Art of Problem Solving

by Art of Problem Solving (AoPS) (website )

A highly rigorous, discovery-based math curriculum designed for advanced students who enjoy complex problem-solving and logical challenges.

Best Fit For

Students who are 'math-gifted,' enjoy puzzles, and possess the persistence to work through difficult problems without immediate answers.

Not Recommended For

Students who need a spiral review approach, those who prefer clear step-by-step demonstrations before practicing, or families looking for a standard grade-level pace.

What Reviewers Say

Reviewers overwhelmingly characterize Art of Problem Solving (AoPS) as the 'gold standard' for mathematically gifted and motivated students. Sources like Cathy Duffy and the Well-Trained Mind forums emphasize its unique 'discovery-based' approach, which requires students to tackle difficult problems before being taught the underlying formula. While this builds deep conceptual understanding and resilience, it is a significant trade-off: many parents report it can be intensely frustrating for children who prefer direct instruction or those who struggle with math anxiety. Beast Academy, the elementary wing, is praised for its engaging graphic novel format, yet reviewers caution that it is significantly more advanced than standard grade-level math. The online community and 'Alcumus' practice tool are highly regarded supplements. Overall, it is a specialist tool that excels for high-performers but is often too demanding for the average or reluctant learner.

How It Works

For elementary students using Beast Academy, the child spends about 45 minutes a day reading a colorful graphic novel guide followed by solving intense puzzles in a practice book. In the middle and high school levels, students work through a textbook where they are presented with a difficult problem first—forcing them to struggle and 'discover' the math—before reading the provided explanation to see the underlying concept. Parents primarily act as facilitators who provide encouragement during moments of frustration rather than lecturers who explain the steps beforehand. A typical week consists of daily deep-dive sessions into a few complex problems rather than a high volume of quick drills, often concluding with a set of extremely challenging 'Challenge Problems' that may take several sittings to complete.

Switching to This?

Parents should use the free 'Are You Ready?' and 'Do You Know?' diagnostic tests on the AoPS website, as the curriculum's difficulty far exceeds standard grade levels. A common rule of thumb in the community is to place students based on these test results even if it means using a book labeled one or two grades 'behind' their current school level. Families can start at any time of year, but it is critical to begin at the start of a specific level rather than jumping into the middle of a book, as the logic builds sequentially. If you are switching from a traditional program like Saxon or public school math, expect a month-long adjustment period where your child may need emotional support to handle the 'discovery' method's focus on productive struggle.

Curriculum Details

Price
$15 - $830

Individual textbooks/solutions range from $45-70 (4500-7000 cents). Beast Academy Online subscriptions are ~$15/month or $108/year. Online instructor-led courses range from $450 to over $800 per course.

Grades
1 - 12
Available As
Digital Print Workbook Video Online Platform
Coverage
Single subject
Subjects
Math

Pacing
Some flexibility
Parent Time
5-45 min/day
Parent Involvement
Moderate
Student Independence
Fully independent

Academic Level
Advanced
Worldview
Secular

Videos

ART OF PROBLEM SOLVING (AOPS): My Honest Thoughts/Review

by citytutoringmath

Reviews We Consulted

Highly recommends the program for gifted, "math-y" students who thrive on discovery-based learning, but notes the unconventional sequence of solving problems before instruction may overwhelm average learners.

"AoPS math courses should be fantastic for avid math students who are eager to learn and go deeper, but they also offer excellent and thorough instruction for the average student. This strategy very much reflects the title of the series, the Art of Problem Solving—students are focused on developing problem-solving skills as well as accuracy."

A critical perspective from a math professional who argues the curriculum's focus on "clever tricks" and extreme difficulty can discourage even very strong students by neglecting foundational practice.

"I feel like students don't get a chance to practice the concepts and the mechanics before being thrown curve-balls left and right. It may be good for the top 1-3% of students but even great students who are typically in the top 5-10% I see getting discouraged by this curriculum."

Describes the program as grueling and time-consuming but credits it with teaching students how to handle failure and "puzzle out" difficult concepts independently.

"It is time-consuming, thorough, difficult, challenging, hard, stimulating, grueling, exciting, and tough. Get the picture? ... I also chose it for one child because the difficult problems enabled my son to face failure and learn to handle getting things wrong."

Praises the deep engagement of the online courses for gifted students but warns it would be a "disaster" for perfectionists or those who do not enjoy the struggle of getting answers wrong.

"If a student that was great in math, but didn’t enjoy math and enjoy struggling with math to get the correct answer - this course would be a disaster. A perfectionist that always has to be 100% 'right' is not going to fare well, because it is really close to impossible to get 100% on the written problems."

Highlights the program's exceptional scope and difficulty, noting that its introductory courses often cover material found in traditional advanced-level high school textbooks.

"AoPS is a discovery based curriculum for students who are good at, and interested in, math. ... In scope and difficulty, AoPS goes way beyond other curricula. The intro to algebra text covers a lot of material traditionally taught in algebra 2."

An engineer-led review that celebrates the "WOW" factor of the discovery method for kids who love a challenge, contrasting its problem-solving focus with more procedural math programs.

"I recommend this program to anyone with mathy kids who LOVE a good challenge. They are those who actually giggle when they struggle for a while first, and then discover the solution. Just giggles and smiles at her achievement."

Updated: March 2026

How This Compares

Compared to Saxon Math, which uses a 'spiral' method of constant repetition and memorized procedures, AoPS focuses on 'mastery' and expects students to derive their own formulas through logic. When weighed against Singapore Math, which is also conceptually rigorous, AoPS is less structured; Singapore provides clear, step-by-step visual models for problem-solving, whereas AoPS intentionally leaves the path to the answer unguided to develop mathematical intuition. Parents choosing between AoPS and standard math curricula often find that AoPS introduces proof-based reasoning and competition-level topics years earlier, making it ideal for mathematically gifted students who find grade-level textbooks too repetitive or unchallenging.