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  2. Pure mathematics - Wikipedia

    en.wikipedia.org/wiki/Pure_mathematics

    Pure mathematics studies the properties and structure of abstract objects, [1] such as the E8 group, in group theory. This may be done without focusing on concrete applications of the concepts in the physical world. Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may ...

  3. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

  4. Number theory - Wikipedia

    en.wikipedia.org/wiki/Number_theory

    Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."

  5. Lists of mathematics topics - Wikipedia

    en.wikipedia.org/wiki/Lists_of_mathematics_topics

    The branch of mathematics deals with the properties and relationships of numbers, especially positive integers. Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory ...

  6. Philosophy of mathematics - Wikipedia

    en.wikipedia.org/wiki/Philosophy_of_mathematics

    In the 19th century, the internal development of geometry (pure mathematics) led to definition and study of non-Euclidean geometries, spaces of dimension higher than three and manifolds. At this time, these concepts seemed totally disconnected from the physical reality, but at the beginning of the 20th century, Albert Einstein developed the ...

  7. 10 Hard Math Problems That Even the Smartest People in the ...

    www.aol.com/10-hard-math-problems-even-150000090...

    The Conjecture lives in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. It looks like a simple, innocuous question, but ...

  8. Definitions of mathematics - Wikipedia

    en.wikipedia.org/wiki/Definitions_of_mathematics

    Rather than characterize mathematics by deductive logic, intuitionism views mathematics as primarily about the construction of ideas in the mind: [9] The only possible foundation of mathematics must be sought in this construction under the obligation carefully to watch which constructions intuition allows and which not. [12] L. E. J. Brouwer 1907

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