AB Duke to Top Math Graduate Program

Hello everybody,

One of my most recent posts was about whether to choose MIT or Harvey Mudd with a merit scholarship for a math major. Quite ironically, I chose neither of those schools. Soon after my post, I was notified that I was selected as an AB Duke scholar, which is a full-ride to Duke, plus a summer stipend for research and travel, plus a 6 week summer program at Oxford.

I am aware that Duke is not the best when it comes to math (even though its still very good by all means). What do I need to do in college to lock up a spot at a top graduate math program (i.e. MIT or Princeton)? What do these top schools look for in an applicant?

I know my question is rather ambiguous, however any feedback helps!

Do well in your math courses.
Do well in undergraduate research and get good recommendations.

All of the above plus–a high score on your GRE.