PROMYS is a challenging program designed to encourage ambitious high school students to explore the creative world of mathematics. Each summer, approximately 80 high school students from around the country gather on the campus of Boston University for six weeks of rigorous mathematical activity. Through their intensive efforts to solve an assortment of unusually challenging problems in Number Theory, participants will practice the art of mathematical discovery. The problem sets encourage students 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.
Students are advised by resident counselors: junior counselors who have just graduated high school and undergraduate counselors who are embarking on their own mathematical careers at some of the finest universities (over half attend Harvard, MIT, or Princeton). In addition, the returning students, who share dormitory rooms with the first-year students, are a constant source of helpful hints and suggestions. Senior mathematicians are a constant resource providing mathematical support and encouragement to the students.
The emphasis at PROMYS is on asking good and creative questions, on hard work and persistence, on clarity of thought and precision of expression, on respect for people and ideas, and on the sheer joy of acquiring mathematical insight. PROMYS participants are asked to work beyond their centers of competence and to push the limits of their knowledge. The PROMYS community network provides all participants with a richly supportive environment within which to learn.
Students who find their PROMYS experience especially worthwhile may be invited to return for a second summer to participate in the advanced PROMYS/CMI activities. To ensure that returning students and counselors find their experience intellectually stimulating, PROMYS, in partnership with the Clay Mathematics Institute, offers a variety of advanced seminars and mentored research projects each summer. In 2015, returning students participated in seminars on Galois Theory, Complex Analysis in Number Theory, and Geometry and Symmetry.
The regular program activities are supplemented by diverse weekly lectures by faculty preceptors and guests of the program. These lectures introduce participants to related scientific fields and include discussions of a broad range of mathematical and math-related topics. Recent guest lecture topics included, for example, "The Schoenflies Conjecture and Morse Theory," "High-Dimensional Mathematics," and "Statistical Inference and Modeling the Unseen: How Bayesian statistics powers Google's voice search." Additionally, the counselors give lectures on topics of special interest and also organize their own weekly seminars on topics of their choosing. Every week, the program members hold informal social gatherings that serve as a forum for open discussion on themes of general interest. Discussion topics have included the relationship between pure and applied science, defense funding of mathematics, and career options.
The PROMYS program aims to provide an environment for talented young people that will arouse their curiosity and encourage a deep personal involvement with the creative and collaborative elements of mathematics and science. It is designed to encourage habits of thought that will lead to scientific independence and creativity. At the same time, it seeks to foster interaction between the PROMYS community and the larger community of research mathematicians and scientists currently working in academia and industry.