PROMYS at Boston University: A Complete Guide

The Program in Mathematics for Young Scientists (PROMYS) provides an excellent environment for aspiring young mathematicians. It celebrates and cultivates students’ deep interest in mathematics.

Each summer, Boston University transforms into a hub where mathematical theories and problems are taught and explored, where students are not just learners but young mathematicians in the making.

What is the PROMYS, and how does it work?

PROMYS, or Program in Mathematics for Young Scientists, at Boston University is an annual six-week summer program for high school students aged 14 to 18. This program dives deep into mathematics, exploring areas that are not typically explored inside the classroom.

Founded in 1989, PROMYS is designed for highly motivated high school students from the U.S. and around the world. It’s a residential program at Boston University where approximately 80 high school students and 25 undergraduate counselors participate.

During the entire program, you’ll attend daily lectures and spend most of your time working on Number Theory problem sets individually and in groups. You’ll engage in exploratory, open-ended labs with other selected students, presenting and discussing your findings with the PROMYS community. The summer program closes with students presenting their research and compiling it into research papers.

Guidance is readily available from resident counselors, including junior counselors recently graduated from high school and undergraduate counselors starting their mathematical journeys at top universities, with more than half from Harvard, MIT, or Princeton.

Returning students, who share rooms with first-year students, often provide valuable advice and insights. Senior mathematicians also offer continual mathematical guidance and support.

PROMYS includes activities like volleyball, basketball, and jogging for relaxation, alongside weekend excursions to places like the MIT Museum and the Boston Museum of Science. Though it offers a balanced experience, PROMYS is considered slightly less intense than other math programs, such as the Ross Program at Ohio State University, which also runs for six weeks each year.

Who is eligible to join the PROMYS?

Students need to meet all of the following requirements to participate in the program:

• Be 14 years of age or older
• Completed 9th grade (or its equivalent)
• Not enrolled as a full-time student at a college or university

Students are eligible to participate during the summer following high school graduation, including during a gap year. However, those already enrolled in university cannot apply as students, although they may qualify to apply for counselor roles.

How do you apply to the PROMYS?

Start preparing your PROMYS application now to have enough time, as it requires a lot of work. You’ll need to provide basic personal information, answer essay questions about your interest in math, solve a complex problem set, submit an official transcript, obtain a recommendation from a math teacher, and have a financial aid form completed by your parent or guardian.

The following must be submitted by the application deadline:

• Solutions to a problem set
• A letter of recommendation from a Math teacher
• High school transcript
• An application form that requires short answers

The main part of the application is the problem set, which should be challenging and stimulate critical and creative thinking in mathematics. You also need to submit a recommendation from a math teacher or mentor that highlights your math skills, work ethic, and potential as a young mathematician.

What is a problem set, and how do you prepare them?

A problem set, often abbreviated as “pset,” is a common educational tool in many universities. It is frequently used in courses such as physics, math, engineering, chemistry, computer science, and even economics.

Essentially, a problem set consists of several moderately challenging questions or exercises that relate to previously covered material. Students are expected to solve these problems with detailed written answers. No additional research is required; the purpose is to deepen understanding of the material and practice solving standard problems.

According to the Derek Bok Center at Harvard University, “Problem sets are great ways to provide students with the practice necessary to gain mastery of new skills that you have introduced in class. Problem sets are also great at reflecting the nature of the scientific process, which so often involves problem solving, and in so doing help reinforce the explanatory power of your discipline.”

Qualities of an effective problem set include:

• Motivation and Learning: They should help students learn new concepts and connect what they’re learning to real-world applications or recent research.
• Skill Reinforcement and Synthesis: They should both reinforce basic skills with straightforward questions and challenge students with complex problems that require synthesizing various skills.
• Cognitive Skills Development: They should cover a wide range of cognitive skills, from simple recall to complex problem-solving, in line with Bloom’s taxonomy.
• Collaborative Engagement: They should encourage teamwork, reflecting the collaborative nature of many professional fields, but students should still submit their own work to ensure honesty.

Important Dates and Information

• Program Dates: June 30 – August 10, 2024
• Open Application: Early January 2024
• Application Deadline: March 1, 2024 at 11:59 EST
• Admissions Decisions: April 30, 2024

Costs

The six-week residential PROMYS program costs $6,100, though the actual cost per student exceeds $8,500. This difference is covered by donations and sponsorships.

Financial Aid and Scholarships

PROMYS is committed to making sure financial constraints do not prevent participation. The program offers free tuition to domestic students from families earning less than $80,000 annually. For information on need-based financial aid, scholarships, fellowships, and other awards, including assistance for international students which is determined individually, visit the Financial Aid & Scholarships page on the PROMYS website.

