Humble Advice on Applying to Graduate School

I receive a nontrivial amount of email from undergraduate students, often at institutions outside of the United States, asking what they should do to be accepted to PhD programs in theoretical computer science/statistics/mathematics/etc.

There is a lot of advice about this online, and I don’t have anything new to contribute, but in case it is of use to someone I will accumulate parts of my responses to these emails here.

(See also: fellowships)

1. (On assembling a strong CV/application, 7/12/21) The most important part of any PhD application is the letters of recommendation. Most importantly, the letters should provide strong evidence that you have demonstrated the ability to do mathematically creative and rigorous research. The strongest letters come from people who have interactions with many successful junior and senior researchers and can therefore compare your abilities and potential favorably to those of others.