Art of Problem Solving

Art of Problem Solving is the math publisher, online school, and community built for the mathematically talented student, the kid who finds Saxon tedious, who asks why the algorithm works rather than what the algorithm is, and who might end up on the MATHCOUNTS team, the USAMO roster, or in a Putnam-prep class by college.

Last updated: 2026-04-24 · Every Homeschool Editorial Team

At a glance

Method	Problem-based, discovery-oriented mathematics; non-routine problem solving
Worldview	Secular
Grades	2-12 (Beast Academy grades 2-5; main AoPS textbooks grades 6-12)
Formats	Print textbooks, self-paced digital, live online classes
Cost tier	Premium (for online classes); Standard (for textbooks only)
Parent intensity	2 (online classes) / 4 (textbook self-study)
ESA-common	Varies; textbooks routinely eligible, online classes less consistently
Accredited	No
Established	2003 (original site and company)
Website	artofproblemsolving.com

Our scoreboard (1-5)

Criterion	Score	One-line reason
Academic rigor	5	Mathematically demanding, problem-based curriculum; competition-prep at serious levels
Ease of teaching	2	Textbooks demand real mathematical engagement from the parent or a capable student; online classes solve this but at premium cost
Content quality	5	Textbook exposition is unusually clear; problems are original and well-crafted
Flexibility	4	Textbooks work à la carte; online classes slot into existing homeschool plans
Value for money	3	Textbooks are fairly priced; online classes are expensive but include live expert instruction
Worldview scope	5	Fully secular; usable across every worldview
Visual/design	4	Beast Academy is genuinely excellent; main AoPS textbooks are clean, dense, functional
Support resources	5	Alcumus adaptive practice, the AoPS community forum, and the class-plus-textbook model are all strong

Who the publisher is

Art of Problem Solving was founded by Richard Rusczyk in 1993 as a book publishing effort; the company in its modern form, including the online school, community, and textbook series, dates to 2003 when Rusczyk incorporated Art of Problem Solving, Inc. The company combines three elements: a textbook series that teaches by posing problems the student works through before seeing the solution; an adaptive online practice system (Alcumus) that drills in the ways competition math demands; and an online school with live instructors.

The scope of the catalog is substantial. The main AoPS textbook sequence spans Prealgebra, Introduction to Algebra, Introduction to Geometry, Introduction to Counting & Probability, Introduction to Number Theory, Intermediate Algebra, Precalculus, and Calculus, along with subject-specific volumes for olympiad-level work. Beast Academy, the elementary line, covers grades 2-5 (with levels 1 and 6 added subsequently) in a comic-book-style illustrated format. The online school, AoPS Online, runs live instructor-led courses at each textbook level, with additional offerings for competition training (MATHCOUNTS, AMC, AIME, olympiad programs).

Related organizations include the Art of Problem Solving Initiative, a nonprofit offering competition-math training to underserved students, and AoPS Academy, a network of physical learning centers in major metropolitan areas. In our assessment, the ecosystem differs from traditional K-12 math publishing in that the company has built a community around the curriculum rather than simply selling textbooks into it.

The core pedagogy

The pedagogical move is old and somewhat risky: teach mathematics by asking the student to discover the structure before showing it. A typical AoPS textbook chapter opens with a handful of problems that draw out the concept the chapter will formalize. The student is expected to struggle, genuinely struggle, for fifteen to thirty minutes per problem, before reading the worked solution. Only after the student has engaged with the problems does the chapter present the formal concepts, definitions, and theorems, followed by exercises that apply the theory to new problems. The result is mathematically demanding.

The Beast Academy elementary line follows the same philosophy in a substantially more playful presentation. Concepts are introduced through comic-book-style illustrated guides featuring cartoon monster characters; the accompanying practice books contain genuinely hard problems that demand the same kind of non-routine thinking the upper textbooks ask for.

Signature mechanics: (1) Problem-first exposition, concepts emerge from problem-solving rather than preceding it. (2) Non-routine problems, exercises are not formulaic drill but genuine thinking problems. (3) Full solutions, textbook solutions don't just give the answer; they show the reasoning, which is where the learning lives. (4) Alcumus adaptive practice, a free online practice system that adapts difficulty to the student's demonstrated mastery. (5) Live online school, instructors teach synchronously with students who have done the textbook work before class. (6) Community forum, the AoPS community is where students discuss problems, prepare for competitions, and form an advanced-math peer group.

What they do exceptionally well

Preparation for real mathematics. In our assessment, students who complete the AoPS textbook sequence from Prealgebra through Precalculus with the problem-first approach come into college or university mathematics with strong problem-solving preparation.

Beast Academy for advanced elementary learners. In our assessment, Beast Academy is a distinctive elementary math product. The comic-book presentation, the cartoon monster characters, and the puzzle-heavy practice books make a curriculum that could be austere feel genuinely engaging.

Textbook writing quality. In our assessment, the writing is unusually good for a math-textbook series. The exposition is tight; the jokes are genuinely funny when they appear; and the solutions are explanatory rather than mechanical. Reading an AoPS solution is a small education in mathematical communication.

