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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. 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."

  4. 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 ...

  5. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures

  6. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    In the present day, the distinction between pure and applied mathematics is more a question of personal research aim of mathematicians than a division of mathematics into broad areas. [ 124 ] [ 125 ] The Mathematics Subject Classification has a section for "general applied mathematics" but does not mention "pure mathematics". [ 14 ]

  7. Riemann hypothesis - Wikipedia

    en.wikipedia.org/wiki/Riemann_hypothesis

    In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part ⁠ 1 / 2 ⁠. Many consider it to be the most important unsolved problem in pure mathematics. [1]

  8. Timeline of mathematics - Wikipedia

    en.wikipedia.org/wiki/Timeline_of_mathematics

    This is a timeline of pure and applied mathematics history.It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic ...

  9. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    The expression "statistical proof" may be used technically or colloquially in areas of pure mathematics, such as involving cryptography, chaotic series, and probabilistic number theory or analytic number theory. [23] [24] [25] It is less commonly used to refer to a mathematical proof in the branch of mathematics known as mathematical statistics.