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Writer's pictureStephen Turban

10 Math Research Programs for High School Students

If you’re looking for a mathematical challenge that introduces you to new concepts and hones your problem-solving skills, then a pre-college research program could be a good fit for you!


Pre-college math research programs can sharpen your analytical skills and connect you with a vibrant community of like-minded peers. They also prove demonstrable interest in a subject, that college admissions boards value highly. 


While no one-size-fits-all policy applies to such programs, it’s a good idea to start by defining your objective: do you want to increase your understanding of math, bolster your college application, or prepare for prestigious math competitions? To help get you started, we’ve compiled a list of 10 mathematics research programs worth considering:


SAMS is a unique six-week in-person summer program for high school juniors interested in math and science. This program is fully funded and is led by Carnegie Mellon faculty to prepare students from underrepresented backgrounds for success in STEM fields. The curriculum blends traditional classroom instruction with hands-on research projects that involve experimental design, data collection, and analysis. You will participate in full-day lectures, meetings, and a final research symposium at the end of the program to present your work. Additionally, Carnegie Mellon organizes virtual training before the program begins to help students develop essential skills for the in-person experience. The program is quite intensive, and Carnegie Mellon expects students accepted into SAMS to be 100% committed and not participate in any other summer opportunity.


Location: Carnegie Mellon University (Pittsburgh, PA)

Cost/Stipend: Fully funded

Program dates: June 22 – August 3, 2024

Application deadline: Closed for 2024

Eligibility: High school juniors from underrepresented communities who are at least 16 years of age at the start of the program


The Lumiere Research Scholar Program in Mathematics offers ambitious high school students the opportunity to conduct research under the guidance of distinguished PhD mentors from Harvard and Oxford Universities. This entirely virtual program allows for participation from anywhere in the world.


Students are paired with a dedicated PhD mentor for a one-on-one research collaboration, working on a high-quality research paper comparable to university-level work. Mathematics is a vast subject, and Lumiere encourages students to explore a wide range of topics and even combine their mathematical interests with other disciplines such as AI, computer science, and more. Students who wish to pursue a research topic outside the program's existing offerings can propose their area of interest.

The Lumiere program typically follows the following structure:

  • Week 1: Students meet with their mentor to define a research topic.

  • Weeks 2-4: The focus shifts to exploring the chosen topic and formulating a specific research question.

  • Weeks 5-9: With ongoing guidance from their mentor, students delve into writing their 15-page research paper.

  • Weeks 10-12: The final phase involves revising, submitting, and presenting the research paper at the Lumiere Research Symposium.


Location: Remote  —  you can participate in this program from anywhere in the world!

Cost: $2800. Need-based financial aid is available

Program dates: The summer cohort runs from June to August, the Fall cohort from September to December, the Winter cohort from December to February, and the Spring cohort from March to June

Application deadline: Deadlines vary based on cohort 

Eligibility: You must be currently enrolled in high school. Students must demonstrate a high level of academic achievement (accepted students have an unweighted GPA of 3.3 out of 4)


Horizon offers trimester-long research programs for high school students across subject areas such as data science, machine learning, political theory, biology, chemistry, neuroscience, psychology, and more! You note that Horizon is one of the very few research programs for high school students that offers you the choice to engage in either quantitative or qualitative research! Once you select a particular subject track as well as the type of research you wish to carry out, Horizon pairs you with a professor/PhD scholar from a reputed university who act as mentor throughout your research journey. As a participant, you will be expected to develop a 20-page research paper that you can send to prestigious journals for publication as a high school student. 


This program is a solid opportunity for you to pursue a research program in highly specialized fields, under the guidance of a top scholar. The program also provides a letter of recommendation for each student, as well as detailed project feedback that you can use to work on future projects. Apply here!


Location: Virtual 

Application Date: May 21, 2024 for the summer cohort, and September 25, 2024 for the fall cohort 

Program Dates: 

  • Summer seminar - June 24, 2024 - September 2, 2024

  • Fall seminar - October 23, 2024 - February 19, 2025

  • Lab dates are flexible, but you must apply 4 weeks in advance.

