They can arise from the world around us, from the pursuit of science, or
from the inner workings of the human mind. Different kinds of patterns give rise to
different branches of mathematics. For example:
Arithmetic and number theory study the patterns of number and counting.

Geometry studies the 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.

Fractal geometry studies the self-similarity found in the natural world.