Out of 15,285 mapped topics, these unlock the most — ranked by how much of human knowledge depends on them, at every level from preschool to the research frontier.
What a child learns before school — and how far it reaches.
1 Equal Groups 2 Halves and Quarters 3 Listening Comprehension 4 Counting to 20 5 Recognizing Basic 2D Shapes 6 Vocabulary BuildingThe grade-school ideas the rest of the map stands on.
7 Place Value for Whole Numbers 8 Multiplying Fractions 9 Area of Rectangles 10 Introduction to Fractions 11 Fractions of a Set 12 Equivalent Fractions 13 Multi-Digit Addition 14 Mean, Median, and Mode 15 Fractions: Halves, Thirds, and Fourths 16 Multiplication Facts Within 100Where abstraction starts paying compound interest.
17 Ratios 18 Exponential Functions and Graphs 19 Multiplying Integers 20 Exponent Rules — Product, Power, and Quotient 21 Variable Expressions 22 Introduction to Square Roots 23 Introduction to Exponents 24 Solving Multi-Step Equations 25 Adding Integers 26 Graphing Linear EquationsThe undergraduate workhorses that open the most doors.
27 Partial Derivatives: Definition and Computation 28 Logarithms Introduction 29 Derivative as Slope of Tangent Line 30 Function Notation Review 31 Intermolecular Forces 32 Introduction to Differential Equations 33 Vectors in R^n 34 Probability Axioms 35 Introduction to Organic Chemistry 36 Trigonometric Ratios Review 37 Covalent Bonding 38 Newton's Second Law: F = ma 39 Set Theory Fundamentals 40 Separable Equations (Intro)Past the textbook frontier, reach narrows but deepens.
41 Quantum Numbers 42 Emission and Absorption Spectra 43 Separation of Variables for Partial Differential Equations 44 Hydrogen Bonding: Energetics and Thermodynamics 45 The Wave Equation and Vibrating Strings 46 Bohr Model of the Hydrogen Atom 47 The One-Dimensional Wave Equation 48 Blackbody Radiation and Planck's Law 49 Solving the Schrödinger Equation for Hydrogen Atom 50 Maxwell's Equations