Most high school students learn math by solving problems from a textbook. But engaging with math outside of the classroom and school curriculum is the way to go, especially if you’re considering a future career in math or scientific research.
One solid way to explore math in an academic setting is by applying to an online math research program.
As a participant, you may be required to write a research paper, analyze a dataset, or work with a mentor who guides you through advanced problems. Most of the online math research programs below are super structured while others give you more independence, but all of them help you move beyond the basics. You’ll build skills in problem solving, writing, and critical thinking that are useful far beyond high school.
To help you get started, here’s a list of 15 online math research programs for high school students!
15 Online Math Research Programs for High School Students
1. Lumiere Research Scholar Program – Mathematics Track
Cost: Full financial aid is available!
Program Dates: Summer: June – August, Fall: September – December, Winter: December – February, Spring: March – June.
Application Deadline: Varying deadlines based on cohort. The regular admissions deadline for the Summer Cohort I is May 11.
Eligibility: Must be enrolled in high school with a GPA of 3.3 or higher; no prior knowledge required.
The Lumiere Research Scholar Program is a 12-week online research program where you work one-on-one with a PhD mentor from top universities like Harvard, MIT, or Stanford. You get to explore a research topic in pure math, applied math, data science, statistics, or a related field.
Your mentor guides you through each step. You’ll build a research question, study background papers, learn the methods, and write a full research paper by the end. You can also submit your work to student journals or present it at high school research conferences. Apply here.
2. Horizon Academic Research Program (HARP)
Cost: Financial aid is available!
Application Deadlines: Priority: March 23; Regular I: April 20; Regular II: May 18
Program Dates: The summer cohort starts June 16. Lab dates are flexible, but you must apply at least four 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.
Horizon offers trimester-long research programs for high school students across subject areas such as data science, machine learning and other mathematical related subjects! Horizon is one of the 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, Horizon pairs you with a professor/PhD scholar who acts as a 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.
The program also provides a letter of recommendation for each student and detailed project feedback that you can use to work on future projects.
3. Stanford University Mathematics Camp (SUMaC Online)
Cost: $3,580
Application Deadline: February 3
Dates: Session One: Online – June 16 – July 4; Session Two: Online – July 7 – July 25
Eligibility: Applicants must be rising juniors and seniors. Additionally, students should have strong math grades and a teacher recommendation.
At SUMaC, you spend three weeks exploring advanced math through daily problem sets, live discussions, and guest lectures. You take one of two courses, either Number Theory and Abstract Algebra or Algebraic Topology, both focused on building proof-based reasoning. You work closely with Stanford teaching assistants, collaborate with other students, and hear from professionals who use math in research and industry.
The schedule is intense and mirrors the pace of college work, so you need to put in time outside of live sessions. To get in, you need strong math grades, test scores, a teacher recommendation, and your performance on the SUMaC entrance exam. Join their mailing list to keep updated.
4. IMA – MathCEP Math Modeling Camp at The University of Minnesota
Cost: None
Application Deadline: May 31
Dates: June 23 – June 27
Eligibility: Must be in high school, complete a year-long single-variable calculus course, and may graduate by summer.
The Math Modeling Camp is a free summer program where high school students use math to solve real-world problems. You might model how traffic patterns affect bridge stability, use differential equations to forecast population growth, or analyze climate data to track changes in natural resources. You work in small groups, break down large questions into solvable steps, and present your results at the end of the program.
5. Awesome Math Summer Program
Cost: Various costs ranging from $1,275 to $1,575
Application Deadline: Regular Round 1 – February 20; Regular Round 2 – March 27; Late Round 1 – April 24; Late Round 2 – May 27
Dates: Session One: Online – June 9 – June 27; Session Two: Online – June 30 – July 18; Session Three: Online – July 21 – Aug 8
Eligibility: Applicants must be rising sophomores or juniors
The AwesomeMath Summer Program, run by AwesomeMath Academy, is a three-week online course that helps high school students improve their math problem-solving skills. You’ll dive deep into topics like algebra, combinatorics, geometry, and number theory, learning methods that can be directly applied to math competitions such as the AMC 10/12, AIME, and USA(J)MO.
