Math programs and competitions for high school students.
Contests, modeling challenges and summer math programs, from your first AMC to the olympiad track.
30 opportunities, 14 free · Links and programs checked October 18, 2026 · By Lokesh Pampatti, founder of Clarity Prep
30 of 30 shown
ProgramFreePittsburgh, PA
Carnegie Mellon University AI Scholars
Carnegie Mellon University
Intro to AI and machine learning for rising seniors from underrepresented backgrounds, at no cost.
Our take: The free, selective CMU program. Not to be confused with the paid CMU Pre-College tracks.
CompetitionFreeOnline
Breakthrough Junior Challenge
Breakthrough Prize Foundation
Global video competition for ages 13–18.
Our take: A three-minute video explaining a scientific idea. The winner gets a $250,000 scholarship; finalists are a real distinction. Thousands enter, so make it genuinely good.
ScholarshipFreeOnline
Davidson Fellows Scholarship
Davidson Institute
Scholarships for students 18 and under who have completed a significant piece of work in their field.
Our take: $10,000 to $50,000 for a significant completed project. Only worth it if you have graduate-level work; if you do, few things read better.
ProgramFreeOnline
Distance Math Program
Georgia Tech School of Mathematics
Georgia Tech mathematics courses delivered to Georgia high schools for students who have exhausted their school's math.
Our take: For Georgia students who have finished AP Calculus BC: Georgia Tech math (Calc III, linear algebra, and beyond) through dual enrollment. A rare and specific signal.
CompetitionFreeRegional symposia → national
Junior Science and Humanities Symposium
JSHS / Department of Defense
Research presentation competition with regional symposia in every state and a national finale.
Our take: Present original research as a talk, not a poster. Fewer entrants than the science fair circuit, real scholarship money.
CompetitionFreeOnline
MathWorks Math Modeling (M3) Challenge
SIAM
Teams of 3–5 juniors and seniors solve an open modeling problem in 14 hours.
Our take: Free, team-based, and the finalists win real scholarship money. Applied math, not olympiad math; good for engineers.
ProgramFreeCambridge, MA
MITES Summer
MIT
Rigorous STEM coursework and projects at MIT for rising seniors. MITES Semester (online) and MITES Saturdays (Boston area) are the sibling tracks.
Our take: One of the few free MIT-run programs. For students from underrepresented or under-resourced backgrounds; if that is you, apply.
Research & internshipsFreeBoston area (PRIMES) or remote nationwide (PRIMES-USA)
PRIMES and PRIMES-USA
MIT Department of Mathematics
Free year-long math and CS research program for high school students.
Our take: Year-long research with an MIT mentor. PRIMES-USA is the remote track for juniors anywhere in the country; the entrance problem set is the application.
CompetitionFreeOnline
Regeneron Science Talent Search
Society for Science
Nationwide competition for original research by high school seniors; 300 scholars, 40 finalists.
Our take: The oldest and most prestigious research competition for seniors. You need completed original research by November of senior year, which means starting as a sophomore or junior.
Research & internshipsFreeCambridge, MA
Center for Excellence in Education / MIT Research Science Institute (RSI)
Center for Excellence in Education / MIT
Six weeks of original STEM research with MIT and Broad Institute mentors, entirely free.
Our take: The most selective summer program in the country, about 100 students worldwide. If you have research already, apply; if not, this is not the place to start.
Research & internshipsFreeStony Brook, NY
Simons Summer Research Program
Stony Brook University
Hands-on research with Stony Brook faculty for rising seniors, with a stipend.
Our take: Real lab, real stipend, a poster at the end. You need a teacher nomination; ask in December.
ProgramFreePittsburgh, PA
Carnegie Mellon University Summer Academy for Math and Science (SAMS)
Carnegie Mellon University
College-level math and science coursework with CMU faculty, plus a project. Fully funded.
Our take: Free and genuinely rigorous. Built for students without easy access to advanced STEM; the application asks you to show that.
CompetitionFreeOnline
USA Computing Olympiad
USACO
Algorithmic programming contests in four divisions, open to anyone.
Our take: Free, online, self-paced, and Gold or Platinum division is one of the clearest CS signals there is. Start in Bronze as a freshman.
CompetitionUnder $1kAt your school
AMC 10/12 → AIME → USA(J)MO
Mathematical Association of America
The standard American math competition sequence. High scores on the AMC qualify you for AIME, then the olympiad.
Our take: Taking the AMC is not the signal. Qualifying for AIME is, and USAMO is elite. If you are serious about math this is the ladder everyone climbs.
CompetitionUnder $1kAt your school
American Association of Physics Teachers F=ma → USAPhO
American Association of Physics Teachers
The U.S. physics olympiad sequence.
Our take: Qualifying for USAPhO from F=ma is the meaningful step. Needs a teacher willing to proctor.
