Counselors - Frequently Asked Questions

Dr. Li-Mei Lim at the board

Q: What Role do Counselors Play at PROMYS?

A: The counselor’s role is central to PROMYS. Counselors encourage, supervise, and grade the work of the students; and they organize the social activities of the program. The counselors are mathematical guides and, in essence, run the program (“Counselors Rule!”), with the support of three experienced Head Counselors and the guidance of the faculty.  Many of the students form close bonds with their counselors. PROMYS is an intense immersive experience, and the counselors keep a protective eye on the students to ensure they are safe and happy.  

Counselors are important role models. The students witness the counselors and adult professionals engaging actively, intensely, collaboratively, and joyfully in creative mathematical endeavors. PROMYS proves to participants that mathematics is a creative and collaborative enterprise, that there is a vibrant community they can choose to join, that mathematics need not be a solitary activity, and that members of the community give each other social and intellectual support. Many alumni have told us that this exposure revolutionized their attitudes toward having a career in mathematics.

Q: What Will I Learn as a Counselor at PROMYS?
A: A defining characteristic of PROMYS is that the program is designed for the mathematical engagement and development of the counselors as well as the students.  It is key that the very talented undergraduate mathematicians have enough variety, challenge and progression to continue to engage themselves in increasingly significant mathematical activity from one summer to the next.  Counselors are asked to supervise the work of three or four students and have time to pursue their own mathematical endeavors as well. Counselors are invited to study mathematics independently by participating in advanced seminars and interacting individually with the faculty. In addition, the counselors are invited to organize minicourses, seminars, and lectures on themes of their own choosing in order to introduce students and fellow counselors to a broad variety of mathematical ideas. See here for a listing of counselor talks from 2011 - 2021. Activities of these kinds are especially important to the health of the PROMYS program and are supported to the greatest extent possible.

Counselors tell us they come to PROMYS, and return to PROMYS, for the same reasons that the students tell us they come to PROMYS and return to PROMYS: the mathematics and the people.

Q: What is PROMYS's Pedagogical Philosophy?
A: It is not so much through the daily mandatory number theory lectures that PROMYS habits of mind are developed as in the extended hours every day that the first-year students work on their carefully crafted daily number theory problem sets - working on their own or collaborating with others.  PROMYS faculty, counselors, and returning students provide encouragement and feedback, inspiration, instruction, and mathematical tools; they don't provide solutions or even hints. 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. These activities help refine the skills of conjecture, analysis, proof, and research - providing firsthand (and often first time) experience of the mechanics of real research.  The learning goals of PROMYS extend considerably beyond the valuable foundation in number theory to the demonstration through firsthand experience of the rewards of delving deeply. 

Often for the first time in their lives, the talented young PROMYS participants find themselves tackling mathematics that is beyond their immediate grasp; are exposed to mathematics that is beautiful and daunting; are held to exacting standards of rigor and precision; meet others with similar levels of talent and passion; and learn, not just as students, but as scientists. PROMYS is non-competitive, and students learn from one another. Many then go on to teach and mentor in the PROMYS way, by giving others the tools to think for themselves.

PROMYS aims to create an authentic experience of doing mathematics within a community of mathematicians having various levels of experience and expertise, every one of whom is actively engaged in significant mathematical activity appropriate to his or her individual level of expertise. In this way, first-time participants are introduced to a spectrum of individuals, from their talented, but still inexperienced, fellow first year students, through college and graduate students, and connecting with seasoned research mathematicians.  

Q: Is any specific mathematical background required?  Are freshmen eligible?  Are non-alums welcome to apply?
A: We consider all applications independent of year in college, and it is not uncommon for us to invite freshmen to be counselors. Yes, we encourage all interested undergraduates to apply; all applications will be given full consideration. Only in borderline cases might former students be given any preference. The main requirements are a high level of mathematical achievement, mathematical maturity, potential for mathematical growth, and interest in working with talented high school students.

Q: Are the Counselor Talks and Seminars all on Number Theory?
A: No! Topics are as varied as the mathematical interests of the counselors. Click here for a list of counselor seminar and minicourse topics in 2011-2021.

Q: Is PROMYS a Traditional REU?
A: For some counselors, mathematical research at PROMYS is self-structured. Other counselors participate in a more formal REU experience such as PROMYS's partnership in 2014 - 2017 with the SMALL REU at Williams College. In 2018, PROMYS partnered with Professor Lionel Levine (Cornell University) to offer a PROMYS REU to five counselors. PROMYS hopes to continue these partnerships in the future and is looking to develop such partnerships for the future. When the program is run in person, all counselors are based at Boston University for the full six weeks of PROMYS.

Q: What do Counselors do After PROMYS? 
A: 75% of counselor alumni who are old enough for graduate school and for whom we have up-to-date educational data (91%), have, or are working on, a doctorate. Over 80% of those doctorates are PhD’s in Mathematics.

Just as the counselors are role models and advisors to the students, so the research mentors, faculty, and visiting mathematicians are role models and advisors for the counselors. And these connections are often lasting since the PROMYS alumni network is very active. With 167 alum professors and 346 alumni with (or working on) PhD's in Mathematics, the alum community, available through online groups as well as regular alum gatherings, is a professional as well as a personal resource.

Many counselors choose to participate in PROMYS for multiple summers. Many continue to return as visitors, guest speakers, research mentors or instructors. The program relishes the long-term involvement of alums. Mathematically and socially, they are PROMYS’s past, present, and future.