Eligibility: High school students with good academic standing (>3.67/4.0 GPA) can apply. Most accepted students are 10th/11th graders! Only a couple of tracks require formal prerequisites, more details of which can be found here.



SUMaC is a rigorous summer program for a select group of rising high school juniors and seniors deeply interested in mathematics. The program is highly selective with an acceptance rate below 10%; there are two enrollment options: a residential program for 40 students and an online program for 64. The curriculum includes tackling challenging problems as a group, engaging in rigorous coursework, and gaining exposure to cutting-edge research areas in mathematics. 


There are two main focus areas: Abstract Algebra & Number Theory and Algebraic Topology. Students will explore fascinating concepts in Abstract Algebra, including limitations of compass-and-straightedge constructions, and symmetry analysis in structures, and delve into error-correcting codes and cryptography. The Algebraic Topology component equips students with techniques for analyzing shapes using algebraic concepts.


Location: Virtual, you can participate from anywhere in the world!

Cost: $3550. Need-based financial aid is available

Program dates: TBD for 2025, likely in June-July

Application deadline: Applications closed for 2024; Likely February 1, 2025, for the same year’s cohort

Eligibility: Rising high school juniors and seniors



RSI is a selective summer program accepting roughly 100 students annually. This six-week program immerses students in advanced STEM fields through coursework and research experiences. 


The program is divided into two distinct sections: the first week features intensive STEM classes led by leading MIT professors, followed by five weeks of hands-on research. During the program, students work under the guidance of experienced scientists and researchers on individual projects. Students can experience the entire research cycle, from familiarizing themselves with current scientific literature to designing a research plan, conducting the research, and ultimately presenting findings through written reports and presentations.


An evening lecture series throughout the summer brings students face-to-face with leading figures in mathematics — including Nobel laureates and entrepreneurs — providing a valuable opportunity for students to learn from and interact with renowned professionals. At the program's conclusion, a panel of scientists selects outstanding research papers and presentations for special recognition. 


Location: Massachusetts Institute of Technology, Cambridge, MA 

Cost: Fully funded

Program dates: June 23 – August 3, 2024

Application deadline: Closed for 2024

Eligibility: Rising high school seniors who demonstrate academic excellence (RSI expects PSAT math scores to be at least 740 and Evidence-Based Reading and Writing scores to be at least 700. ACT math scores should be at least 33 and verbal scores at least 34. International students have separate admission criteria that can be viewed here



This intensive three-week summer program at New York University's Center for Mathematical Talent offers high school students (grades 9-12) the opportunity to explore advanced mathematics beyond the typical high school curriculum. The program delves into various undergraduate-level math topics, including number theory, graph theory, knots and surfaces, and computer science. Students gain exposure to these concepts through lectures, problem-solving activities, and engaging mathematical games. 


Daily sessions explore the applications of mathematics in various scientific fields, as well as offer guidance on college admissions and life. Lectures are led by NYU’s Courant Institute of Mathematics faculty, which rank among the top five globally. Participants can attend guest lectures by prominent mathematicians, gaining insights into current research and potential career paths in mathematics. 


Location: New York University (NYU), New York.

Cost: $1,750. Limited scholarships are available.

Program dates: August 12 – 30, 2024

Application deadline: Closed for 2024

Eligibility: Current high school students in grades 9-11, 10, and 11 with a B- grade in Algebra I


The Math Modeling Camp is a week-long commuter program offered to Minnesota high school students, particularly those in the Twin Cities area, to delve into mathematical modeling. 

Through this program, students will:

  • Apply mathematical concepts to analyze real-world scenarios.

  • Hone problem-solving and analytical skills.

  • Strengthen collaborative teamwork abilities, and

  • Develop focus and attention to detail for sustained work.


To apply, you must have completed a single-variable calculus course and submit a recommendation letter from a math teacher.