Here is a list of scholarships that PROMYS offers with the help of sponsors and donors:

Scholarships	Descriptions
AMS Scholarships	Through the American Mathematical Society (AMS) Epsilon Fund, PROMYS is offers the Ky and Yu-Fen Fan Scholarship. This scholarship covers a substantial amount, potentially up to the full cost, for a deserving high school student. Applicants do not need to fill out a separate application for this scholarship.
Breakout Fellowship to PROMYS	All PROMYS applicants, whether from the U.S. or abroad, are automatically considered for a Breakout Fellowship, which is a full scholarship with no separate application required. Funded by mathematicians Jacob Lurie, Terence Tao, and Richard Taylor, and supported by donations from PROMYS alumni, this fellowship aims to support talented students who might not otherwise afford to attend. Each year, one scholarship is fully funded through an established endowment.
Jane Street Fellowships	In 2023, PROMYS was pleased to offer two Jane Street Fellowships to students. All applicants eligible for financial aid will be considered for these full scholarships if they are available again in 2024.

What do the courses in PROMYS look like?

PROMYS advisors suggest reviewing topics such as Number Theory, Algebra, Combinatorics, Topology, Geometry, Calculus, Probability, Set Theory, Logic, and more. For additional math help, consider using resources like the Art of Problem Solving Online, Khan Academy, or the National Math Club.

In 2017, returning PROMYS students attended seminars on topics like The Analytic Class Number Formula, Algebra, and Geometry and Symmetry. PROMYS also runs a “Math Circle” (PMC) both in-person and virtually, targeting mathematically gifted students from low-income families and those underrepresented in STEM fields.

Number Theory

Every weekday from 9:00 to 10:30 a.m., all participants attend a lecture on Number Theory. The main task for first-year attendees involves solving a variety of difficult problems in Number Theory. These daily problem sets push participants to run their own numerical experiments and use analytical skills to identify patterns, develop hypotheses, and create their own mathematical proofs.

Advanced Seminars

Each summer, both returning students and ambitious first-year attendees can participate in Advanced Seminars on a range of topics. These seminars are led by PROMYS faculty and guest mathematicians and typically meet two to three times a week. They include lectures and challenging problem sets. In 2024, the seminars will cover topics such as Discrete Dynamical Systems and the Poincaré Recurrence Theorem, Galois Theory, and others yet to be determined.

2024 Advanced Seminars
Topic and Speaker	Description
Discrete Dynamical Systems and the Poincaré Recurrence Theorem by Margaret Beck from Boston University	Discrete dynamical systems are intriguing not only because of the chaotic behavior they can produce but also because they relate to other mathematical areas like number theory. You’ll explore these concepts using tools such as symbolic dynamics, invariant measures, recurrence, and ergodicity. You’ll also prove the Poincaré Recurrence Theorem, which shows that under certain conditions, paths in a dynamical system repeatedly return to their starting points. Additionally, you’ll examine various effects and interpretations of this theorem.
Galois Theory by David Speyer from the University of Michigan	This course will guide you through proving Abel’s theorem, which states that there is no general formula to solve quintic equations and introduce you to the basics of Galois’s theory. The classes will be interactive, focusing heavily on solving problems during class time. To follow along, you only need a basic understanding from the first-year PROMYS material and some experience with writing proofs. Knowledge of linear algebra is beneficial but not necessary, and this course might even change how you understand it.
Graph Theory by Marjory Baruch from Syracuse University	Graph theory is a versatile tool used for various applications such as designing street maps, understanding dice shapes, coloring maps, and analyzing internet trends. It’s also essential in cyber security. This course covers basic graph theory, exploring how many colors are needed to color a map on a curved surface like a bagel. You’ll have the chance to deepen your understanding by working through examples and developing your own theories.

Guest Lectures

In addition to the regular weekly activities, the program offers a variety of lectures from faculty and guest speakers. These lectures enhance participants’ understanding by exploring related scientific fields, discussing ethical and philosophical issues in science, examining the connection between pure and applied science, and exploring various career paths.

Frequently Asked Questions about PROMYS

1. Where have PROMYS alums gone to college?

Over half the alumni have attended Harvard, MIT, Princeton, Stanford, UC Berkeley, or Caltech as undergraduates (the other half attended one of more than 160 other institutions). Of the alumni for whom the the undergraduate major was known, 60% have majored in mathematics with many others majoring in engineering, computer science, physics, chemistry and/or biology. (PROMYS has post-secondary school educational data on 97% of our 1,799 alumni and recently updated education/career data on around 90%).

