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  2. 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.

  3. Wiles's proof of Fermat's Last Theorem - Wikipedia

    en.wikipedia.org/wiki/Wiles's_proof_of_Fermat's...

    That would mean there is at least one non-zero solution (a, b, c, n) (with all numbers rational and n > 2 and prime) to a n + b n = c n. 2 Ribet's theorem (using Frey and Serre's work) shows that using the solution (a, b, c, n), we can create a semistable elliptic Frey curve (which we will call E) which is never modular.

  4. Algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Algebraic_geometry

    Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic ...

  5. Big Ideas Learning - Wikipedia

    en.wikipedia.org/wiki/Big_Ideas_Learning

    www.BigIdeasLearning.com. Big Ideas Learning, LLC is an educational publisher in the United States. The company's headquarters is located in Erie, Pennsylvania. It publishes mathematics textbooks and instructional technology materials. Big Ideas Learning is a privately owned Limited liability company. [1]

  6. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    t. e. The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US$ 1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved ...

  7. Van Hiele model - Wikipedia

    en.wikipedia.org/wiki/Van_Hiele_model

    Van Hiele model. In mathematics education, the Van Hiele model is a theory that describes how students learn geometry. The theory originated in 1957 in the doctoral dissertations of Dina van Hiele-Geldof and Pierre van Hiele (wife and husband) at Utrecht University, in the Netherlands. The Soviets did research on the theory in the 1960s and ...

  8. Fermat's Last Theorem - Wikipedia

    en.wikipedia.org/wiki/Fermat's_Last_Theorem

    In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.

  9. List of mathematical conjectures - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical...

    The following list is meant to serve as a repository for compiling a list of such ideas. The idea of the Pythagoreans that all numbers can be expressed as a ratio of two whole numbers . This was disproved by one of Pythagoras ' own disciples, Hippasus , who showed that the square root of two is what we today call an irrational number .

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