Location: On-campus at the University of Minnesota. Limited slots are available for students who wish to participate remotely 

Cost: Fully funded. Students will have to arrange their own transportation to the campus. 

Program dates: June 24 – June 28, 2024 (2025 dates TBD)

Application deadline: Closed for 2024

Eligibility: Students must currently be enrolled in high school and have completed a year-long course in single variable calculus by the end of the 2023–2024 school year. High school seniors who will have graduated by July are also eligible


Canada/USA Mathcamp is a five-week program where students can delve deeply into advanced mathematical concepts, collaborate with peers, and learn from esteemed faculty. With an acceptance rate of only 5%, this highly selective program admits only 120 students every year.


Mathcamp offers courses covering various mathematical fields, including algebra, geometry, number theory, combinatorics, and topology. Participants can choose their method of instruction, such as lectures, research projects, and more. 


Location: Tacoma, Washington State (2024). The program location alternates between the U.S. and Canada annually

Cost: $5,500. Need-based financial aid is available

Program dates: June 30 – August 4, 2024. TBD for 2025

Application deadline: Closed for 2024. Applications are typically open till March

Eligibility: High-school and middle-school students aged 13-18 


The Rochester Institute of Technology (RIT) Math Summer Workshop is an intensive, fully funded program designed for mathematically advanced high school students in the U.S. This program offers students several topics to study, including:

  • Probability: Explore the concepts of chance and uncertainty.

  • Functions: Deepen your understanding of functions, the building blocks of mathematical modeling.

  • Math Biology: See how mathematics is applied to solve problems in the biological world, and

  • Beyond Traditional Solutions: Delve into the imaginative problem-solving techniques exemplified by the Sisyphus function, the "insane grocery shopper's problem," and the concept of "escaping the executioner.”


In this program, students delve into hands-on learning through participation in math labs where they engage in experiments and activities that illustrate mathematical principles, providing practical experience and reinforcing theoretical knowledge. Students are also introduced to mathematical modeling and how it is used to solve real-world problems. 


Location: RIT, New York.

Cost: Fully funded.

Program dates: July 1 - July 5, 2024.

Application deadline: There is no specific deadline. Applications will be accepted and reviewed throughout the year.

Eligibility: Students must be enrolled in a U.S. high school.


The AwesomeMath Summer Program is a rigorous online program geared toward mathematically talented middle and high school students worldwide. It aims to develop problem-solving skills and improve mathematical understanding among students, with a focus on preparing them for contests like AMC10/12, AIME, and USA(J)MO.


Renowned lecturers and Olympiad coaches teach students participating in the program. The program emphasizes both theoretical understanding and practical application in learning advanced mathematics, offering a range of problem-solving courses tailored to the age and interests of participants. Students accepted into the program can choose the session(s) they wish to participate in and the number of courses they enroll in per session. Courses include Algebra, Combinatorics, Geometry, Number Theory, and more. While there is no limit to the number of courses a student can take, organizers recommend a maximum of two.


Location: Virtual

Cost: $1,175 – $1,475, depending on the date of application/payment

Program dates: 

  • Session 1: June 10 – 28, 2024

  • Session 2: July 1 – 19, 2024

  • Session 3: July 22 – August 9, 2024

Application deadline: Closed for 2024. Applications typically close by February

Eligibility: Open to students aged 12-18. There are 4 course levels in the program; eligibility varies depending on the chosen level



One other option - the Lumiere Research Scholar Program

If you’re interested in pursuing independent research, you could also consider applying to one of the Lumiere Research Scholar Programs, selective online high school programs for students founded with researchers at Harvard and Oxford. Last year, we had over 4000 students apply for 500 spots in the program! You can find the application form here.


Also check out the Lumiere Research Inclusion Foundation, a non-profit research program for talented, low-income students. Last year, we had 150 students on full need-based financial aid!


Stephen is one of the founders of Lumiere and a Harvard College graduate. He founded Lumiere as a Ph.D. student at Harvard Business School. Lumiere is a selective research program where students work 1-1 with a research mentor to develop an independent research paper.



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