2. How many alums have chosen to acquire a doctorate?

At least 631 alumni have, or are working on, a doctorate. This represents 53% of all old enough alumni for whose educational information was reported (or 45% of all alumni old enough for graduate school). 

Five hundred and twenty-eight of the doctorates are Ph.D.’s, 509 (96%) of which are STEM PhDs. Three hundred and twenty-seven alumni have or are currently working on, a Ph.D. in Mathematics. Forty-seven percent of alum Ph.D.’s in Mathematics are from MIT, Harvard, Berkeley, University of Chicago, Princeton, or Stanford.

3. How many of the alums have become professors?

At least 161 of the alumni are currently professors (79 are Full or Associate Professors). One hundred are professors of mathematics; others are professors of computer science, physics, finance, economics, chemistry, biology, meteorology, philosophy, medicine, business, public policy, management, English, sociology, urban education, or the law. 

Alumni are on the faculty at a great many institutions including six at Harvard University, three at MIT, five at Cornell University, six at University of Chicago, three at Columbia University, four at University of Pennsylvania, three at University of Michigan, and two at University of California Berkeley.

4. What are some PROMYS alumni awards and distinctions?

Alums have mentored other alums in prize-winning research projects including a 1st Place award in the Siemens Westinghouse Competition, an Intel STS 3rd Prize, and an ISEF 3rd Place in Mathematics.

• 10 International Physics Olympiad (IPhO) Team Members with 2 gold, 1 silver, and 1 bronze medals at IPhO
• 2 International Chemistry Olympiad (IChO) Team Members with a silver medal at IChO
• 1 Winner of US Chemistry Olympiad
• 2 International Linguistics Olympiad Team Member and a silver medal at ILO
• 2 ISEF Award Grand Prizes in 2012 alone
• 12 Presidential Scholars

5. Do all problems on the problem set need to be answered on the application?

Not necessarily. The program evaluates your mathematical readiness for PROMYS through a holistic approach, considering various factors including your mathematical background. The problem set is a crucial part of the application, as it allows them to assess how you approach, solve, and explain complex problems with creativity, enthusiasm, and persistence.

6. What is the acceptance rate at PROMYS?

While the acceptance rate at PROMYS changes annually, gaining admission is competitive. Unfortunately, they have to decline many qualified candidates each year and hope these individuals will reapply in the future if still eligible. Since not all students are accommodated at PROMYS, they encourage applicants to consider other programs as well.

7. What does the housing arrangement look like during the program?

PROMYS students are housed in Warren Towers at Boston University, which is designated for pre-college summer programs. Rooms are double occupancy and assigned based on gender identity, with each floor also designated by gender and supervised by BU Residential Life counselors. PROMYS counselors stay on the same floors to facilitate close supervision and mentoring of the students they oversee.

8. Am I allowed to live off campus and commute instead?

Unfortunately, living off campus is not allowed. Living and engaging with mathematics is a core part of the PROMYS experience, often happening in the common areas and dorm rooms late into the night.

9. Am I allowed to do other engagements or take on other commitments while doing PROMYS?

Once you decide to participate in PROMYS, you’ll need to set aside other commitments. The program is intensively designed to engage students throughout the six-week duration fully. Although weekends have a lighter schedule than weekdays, they are still focused on mathematics, and students are expected to stay on campus and concentrate on their studies in the program.

Is PROMYS worth it?

Participating in PROMYS can be highly beneficial for your college admissions and future career, particularly if you’re interested in mathematics or related fields. Here’s why it is worth it:

Strengthening your college application

PROMYS is a prestigious program known for its intensive mathematical training. Having it on your application not only highlights your mathematical abilities but also demonstrates your commitment and passion for deep intellectual engagement. Colleges often look favorably on applicants who have successfully tackled challenging programs like PROMYS, as it suggests readiness for university-level coursework.

Developing advanced skills

The program focuses on problem-solving, critical thinking, and the ability to work collaboratively—skills that are valuable in any academic or professional setting. This experience can give you a solid foundation in mathematical concepts, potentially placing you ahead of your peers in college, especially in STEM courses.

Exposure to advanced Mathematical concepts

The focus on areas like number theory and the development of new problem-solving techniques can spark interest in specialized fields of study or research that you might pursue in college and beyond.

Potential for scholarships and recognition

Success in programs like PROMYS can help you qualify for scholarships and other forms of recognition that support your educational journey and make your applications stand out.

In summary, if you have a strong interest in mathematics and are eager for a challenge, PROMYS can provide significant advantages for your educational and career paths. It’s a commitment, but one that can pay substantial dividends in terms of your personal, academic, and professional development.