mathematics
Sign in to saveMathematics is a field of study that discovers and organizes methods, theories, and theorems that are developed and proved either in response to the needs of empirical sciences or the needs of mathematics itself. There are many areas of mathematics, including number theory (the study of integers and arithmetic functions), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of approximating continuous changes), and set theory (presently used as a foundation for all mathematics).
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Mathematics is a field that discovers and organizes methods, theories, and theorems developed to address both the practical needs of science and questions that arise within mathematics itself. It encompasses diverse areas—such as number theory, algebra, geometry, analysis, and set theory—that together provide the foundations and tools for understanding everything from basic arithmetic to the most abstract mathematical structures.
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Wikidata facts
- Instance of
- academic major
- Subclass of
- natural science
- Part of
- exact science
- Has part
- arithmetic
- Image
- Mathematics.png
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Article
40 sectionsContents
- Areas of mathematics
- Number theory
- Geometry
- Algebra
- Calculus and analysis
- Discrete mathematics
- Mathematical logic and set theory
- Computational mathematics
- History
- Etymology
- Ancient
- Medieval and later
- Symbolic notation and terminology
- Relationship with sciences
- Pure and applied mathematics
- Unreasonable effectiveness
- Specific sciences
- Physics
- Computing
- Statistics and other decision sciences
- Biology and chemistry
- Earth sciences
- Social sciences
- Philosophy
- Reality
- Proposed definitions
- Rigor
- Training and practice
- Education
- Psychology (aesthetic, creativity and intuition)
- Cultural impact
- Artistic expression
- Popularization
- Awards and prize problems
- See also
- Notes
- References
- Citations
- Other sources
- Further reading
Mathematics is a field of study that discovers and organizes methods, theories, and theorems that are developed and proved either in response to the needs of empirical sciences or the needs of mathematics itself. There are many areas of mathematics, including number theory (the study of integers and arithmetic functions), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of approximating continuous changes), and set theory (presently used as a foundation for all mathematics).
Mathematics involves the description and manipulation of abstract objects that are either abstractions from nature or purely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove the properties of objects through proofs, which consist of a succession of applications of deductive rules to already established results. These results, called theorems, include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of the theory under consideration.