Straightforward explanations of the following big ideas are included: Number systems, Fractions, Squares and square roots, Infinity, Imaginary numbers, Primes, Perfect numbers, Fibonacci numbers, Golden rectangles, Algebra, Pascal's triangle, Logic, Euclid's division algorithm, Proof, Set theory, Calculus, Constructivity, Triangles, Curves, Topology, Dimension, Fractals, Chaos theory, The parallel postulate, Discrete geometry, Graphs, The four-colour problem, Probability, Bayes' theory, Genetics, The birthday problem, Discrete distributions, The normal curve, Codes, Correlation and regression, Group theory, Matrix algebra, Game theory, Combinatorics, Magic squares, Money mathematics, Relativity, The Riemann hypothesis and Fermat's last theorem.