CompetitionUnder $1kRegional → state → international
Regeneron ISEF (via your regional fair)
Society for Science
The world's largest pre-college science competition, fed by affiliated fairs.
Our take: You get there by winning your regional and state fair. Even a state-level award is a real line; ISEF itself is a big one.
Research & internshipsCost variesNew Mexico, Colorado, Indiana, and others
Summer Science Program (SSP)
Summer Science Program
Immersive team research program with a 60-year track record.
Our take: Need-blind admission and a sliding-scale fee down to zero. Astrophysics, biochemistry, genomics, or synthetic chemistry, in a team, at full intensity.
Program$1k–5kUC Davis, Irvine, San Diego, Santa Cruz, LA
COSMOS — California State Summer School for Mathematics and Science
University of California
Four-week residential STEM program across UC campuses, with clusters in specific topics.
Our take: For California students this is the one to get. Out-of-state applicants are admitted at a higher cost and lower odds.
Program$1k–5kEast Lansing, MI
High School Honors Science, Math and Engineering Program
Michigan State University
Full-time research placement for rising seniors, with a final presentation.
Our take: Seven weeks in a real lab with an MSU researcher, small cohort, long track record. Underrated.
ProgramOver $5kRotating campus
Canada/USA Mathcamp
Mathematics Foundation of America
Five weeks of advanced mathematics with a flexible schedule and a famously close community.
Our take: Choose-your-own-classes format, college and graduate-level topics. Strong need-based aid, including full rides.
ProgramOver $5kBoston, MA
Boston University PROMYS
Boston University
Six weeks of immersive mathematics built around a daily problem set and exploration, not lectures.
Our take: Number theory taught by discovery; alumni go back as counselors for years. Full aid is real, so cost should not stop you.
ProgramOver $5kOhio and Indiana campuses
Ross Mathematics Program
Ross Program
Intensive number-theory program in the PROMYS tradition (PROMYS grew out of Ross). Aid available.
Our take: "Think deeply about simple things." The admissions problems are the point; spend real time on them.
ProgramOver $5kStanford, CA + online
Stanford University Mathematics Camp (SUMaC)
Stanford Pre-Collegiate Studies
Proof-based mathematics for students who want to see what research-level math looks like.
Our take: The one Stanford summer program that is actually selective. Abstract algebra or topology at real depth.
CompetitionFreeRegional → national finals in Washington, DC
National Science Bowl
U.S. Department of Energy
Team quiz competition for high school students.
Our take: Fast-buzzer science trivia at a high level. Winning your regional is the achievement; nationals is all-expenses-paid.
CompetitionUnder $1kOnline
COMAP HiMCM
COMAP
Teams write a modeling paper on a real-world problem over several days.
Our take: The high school version of the college modeling contest. Outstanding designations are rare and mean something.
ProgramCost variesPartner campuses + online
AI4ALL Summer Programs
AI4ALL (university partners)
AI education programs for underrepresented students, hosted by universities around the country.
Our take: Quality depends on the host campus; several are free. Read the specific site before assuming.
Program$1k–5kOnline + campus sessions
AwesomeMath Summer Program
AwesomeMath
Olympiad-style problem solving with an admission test. Multiple sessions.
Our take: Competition-math training, not research math. Right if AIME or USAMO is the goal.
Program$1k–5kAnn Arbor, MI
Michigan Math and Science Scholars
University of Michigan
Intensive courses in math and science taught by university faculty.
Our take: Two-week deep dives taught by Michigan faculty. Reasonable cost for the category; scholarships exist.
ProgramOver $5kAmherst, MA
Hampshire College Summer Studies in Mathematics
Hampshire College
Six weeks of collaborative, proof-based mathematics well past the standard curriculum.
Our take: Less known than PROMYS or Ross, similarly serious. Good option if those say no.
ProgramOver $5kBryn Mawr, PA
MathILy / MathILy-Er
MathILy
Discovery-based advanced mathematics in "braided" strands of topics.
Our take: Serious and playful at once. MathILy-Er is the on-ramp if you are newer to proofs.
“Helps an application” is our read on how much an admissions reader is likely to weigh it: Strong means getting in or placing is a real achievement, Solid means it shows real interest and effort, and Light usually means most students who apply and pay can attend. It’s our opinion, not a ranking from any college, and a light one can still be a great summer.
Want a list picked for you?
Clarity Prep members get opportunities matched to their grade, interests and state in the app, plus a mentor who helps them decide what’s worth applying to and checks in every week until the applications are in.
Free tools: GPA calculator · chances calculator · college acceptance rates · essay grader
Every program here is real and links to its own official site. Dates, costs and rules change every year, so check the official page before you apply. Deadlines are shown as the months they usually close. Spot something out of date? Email sessions@joinclarityprep.com.