In mathematics, maybe more than in any other science, research is an activity of the mind. The primary goal of the mathematician is to understand - to discover essential ingredients of complex systems in order to render them simple, to find order within apparent chaos, to draw analogies between different structures, and to find connections between seemingly disparate branches of mathematics and science. To make interesting new contributions in the field of mathematics requires a healthy mix of creativity, experience and hard work.
The day begins with the Number Theory lecture which meets Monday through Friday from 9:00 a.m. to 10:00 a.m. The more experienced students will also attend advanced classes. In 2012, we offered advanced seminars in Geometry and Symmetry, The Analytic Class Number Formula, and Algebra. Participants spend most of the remainder of their time working independently or in small groups on problem sets distributed at the end of each class meeting. The problems will encourage students to design their own numerical experiments and to employ their own powers of observation to discover mathematical patterns, to formulate and test conjectures, and to justify their ideas by devising their own mathematical proofs.
They continue to work on problem sets throughout the day (and night). Some may work in groups; others individually. Counselors review student problem sets daily and are always available to help guide students in the right direction.
Many first-year students also meet in small groups to work on exploration projects, guided by a counselor. Returning students have an opportunity to work on research projects proposed by visiting mentors.
Students experience real college dormitory living. It is an excellent opportunity for high school students to experience what college life will be like. There are separate male and female living quarters, and curfews as well as visiting rules do apply. All PROMYS students and their counselors live on the same floors in the dorm. A counselor is usually placed within close proximity to the three or four students that he/she is supervising. There are laundry facilities in the dorm, so bring some money for laundry and detergent. Meals are served in the dining room in Towers during specified hours. The cafeteria offers a range of hot and cold meals and always has a vegetarian option. The Kosher menu is not available during the summer.
Every Saturday morning from 9:00 A.M. until noon, we reserve the gym for volleyball and/or basketball for anyone who wants to participate. "Early risers" have also been known to jog along the Charles River before morning lecture. Some students bring their musical instruments with them and wish to practice on a regular basis. The dorm has a single practice room with a piano. In addition, a music card is available through the Music Department, for a small fee, which allows summer term students to reserve a room and schedule individual practice times.
Special activities include an annual Ultimate Frisbee match against RSI at MIT and have included visits to the MIT robotics laboratory and nuclear reactor, the Boston Museum of Science and the Boston Computer Museum. Additionally, counselors and faculty plan activities that vary from year to year and are organized according to demand. However, during the 6 weeks of the program, participants devote the bulk of their time and attention to mathematics.