PROMYS Europe moves beyond the secondary 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 Europe faculty and counsellors and in collaboration with other students, help refine the skills of conjecture, proof, analysis, and research.
Mentors pose new research problems at the start of the summer. The materials include problem statements, hints for getting started, and references to the pertinent literature. Each returning PROMYS Europe participant selects a problem and is placed in a team. 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 programme, students give presentations to the PROMYS Europe faculty, counsellors, and all of the PROMYS Europe participants. The research write-ups are then shared with the extended PROMYS Europe community.