Letters of Recommendation

Most grad programs require you to submit three letters of recommendation. This is one of the most important parts of your application. If you're still in your junior year, you should plan ahead for who your letter writers will be, and try to get to know them better.

Who to Ask

Some general criteria to keep in mind when choosing letter writers:

Fancy people's letters mean more.
The graduate admissions committee is made up of mathematicians. Lots of those mathematicians know each other. If they see a letter written by their friend, or someone they respect, it will mean more to them. This is one of the ways the "old boys club" perpetuates itself in math. Playing the system means asking well-known, established professors to write you letters. Ask professors, not postdocs.

They should know you well.
If you've never spoken to the professor outside of class, they won't have much material to write about. Go to office hours. Ask questions. If there aren't office hours, email the professor and ask to meet one-on-one to answer questions. If you don't have questions, make some up. Ask about further directions or for counter-examples. Show the professor that you've put in effort to understand the material and care about math. The best way to get a good letter is to take a reading course or independent study. You could also do a UROP or an REU with someone.

If you are unsure of whether or not you know a professor well enough to write a letter, you can ask them if they feel like they could write you a "strong" letter.

Ask early.
Ideally your letter writers will have known you for at least a month before you approach them about writing a letter. You should ask them to be a letter writer about a month before the application is due. You'll almost certainly have to remind them (maybe even a few times) to submit their letter.

Recent interactions are preferable.
As you've probably noticed, math professors can be forgetful. If you haven't interacted with a professor since your first or second year, they might not remember you. Aim to ask people who you've had meaningful interactions with in your third or fourth year (or the summer in between).

How to Ask

You can either ask in person or over email. You should not ask in front of other people. For example, don't ask the professor after class while other students are still milling around. Don't scheduele a meeting just to ask. You can say something like

"I'm applying for math graduate school this year. Would you be willing to write me a letter of recommendation? The application is due ____."

Once they agree, they might ask for more information about you to help them write their letter. This might include your transcript, a CV, or a list of where you are applying.

Personal Testimony

Below is a more personal experience of how a current MIT graduate student got their recommendation letters:

"When I asked people to be my recommenders they didn’t just offer to write letters; they took an active interest in helping me choose programs to apply to and to tailor my part of the application. My undergraduate advisor had already been encouraging me to take the most rigorous classes possible in order to be well-prepared for graduate school. Some of the professors from these classes became my letter-writers. I asked my recommenders if they would be willing to write for me during my junior year and told them I would keep them posted about the precise list of schools I was applying to. They all had some suggestions, based on my interests and their knowledge of various math departments through colleagues and friends. My final list of schools ended up being the union of all of their suggestions plus a few more as well. That fall, I sent each a spreadsheet with the schools I was applying to, the deadlines for each part of the application, and my intended advisor at each school, if applicable. I also sent each my CV, my transcript, and my NSF application materials."