Through hands-on practice, you’ll work through challenging problems, interact with advanced content that goes beyond your regular schoolwork, and collaborate with other math enthusiasts. The program is designed to strengthen your logical thinking, boost your ability to tackle abstract concepts, and build your skills in finding creative solutions.
6. MIT PRIMES, MIT Mathematics
Cost: Free
Application Deadline: November 18
Dates: Annual program from Jan to December
Eligibility: High school juniors and sophomores (including home-schooled) residing in the United States are eligible if they live no closer than 50 miles from Boston
PRIMES-USA is a year-long online math research program run by MIT for high school sophomores and juniors who live outside the Greater Boston area. You work on original research with guidance from MIT faculty, grad students, or local mentors. The program starts with a reading phase where you study advanced math material and write a short report to show your understanding.
Once accepted into the research phase, you meet regularly with your mentor to explore open problems, write proofs, and build your results. You submit progress reports, write a final paper, and present your work at the PRIMES Fall Conference. Many students also end up publishing their research in journals or presenting at national math conferences.
7. Stanford Pre-Collegiate University-Level Online Math
Cost: $1,600
Application Deadline: January 6
Dates: January 27 – May 16
Eligibility: Applicants must be high school students from Grade 9-12
The Stanford Pre-Collegiate University-Level Online Math program gives you a way to study advanced college-level math while still in high school. The courses are self-paced and fully online, covering subjects like multivariable calculus, linear and abstract algebra, real and complex analysis, number theory, and differential equations. Some courses also connect math with physics by focusing on the mathematical side of physical theories.
You work through structured problem sets and readings, and you can get help from instructors during optional office hours. You’ll practice writing formal proofs, working with abstract ideas, and applying math to real systems. The courses help you build skills in independent learning and logical thinking, which are useful for college and future research. Each course comes with Stanford Continuing Studies credit and an official transcript.
8. Secondary School Program, Harvard Summer School
Cost: $4,050–$14,950 + $75 application fee
Application Deadline: Feb 12 (regular); April 9 (late)
Dates: June 21–August 9
Eligibility: Applicants must graduate from high school and enter college in the next three years, and be at least 16 years old
Harvard’s Secondary School Program lets you take real college courses for credit over seven weeks. You can join online, commute, or live on campus. You’ll study alongside college students and work through full-length Harvard classes in subjects like math and physics.
The courses follow a university format with lectures, discussions, and assignments that teach you how to think through complex problems, use mathematical tools, and apply physics concepts in different settings. You’ll also get experience with academic research and independent learning. When the program ends, you’ll receive a Harvard transcript and letter grade.
9. Mathematics Camp | Illinois Institute of Technology
Cost: Not mentioned
Application Deadline: Not mentioned, however, you can email [email protected] for additional details
Dates: Session One: June 10–14
Eligibility: Applicants must be rising ninth through 12th graders and must be at least 14 years old
The Illinois Institute of Technology offers this online math program to help you explore areas of mathematics that most high school classes don’t cover. You’ll learn about topics like the infinitude of primes and how math applies to real-world problems, from web search algorithms to space imaging.
The program focuses on building your problem-solving skills, introducing you to advanced ideas, and helping you see how math works outside textbooks. You’ll also practice writing and explaining your work using proper notation and clear reasoning, the way it’s done in higher-level math.
10. Ideas in Mathematics, University of Pennsylvania Summer Pre-College
Cost: Not mentioned
Application Deadline: April 27
Dates: July 3 – August 8
Eligibility: Applicants must be rising ninth through 12th graders and must be at least 14 years old
Offered by the University of Pennsylvania through its Pre-College Online Program, Ideas in Mathematics (MATH 1700 920) is a for-credit summer course made for high school students ready to try university-level math. You’ll explore topics like logic, sets, probability, game theory, geometry, calculus, and even the philosophy of math.
Instead of just solving equations, you’ll focus on how to think about math clearly and connect it to real questions in science and society. The course pushes you to understand abstract ideas, build strong arguments, and write about math in a way that makes sense.
