PROMYS moves beyond the high school curriculum by offering students the opportunity to participate in the process of scientific research. The problems encourage students to design their own numerical experiments and to employ their own powers of observation to discover mathematical patterns, formulate and test conjectures, and justify their ideas by devising their own mathematical proofs. These activities, done with support from PROMYS faculty and counselors and in collaboration with other students, help refine the skills of conjecture, proof, analysis, and research.
Since 1999, the CMI/PROMYS partnership has run the research labs and the advanced seminars. Recent Mentors have included Avner Ash, Amanda Beeson, Ben Brubaker, Bryden Cais, Henry Cohn, Keith Conrad, Ed Early, Cameron Freer, Ira Gessel, Paul E. Gunnells, Jonathan Hanke, Ben Harris, Kiran Kedlaya, Jonathan Lubin, Steven Miller, Robert Pollack, Aaron Silberstein, Dev Sinha, Jared Weinstein, and Kirsten Wickelgren.
Mentors pose new research problems at the start of each summer. The materials include problem statements, hints for getting started, and references to the pertinent literature. Each returning PROMYS participant selects a problem and is placed in a team of four. Teams engage in open-ended exploratory projects under the guidance of the Mentors and other research mathematicians. As participants work on these team projects, they develop habits of thought associated with creative scientific research.
At the end of the summer program, students give presentations to the PROMYS faculty, counselors, and all of the PROMYS participants. The research write-ups are then shared with the extended PROMYS community via the alum site.
Please see the separate pages in this section for listings of the research projects from 2002 through 2016.