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Mathematics is the science of space, number and quantity.

The traditional division of mathematics into sub-disciplines is as follows:

  • Arithmetic - The study of whole numbers and fractions.
Sample theorem: If you subtract an odd number from an even number you get an odd number.
  • Geometry - The study of figures in space; points, lines, curves and three-dimensional objects.
Sample theorem: The angles in a triangle on a flat surface add up to 180 degrees.
  • Algebra - The use of abstract symbols to represent mathematical objects (numbers, lines, matrices, transformations), and the study of the rules for combining those symbols.
Sample theorem: For any two numbers [math]\displaystyle{ a }[/math] and [math]\displaystyle{ b }[/math], [math]\displaystyle{ (a + b) * (a - b)\,=\,a^2\,-\,b^2 }[/math].
Sample theorem: The harmonic series is divergent; it increases without limit.

Modern mathematics of course contains much more than this; there is set theory, complex analysis, statistics, topology, and lots more. The area of mathematics that is concerned with numbers - though not just prime numbers - is called number theory.

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