Outline of mathematics

Mathematics is a field of study that investigates topics such as number, space, structure, and change. More on the relationship between mathematics and science can be found at Mathematics and science.


  • Definitions of mathematics – Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions, all of which are controversial.
  • Philosophy of mathematics – its aim is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives.

Mathematics isEdit

  • An academic discipline – branch of knowledge that is taught at all levels of education and researched typically at the college or university level. Disciplines are defined (in part), and recognized by the academic journals in which research is published, and the learned societies and academic departments or faculties to which their practitioners belong.
  • A formal science – branch of knowledge concerned with the properties of formal systems based on definitions and rules of inference. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the physical world.


Branches and subjectsEdit





Foundations and philosophyEdit

Mathematical logicEdit

Discrete mathematicsEdit

Applied mathematicsEdit



Influential mathematiciansEdit

See Lists of mathematicians.

Mathematical notationEdit

Classification systemsEdit

Journals and databasesEdit

  • Mathematical Reviews – journal and online database published by the American Mathematical Society (AMS) that contains brief synopses (and occasionally evaluations) of many articles in mathematics, statistics and theoretical computer science.
  • Zentralblatt MATH – service providing reviews and abstracts for articles in pure and applied mathematics, published by Springer Science+Business Media. It is a major international reviewing service which covers the entire field of mathematics. It uses the Mathematics Subject Classification codes for organizing their reviews by topic.

See alsoEdit




  1. ^ "The Definitive Glossary of Higher Mathematical Jargon — Mathemaical Structure". Math Vault. 2019-08-01. Retrieved 2019-12-09.
  2. ^ "The Definitive Glossary of Higher Mathematical Jargon — Operation". Math Vault. 2019-08-01. Retrieved 2019-12-10.


  1. ^ For a partial list of objects, see Mathematical object.
  2. ^ See Object and Abstract and concrete for further information on the philisophical foundations of objects.

External linksEdit