Mathematics is the science of patterns. Different kind of patterns give rise to different branches of mathematics. For example:
- Arithmetic and number theory study patterns of number and counting
- Geometry studies patterns of shape
- Calculus allows us to handle patterns of motion
- Logic studies patterns of reasoning
- Probability theory deals with patterns of chance
- Topology studies patterns of closeness and position
Mathematics, the science of patterns, is a way of looking at the world. The study of mathematics is ultimately a study of humanity itself. For none of the entities that form the substrate of mathematics exist in the physical world.; the numbers, the points, the lines and planes, the surfaces, the geometric figures, the functions and so forth are pure abstractions that exist only in the humanity's collective mind.
There is scarcely any aspect of our life that is not affected, to a greater or lesser extent, by mathematics, for abstract patterns are the very essence of thought, of comunication, of computation, of society, and of life itself.