PROMYS is a six-week summer program in mathematics for strongly motivated high school students who are carefully selected from across the U.S. and around the world. Founded in 1989, PROMYS is a residential program held on the campus of Boston University with approximately 80 high school students and 25 undergraduate counselors. Number Theory Each weekday begins with all participants attending Number Theory lecture from 9:00–10:30 a.m. The main activity of first-year participants is their intensive efforts to solve an assortment of challenging problems in Number Theory. Daily problem sets encourage participants to design their own numerical experiments and to employ their own powers of analysis to discover mathematical patterns, formulate and test conjectures, and justify their ideas by devising their own mathematical proofs. Advanced SeminarsLi-Mei Lim teaching advanced seminar Each summer, returning students and motivated first-year participants take one or more of the Advanced Seminars offered on diverse topics. PROMYS faculty and visiting mathematicians lead the seminars which meet two or three times per week for lecture and also feature engaging problem sets. In 2023, we offered the following seminars: Abstract Algebra; Modular Forms; and Primes and Zeta Functions. Guest Lectures Our regular weekly activities are supplemented by diverse lectures by faculty and guests of the program. These lectures introduce participants to related scientific fields and include discussions of the ethics and philosophy of science, the relationship between pure and applied science, and career options. Research Projects All students have the opportunity to participate in the process of scientific research — PROMYS-designed exploration labs for first-year students and research projects mentored by professional mathematicians for returning students. Every summer, research mathematicians propose original problem statements for the PROMYS program. Each returning student selects a problem, then teams of four engage in open-ended exploration under the mentor's guidance. At the end of the summer, students write up and present their research to the entire PROMYS community. Some of these papers have been published or presented at conferences like the Joint Mathematics Meetings. Exploration Labs First-year students may also choose to participate in open-ended projects called Exploration Labs. They work in small groups, guided by a counselor and faculty member. At the end of the summer, the students write up their findings and make a presentation of their research to the assembled PROMYS community. Counselor Minicourses Counselors contribute to the mathematically rich environment at PROMYS by doing their own research and by designing and presenting a wide range of lectures on topics of special interest. They organize minicourses open to all participants and counselor seminars intended for their peers.