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. It is also the only publisher in this category that has genuinely scaled: Richard Rusczyk's thirty-year project has become the de facto standard for advanced homeschool math.

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	Genuinely the hardest mainstream homeschool math 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. Rusczyk, a Princeton graduate (1993) and former MATHCOUNTS champion turned math-education entrepreneur, built the company around a thesis that American math education for talented students was systematically failing to prepare them for the kind of open-ended, non-routine problem solving that real mathematics demands. The solution, as he built it, combined 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 launched in 2012, 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). The AoPS community forum is the largest online competition-math community, with hundreds of thousands of members.

Rusczyk also founded 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. The ecosystem is larger than any other homeschool math publisher's, and substantively different 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: a fifth-grader using Prealgebra is expected to do the kind of thinking that in other curricula might not appear until Algebra II.

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. A fourth-grader using Beast Academy solves problems that most fourth-grade programs would never assign, and does them comfortably, over time, because the progression is built to support it.

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.

A day in the life

A seventh-grader using Introduction to Algebra through self-study spends roughly 45–75 minutes daily on math. A representative session: read the next two or three pages of the chapter, which pose a series of increasingly challenging problems about, say, linear equations with multiple variables. Work through each problem before looking at the solution, typically getting some right and some wrong; read the solutions carefully to understand where the reasoning broke down. After the exposition, attempt the chapter's practice problems, typically 8–15 exercises that apply the concept in progressively harder settings. Check answers against the solutions manual and rework any misses. The student might also spend 15–20 minutes on Alcumus for adaptive drill on previously-covered topics.

A student enrolled in the AoPS Online version of the same course has a different rhythm. Weekly live class runs 60–90 minutes synchronously, with the instructor walking through problems and facilitating discussion. Before class, the student reads the assigned textbook sections and attempts the homework problems; after class, the student completes problem sets and submits them via the online platform for feedback. Total weekly time on math: roughly 6–10 hours depending on the course level.

Parent involvement is low if the student is capable and motivated. The curriculum is designed to be self-driven; the parent's job is to ensure the student is actually engaging rather than skimming, and to provide tutoring only when the student is genuinely stuck on a foundational concept. For capable students enrolled in AoPS Online, parent involvement is often near-zero during the academic portion of the day.

What they do exceptionally well

Preparation for real mathematics. Students who complete the AoPS textbook sequence from Prealgebra through Precalculus with the problem-first approach come into college or university mathematics with a level of problem-solving maturity that most curricula do not produce. The difference shows up in Calculus BC scores, in competition results (MATHCOUNTS, AMC, AIME, USAMO), in strong performance in Putnam prep, and in the kind of comfort with abstraction that engineering and physics majors need and often lack.

Beast Academy for advanced elementary learners. Beast Academy is among the most distinctive elementary math products on the market. The comic-book presentation, the cartoon monster characters, and the puzzle-heavy practice books make a curriculum that could be austere feel genuinely engaging. Advanced elementary students routinely tell parents that Beast Academy is their favorite subject, a rare endorsement for elementary math.

Textbook writing quality. Rusczyk and his co-authors are unusually good writers for a math-textbook team. 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. But the result is that parents who buy AoPS hoping it will make a struggling student excel typically see the opposite outcome. The curriculum is not remedial.

Parent math background matters. A seventh-grader working through Introduction to Algebra independently can and does 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. Families attempting to align AoPS math with Saxon-paced science or Abeka-paced language arts find the rhythms difficult to synchronize. 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 and historical information verified through the AoPS Wiki Richard Rusczyk entry, the Simple Wikipedia entry for Richard Rusczyk, and the Quanta Magazine profile of Rusczyk. Pricing cross-referenced with AoPS Academy Virtual Campus course pages. Prices and program details verified April 2026.