellent GRE scores, not a few of them perfect. As a consequence, excellent GRE scores won't make an applicant stand out from the crowd. The selection committee will note whether the scores are excellent, but it is the usually the other parts of the application that separate the winners from the rest. Similar comments apply to the GPA.

Success in a doctoral program depends on somewhat different skills than those of a top undergraduate student, and the selection committee will be most interested in these, especially originality and the depth of your interest in mathematics. Since GREs and GPAs don't reveal these traits, the recommendation letters and personal statements are the most important components of the application.

Reference letters. You will need to select four references for the NSF Fellowship, and usually about this many for other fellowships. An ideal reference would be from a well-known professor, with whom you had a difficult class in which you performed well, and with whom you had several scientific discussions. Many can also add a supervising professor from an REU, or senior project. Reports about your interest in and experiences with independent work are of great value for the selection committee, and hence for your application. If you have four such professors then great. If not, a good fall back would be the professor with whom you have a difficult class. Even if there was limited interactions with the professor, he or she will likely have an informed opinion about your intellectual abilities.

Supporting statements. There are four supporting statements in the NSF application. These give you the opportunity to describe your motivation and desire to pursue advanced study, and the educational experiences that led you there; ways you advance diversity, help with public understanding, or benefit society; your plans for research in graduate school; and your prior research experiences, or experiences you have had which have prepared you for research.

All four of these statements will read as a whole, yet the second two are probably what should be written first, and revised the most carefully. Don't feel that you have to be outstanding on all fronts, and by all means don't bluff where you don't really have much to say. Rather, just play to your strengths.

In the Previous Research Experience, it clearly states that if an applicant has not had prior research experience, then you should "describe any activities that you believe have prepared you to undertake research." There are a large number of mathematicians who feel that solving problems is excellent training. Indeed, conducting research frequently entails solving many small problems. Those with less sophisticated problem solving skills then face more hurdles in completing the research.

What is most important about the proposed research statement is that it reflect "your understanding of a mathematical problem and the methods needed to solve it." That is, it is NOT the research that you propose to do for your thesis, let alone your entire professional career. It should be a question that you have found intriguing, and can talk about with conviction, overview and detail.

Personal statement: This should be an opportunity for you present yourself in a good light, but also to accent those things which were either omitted or too lightly touched upon in other parts of your application. It is important to remember that a personal statement will be read by a broad range of people with a similarly broad range of personalities. There is not a right or wrong answer. A metaphor that strikes some of your readers as artificial could easily touch other readers.

Grantsmanship 101. With the panel doing its work in two very full days, the panel members will be reading a large number of applications. Make it easy for them to see why you are special. Use twelve point type, and lay out your essays clearly. Avoid convoluted sentences and long paragraphs, and take care to structure your statements visually. Present your ideas so that the combinatorialist, the statistician, and the differential geometer on the panel will all understand, not just the one you would most like to impress.

The NSF application comes in about 20 sections, which can be done piecemeal through the online FASTLANE system at the NSF. The deadline is the first Thursday in November, at 5pm local time for that applicant. Take care of some of the "Name and Social Security" portions early, as the load on the system on the day of the deadline will be big. On Thursday November 5, 2002, the deadline for the NSF competition, the FASTLANE system experienced problems right at 5pm east coast time. (The NSF uniformly extended the deadline for all applicants by 24 hours.)

References can also be uploaded through NSF's FASTLANE. In any case, the deadline is one month after the student's application, in early December. Professors who are teaching your fall classes can write a recommendation for you. Make it easy for them to write the letters. A gentle reminder is not a bad idea.

Fellowships awarded by universities. The national fellowships are not the only games in town. Many mathematics departments have their own resources to offer for full or supplementary fellowships. These are sometimes from endowments or from institutional funds that have been committed to enhance university programs. Supplemental fellowships that might pay $1000 a year and give you a better office or a travel budget will have names like the Dean's Scholarship, or the Webistics Corporation Fund, depending on who had to be talked out of the money. Often a department will have fellowships that are the equal of the major national fellowships, because it was the department that competed for them, saving you the trouble. The most widespread source of these fellowships is NSF's VIGRE program.

The award of an in-house fellowship is at the discretion of the department and is usually part of recruiting. If a graduate school really wants you, a graduate coordinator may offer one of these fellowships as an inducement for you to enroll in his or her program rather than another one that has accepted you. It doesn't hurt to ask a graduate coordinator about resources like this, especially if you have some good cards to play. (Ouch! The coauthor who is a graduate coordinator isn't sure we should have admitted that.)

Evans Harrell is the Associate Chair for Graduate Studies in Mathematics, and Michael Lacey is the former Associate Chair for Undergraduate Studies in Mathematics, at Georgia Tech. Please write them about problems with this website or questions that should be archived in its FAQ list.