Free tools complement paid products. Alcumus, the adaptive practice system, is free to use. The community forum is free. The Videos section hosts hundreds of free instructional videos. Families can engage substantially with AoPS without spending on classes; the paid products (textbooks, online classes) add structured instruction but are not prerequisites for using the ecosystem.

What they do poorly

Wrong for students who aren't mathematically advanced. AoPS is designed for students who find conventional math too easy and too formulaic. Students for whom math is a struggle at grade level will find AoPS demoralizing rather than stretching. This is not a flaw in the curriculum, it is the design. The curriculum is not remedial.

Parent math background matters. A student working through Introduction to Algebra independently can get stuck on genuinely hard problems. If the parent cannot read the solution manual and reconstruct the reasoning, which requires some comfort with pre-college math, the student has limited recourse. Online classes solve this but at significant cost. Self-study AoPS is effectively a two-person endeavor for students not yet fully self-sufficient.

Online class tuition is meaningful. AoPS Online courses typically run approximately $495–$1,000 per course depending on length and level; the AoPS Academy Virtual Campus Honors Math 7 course runs approximately $945 for a full academic year as of April 2026. For a family taking two or three AoPS Online courses across the high school years, the cumulative cost is substantial. Textbook self-study is far cheaper but demands more from the student and parent.

Pace mismatch with other homeschool subjects. A student running AoPS at the intended pace will cover math more slowly than peers using conventional curricula, the program is deeper, not faster. This is a minor issue but a real one in practice.

Who it fits / who it doesn't

• Pick Art of Problem Solving if: you have a mathematically talented child who finds conventional math boring or too easy; you want genuine preparation for competition math or top-tier STEM college work; you are comfortable with problem-based pedagogy and willing to let the student struggle; you have either capable-parent math support or budget for online classes; you value depth over breadth.

• Skip Art of Problem Solving if: your child struggles with math at grade level and needs remediation or support; you want a scripted, worked-example-first approach; you need a fast-paced curriculum that moves through many topics; you are budget-constrained and cannot afford online classes if the textbooks prove too demanding; you need a Christian-framed or classical-framed math spine.

Cost honest assessment

Textbook prices as of April 2026: Prealgebra textbook and solutions manual bundle runs approximately $60–$75 total; Introduction to Algebra bundle similar; higher-level textbooks (Intermediate Algebra, Precalculus, Calculus) run $65–$85 per bundle. Beast Academy grade-level bundles (guide plus practice for each half-level, e.g., 3A and 3B) run approximately $25–$40 each, or approximately $100–$160 for a full grade level.

Online class pricing: AoPS Online self-paced courses run approximately $500–$550; live-instructor courses run approximately $495–$1,000 depending on course length. Full-year courses like the AoPS Academy Virtual Campus Honors Math 7 run approximately $945 for the academic year.

Compared to Saxon Math (roughly $100–$150 per grade level), Singapore Math (roughly $80–$150 per grade level), and Math-U-See (roughly $120–$200 per level with manipulatives), AoPS textbooks are competitively priced. The cost premium comes with online classes, a family going textbook-only can spend $150–$250 per year on AoPS math; a family enrolling in two or three online classes spends $1,500–$3,000+.

A realistic advanced-math household annual budget: $150–$400 for textbook-only self-study; $1,200–$3,000 for a child in one or two AoPS Online classes; $3,000–$5,000 for a high schooler taking multiple AoPS Online courses with competition prep.

ESA eligibility notes

AoPS textbooks are routinely eligible on state ESA marketplaces because they are secular curriculum. Arizona's ClassWallet, Florida's Step Up For Students MyScholarShop, and several other state marketplaces have included AoPS textbook SKUs in their catalogs. Beast Academy materials typically qualify on similar marketplaces. Online classes are less consistently eligible, some state programs treat online academy courses differently from curriculum materials, and the ESA reimbursement workflow for a synchronous online class is structurally different from reimbursement for a textbook. Families should verify both the specific product and their state's treatment of online coursework before committing ESA funds.

Alternatives

• Singapore Math (Dimensions Math), a family would pick Singapore over AoPS if they want a rigorous but more conventionally-paced math program with bar-model visualizations and clear teacher support, accessible to a wider range of students.
• Saxon Math, a family would pick Saxon over AoPS if they want incremental spiral review with heavy drill, suitable for students who need repetition and consolidation rather than conceptual challenge.
• Math-U-See, a family would pick Math-U-See over AoPS if they want a manipulative-heavy, video-taught mastery-based program for a student who benefits from concrete visualization before abstraction.

How we verified this

Our editorial team reviewed the Art of Problem Solving catalog and store at artofproblemsolving.com, the AoPS Online school pages, Beast Academy product pages, and individual textbook listings for Prealgebra and Introduction to Algebra. Founding information verified through the AoPS Wiki Richard Rusczyk entry. Pricing cross-referenced with AoPS Academy Virtual Campus course pages. Prices and program details verified April 2026.