Science that involves the use of deductive reasoning, to study the properties of abstract concepts such as numbers, geometric figures, functions, spaces, structures, etc., and the relationships between them

  • Pure mathematics

    Mathematical discipline that deals in an abstract way with the properties of numbers and figures.

  • Applied mathematics

    Mathematical discipline that deals with the physical sciences.


  • Algebra and geometry belong to the field of pure mathematics.
  • Astronomy and mechanics belong to the field of applied mathematics.

Historical note

The term “mathematics” is derived from the Greek term mathesis (μαθησισ), meaning “the process of learning,” or from mathema (μαθημα), meaning “that which is learnt.” The Greek philosopher Plato stated that none can consider themselves fully educated until they have developed their mental capacities, that is, their ability to learn. Mathematics has provided people throughout the ages with tools that have helped them to better understand and interpret the real world and to describe it using appropriate models.

Up until the first half of the 20th century, subjects such as arithmetic, plane geometry, analytic geometry, algebra, trigonometry, statistics, differential and integral calculus were taught in separate courses and using different manuals. It is only recently (19th century) that various attempts were made to unify the discipline into an entirely deductive, formal and axiomatized science.

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