Games
43Play to learn: every game is tied to a library topic.
Arithmetic and number theory8
Sieve SprintBeat the number grid with the sieve of Eratosthenes: count primes, factorize, gcd–lcm and divisibility rules across 8 rounds.RSA DecoderSpin the cipher wheel: modular arithmetic, inverses and Fermat's little theorem power a tiny RSA lock you crack digit by digit.Goldbach GuildMine even numbers into prime pairs, assay the representation count, and follow the circle method from Vinogradov to Chen — the conjecture is still open.Fraction KitchenSlice cakes into fractions: simplify, compare, add over a common denominator, convert to decimals and scale a recipe — seven rounds in the kitchen.Fraction MarketCompare unit prices, match equivalent price tags, follow a number line, and build an exact basket in seven market challenges.Fraction BridgeCross a number-line bridge by locating, ordering and matching fractions, choosing common denominators, finding rational midpoints and completing a four-station relay.Decimal BakeryRide the digit conveyor through seven decimal challenges: place value, rounding, multiplication, division and comparison.Percent LabFill a hundred-grid, measure proportional parts, compare real savings and reverse tax calculations in seven percent challenges.
Algebra6
Function RainbowTune the parameters of a function so its graph catches every star and dodges every bomb.🌊 Exp-Log OceanSail a ship over waves of exponents and logarithms. 7 rounds: exponential equations, logarithm readings, growth curves, asymptotes, log rules, compound interest and a ciphered map.Matrix FlipWatch a 2×2 matrix stretch, rotate and flip the plane — then predict determinants, inverses, eigenvalues and products.Pi ScaleEvery linear equation is a balance scale. Solve, evaluate, transform and translate word problems while keeping both pans level.Complex VectorSteer arrows on the complex plane: quadrants, moduli, vector sums, conjugate mirrors and 90° turns by i.Cayley TableRead and complete multiplication tables of finite groups: products, identity, inverses, orders, subgroups and generators.
Geometry5
Conic CutterTilt the slicing plane and shift the eccentricity to cut ellipses, parabolas and hyperbolas out of a cone.Trig CannonAim a cannon by firing angle θ and muzzle speed v₀ using the range formula R = v₀²·sin(2θ)/g. 7 rounds: maximum range, complementary angles, hitting a flag by angle or by speed, special trig values, reading a sine wave, and a boss fight against an elevated target.Poincaré NavigatorNavigate a disk where straight lines bow toward the rim, parallels multiply without end, and the boundary lies at infinity. Seven rounds of real hyperbolic geometry: geodesics, triangle angle sums, the metric d(0,z) = 2·artanh|z| and horocycles.🗼 Thales TowerMeasure like Thales of Miletus: tower height from its shadow, Pythagorean triples, missing sides, parallel-line proportions and the width of a river — 7 rounds of similar-triangle surveying.Chord SniperSnipe every quantity of the circle: chords, arcs, inscribed angles, tangents and cyclic quadrilaterals across 7 rounds.
Topology6
Metric GaugeLopsided balls, sequences that refuse to converge, sets of diameter 1 — explore metric spaces across 8 rounds.🍩 Topo FoldStretch, squish and fold rubber shapes: decide which spaces are the same to a topologist, count $V - E + F$, and shrink loops to find the fundamental group.Unit Ball GalleryExplore norm-ball geometry, containment, boundaries, and the topology induced by distance.Convergence ClinicDiagnose metric convergence through sequence behavior, epsilon-balls, equivalent finite-dimensional norms, uniqueness of limits, and completeness.Cauchy QuestTrack shrinking tails, use the ε-diameter test, and uncover the missing limit that makes the rationals incomplete.Completing the SpaceBuild points from Cauchy sequences, then use contractions to find fixed points and certify error bounds.
Analysis10
Tangent HunterRead the sign of f′ and place tangent lines to hunt down extrema before time runs out.Fourier WavesSynthesize periodic signals out of pure sines: tune Fourier coefficients, read a spectrum like a fingerprint, and feel the Gibbs overshoot — from a single sine to a square-wave boss.Sequence TightropeParachute the terms of a sequence onto the limit rope: compute lim (an+b)/(cn+d), sum infinite geometric series, spot the divergent sequence and find the smallest N for an ε-band.⏪ Antiderivative RewindRewind differentiation: given f, pick the F whose slope is f. Power, exponential, logarithm, trig and linear-substitution antiderivatives across 8 rounds, ending with a boss that must also hit F(0) = c.Area UnderSlice regions into rectangles, measure the area under lines and parabolas, watch integrals go negative, and hunt the bound that hits the target area.Hessian PeakRead contour maps of f(x, y): partial slopes, the gradient’s steepest-ascent arrow, critical points, the Hessian sign test and directional derivatives — then plant your flag on the summit.Integral OrbitRide the cumulative trail using the Fundamental Theorem, recover missing endpoints, compare signed change with total area, and integrate rates with jumps.Riemann RushRace through left, right, and midpoint sums, refine a partition with a slider, and compare each numerical estimate with the exact integral.Integral PercentFollow rates along a timeline to measure flow, distance and signed change, read cumulative data, and work backward from a total.Volume VaultRotate a profile around the x-axis, build a solid from disk cross-sections, and use exact integrals and scaling laws to unlock its volume.
Differential equations and dynamical systems1
Combinatorics and discrete mathematics4
Pigeon ParadeMore pigeons than holes — somebody must share. Spot the forced collision.Chroma MapColor regions so neighbors never match — using as few colors as possible.Euler WandererWalk every road exactly once! Learn Euler's degree-parity rule on random maps, then solve the 7 bridges of Königsberg — the 1736 problem that founded graph theory.Party ArrangePlan the perfect party: seat guests in a row, pick a committee, share identical candies — every round is a counting-rule puzzle.