A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
G. H. Hardy, 1940

Mathematics deals with the study of quantity, structure, space and change. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Some branches of mathematics are number theory, algebra, geometry, and analysis. Number theory involves the study of integers. Algebra includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. Geometry involves the study of the properties of space that are related with distance, shape, size, and relative position of figures. Topology is concerned with the properties that are preserved through deformations, twistings, and stretchings of objects. Calculus involves the mathematical study of continuous change and mathematical analysis includes the study of the theory of calculus. Statistics is concerned with the collection, organization, analysis, interpretation, and presentation of data.

Mathematics is used in various ways in our daily life. It is used in science, engineering, business, and industry. Cryptography, the practice and study of techniques for secure communication, relies heavily on mathematics. Many cryptographic algorithms are based on the computational complexity of hard problems in number theory.