## What are Your Math Research Interests?

For students applying to PRIMES, we have a question about their research interests. RSI asks a similar question from their applicants.

I am looking at all the submissions, and this essay will help our applicants to get projects that are well-suited for them.

We, at PRIMES and RSI Math, usually have research projects lined up in advance. That means, we are not creating projects to match applicants’ requests. We match existing projects to students’ backgrounds and interests.

If you are applying to one of these programs, here is my advice.

Don’t be too specific about what you want. Suppose you want to study the symmetries of an icosahedron. This request is too narrow: there is a high probability we do not have such a project. How will we match you to a project? Our hope, in this case, is to find clues in your essay. For example, we might discover that you heard a fascinating lecture on icosahedron’s symmetries, which is why you requested the topic. In this case, we assume that another fascinating lecture on a different topic might also excite you, and you will be matched with a random project. But if your description is broader, say, if you write that you like group theory or geometry, your match won’t be as random.

Add more information if your first choice is number theory. Almost every year, we have several students requesting number theory. This might be explained by the successes of the Ross and PROMYS summer programs. The graduates from these programs love number theory and have a good number theory background. However, modern number theory is very advanced, and we seldom have these types of projects. So, if number theory is your top choice, there are two things you can do. First, mention your second choice. Second, specify what you like about number theory. For example, if you are into the more abstract parts of number theory, another abstract project might be a good fit.

Describe your priorities in broader terms. It is beneficial for every starting mathematician to figure out the area they like by asking themselves broader questions. If you know the answers to the questions below, it is helpful to write them on the application form.

• Do you love or hate abstractions?
• Do you prefer discreet or continuous problems?
• Is the real-life impact or inner beauty of your project more important to you?
• Do you enjoy having a visual component to your project?
• Do you like when problems involve programs and calculations?