What are math research programs looking for?

<p>I'm a freshman math major, and for this summer I applied to two summer math research programs. The first program didn't accept me. However, a professor from the second program emailed me some of his research papers and asked me to look over them and tell me what I thought. But then I ended up not getting a position. </p>

<p>Does anyone know what sorts of qualities/accomplishments math professors are looking for? A strong GPA? Advanced math classes? Leadership? Extracurriculars? Math contests? </p>

<p>Thanks for any input.</p>