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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. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

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

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

    Some math problems have been challenging us for centuries, and while brain-busters like these hard math problems may seem impossible, someone is bound to solve ’em eventually. Well, m aybe .

  6. 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.

  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. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Another approach for defining mathematics is to use its methods. For example, an area of study is often qualified as mathematics as soon as one can prove theorems—assertions whose validity relies on a proof, that is, a purely-logical deduction. [d] [176] [failed verification]

  9. Elementary mathematics - Wikipedia

    en.wikipedia.org/wiki/Elementary_mathematics

    Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical concepts and skills, including number sense , algebra , geometry , measurement , and data analysis .