What does pure mathematics mean?

Definitions for pure mathematics
pure math·e·mat·ics

This dictionary definitions page includes all the possible meanings, example usage and translations of the word pure mathematics.

Princeton's WordNet

  1. pure mathematicsnoun

    the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness

Wiktionary

  1. pure mathematicsnoun

    Mathematics which is done for its own sake rather than being motivated by other sciences.

Wikipedia

  1. Pure mathematics

    Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but pure mathematicians are not primarily motivated by such applications. Instead, the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles. While pure mathematics has existed as an activity since at least Ancient Greece, the concept was elaborated upon around the year 1900, after the introduction of theories with counter-intuitive properties (such as non-Euclidean geometries and Cantor's theory of infinite sets), and the discovery of apparent paradoxes (such as continuous functions that are nowhere differentiable, and Russell's paradox). This introduced the need to renew the concept of mathematical rigor and rewrite all mathematics accordingly, with a systematic use of axiomatic methods. This led many mathematicians to focus on mathematics for its own sake, that is, pure mathematics. Nevertheless, almost all mathematical theories remained motivated by problems coming from the real world or from less abstract mathematical theories. Also, many mathematical theories, which had seemed to be totally pure mathematics, were eventually used in applied areas, mainly physics and computer science. A famous early example is Isaac Newton's demonstration that his law of universal gravitation implied that planets move in orbits that are conic sections, geometrical curves that had been studied in antiquity by Apollonius. Another example is the problem of factoring large integers, which is the basis of the RSA cryptosystem, widely used to secure internet communications.It follows that, presently, the distinction between pure and applied mathematics is more a philosophical point of view or a mathematician's preference rather than a rigid subdivision of mathematics. In particular, it is not uncommon that some members of a department of applied mathematics describe themselves as pure mathematicians.

ChatGPT

  1. pure mathematics

    Pure mathematics is a branch of mathematics that deals with abstract concepts and principles, without any concern for their direct application to the real world. It is often studied for its intrinsic beauty and intellectual challenge, rather than for practical purposes. This includes areas such as algebra, geometry, calculus, number theory, topology, set theory, and so on. The findings of pure mathematics may often find utility in applied mathematics and other scientific fields, but this is not its primary goal.

Wikidata

  1. Pure mathematics

    Broadly speaking, pure mathematics is mathematics which studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of navigation, astronomy, physics, engineering, and so on. Another insightful view put forth is that pure mathematics is not necessarily applied mathematics: it is possible to study abstract entities with respect to their intrinsic nature, and not be concerned with how they manifest in the real world. Even though the pure and applied viewpoints are distinct philosophical positions, in practice there is much overlap in the activity of pure and applied mathematicians. To develop accurate models for describing the real world, many applied mathematicians draw on tools and techniques which are often considered to be "pure" mathematics. On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research.

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Numerology

  1. Chaldean Numerology

    The numerical value of pure mathematics in Chaldean Numerology is: 2

  2. Pythagorean Numerology

    The numerical value of pure mathematics in Pythagorean Numerology is: 1


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"pure mathematics." Definitions.net. STANDS4 LLC, 2024. Web. 14 Jun 2024. <https://www.definitions.net/definition/pure+mathematics>.

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