11. Stanford Math Circle
Cost: $495 each quarter
Application Deadline: Not mentioned, however, you can email [email protected] for additional details
Dates: April 1 – June 5
Eligibility: Applicants must be rising ninth through 12th graders and must be at least 14 years old
Offered by Stanford University, the Stanford Math Circle is a quarter-long online program open to students in grades 1 through 12, with advanced content geared toward middle and high school students. In the high school-level sessions, you will study topics like abstract algebra, number theory, combinatorics, and logic, subjects not usually covered in school.
Weekly live sessions are led by instructors with ties to Stanford. You will learn how to write proofs, think abstractly, and solve problems using methods that mirror college-level research. The program helps you build the kind of mathematical thinking that supports future work in areas like physics and computer science, where modeling and logical reasoning play a central role.
12. Online School, Art of Problem Solving: Calculus
Cost: $810 (~$33 per lesson) OR $869 with books
Application Deadline: Not mentioned, however, you can join the mailing list by clicking here
Dates: Mar 30–Oct 5 (Sun), May 27–Nov 11 (Tue), June 25–Dec 17 (Wed)
Eligibility: Applicants must be rising ninth through 12th graders and must be at least 14 years old
Offered by the Art of Problem Solving (AoPS), the AP Calculus BC Online Course is a year-long program for high school students who have already studied algebra, geometry, and trigonometry. The course covers key topics in single-variable calculus, including limits, derivatives, integrals, infinite series, polar and parametric functions, and basic differential equations.
You will work through challenging problems that require careful reasoning rather than memorization. The course focuses on how to apply calculus concepts to complex scenarios, helping you develop a way of thinking that’s useful for mathematical research and fields like physics, where calculus is used to model systems, describe motion, and understand change.
13. Aspiring Scientists Summer Internship Program (ASSIP), GMU College of Science
Cost: No cost, except the $25 application fee
Application Deadline: February 2
Dates: June 18th – Aug 8th
Eligibility: Applicants must be 15 years or older by June 18th of the application year. Note: A few research labs may be unavailable for non-US citizens
The Aspiring Scientists Summer Internship Program (ASSIP) at George Mason University offers a virtual research-focused internship for high school students interested in advanced mathematics and its applications in STEM fields. You will work directly with faculty mentors on research projects in areas such as mathematical modeling, cryptography, machine learning, data science, and computer simulations.
Throughout the program, you will gain hands-on experience using mathematical software, coding for data analysis, and applying techniques for modeling real-world systems. These skills are essential for physics research, where mathematics helps model and analyze physical phenomena.
14. Mathematics for Machine Learning Imperial College of London and Coursera
Cost: Free to enroll
Application Deadline: Rolling
Dates: Flexible starting April 8, requiring 1 month to complete at 10 hours per week.
Eligibility: All can apply as this is a beginner-level course
The Mathematics for Machine Learning Specialization offered by Imperial College London is an online, three-course series designed to build essential mathematical skills for machine learning, data science, and applied physics. You will focus on core concepts such as linear algebra and multivariate calculus, learning about vectors, matrices, and optimization techniques for analyzing high-dimensional data.
The program also includes hands-on computational work using Python and NumPy. You will implement algorithms like PageRank, train neural networks with gradient-based optimization, perform nonlinear regression, and apply principal component analysis (PCA) to reduce the complexity of large datasets like MNIST.
15. PROMYS Online Program
Cost: $2,500 (financial aid available, covering up to 100% of tuition)
Application Deadline: April 1
Dates: July 6 – August 16
Eligibility: High school students in grades 9-12, at least 14 years old, with a strong interest in mathematics; completion of Algebra II recommended.
PROMYS Online is a six-week summer program for high school students who want to explore advanced math from home. You’ll focus on number theory by attending daily lectures, solving problem sets, and joining small group seminars. You’ll work with other students and mentors to build proofs, ask questions, and think in new ways.
Topics include modular arithmetic, Diophantine equations, and other ideas not usually covered in school. The program also brings in guest speakers and ends with a final session where you can share what you’ve learned.
Image source – Imperial College London
