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  2. Exercise (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Exercise_(mathematics)

    An artificially produced word problem is a genre of exercise intended to keep mathematics relevant. Stephen Leacock described this type: [1] The student of arithmetic who has mastered the first four rules of his art and successfully striven with sums and fractions finds himself confronted by an unbroken expanse of questions known as problems ...

  3. Diophantine approximation - Wikipedia

    en.wikipedia.org/wiki/Diophantine_approximation

    The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number p/q is a "good" approximation of a real number α if the absolute value of the difference between p/q and α may not decrease if p/q is replaced by another

  4. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Dirichlet function: is an indicator function that matches 1 to rational numbers and 0 to irrationals. It is nowhere continuous. Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function.

  5. Birch and Swinnerton-Dyer conjecture - Wikipedia

    en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer...

    Every positive integer n ≡ 5, 6 or 7 (mod 8) is a congruent number. The elliptic curve given by y 2 = x 3 + ax + b where a ≡ b (mod 2) has infinitely many solutions over (). Every positive rational number d can be written in the form d = s 2 (t 3 – 91t – 182) for s and t in .

  6. Congruent number problem - Wikipedia

    en.wikipedia.org/wiki/Congruent_number

    For example, 5 is a congruent number because it is the area of a (20/3, 3/2, 41/6) triangle. Similarly, 6 is a congruent number because it is the area of a (3,4,5) triangle. 3 and 4 are not congruent numbers.

  7. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    The modern study of number theory in its abstract form is largely attributed to Pierre de Fermat and Leonhard Euler. The field came to full fruition with the contributions of Adrien-Marie Legendre and Carl Friedrich Gauss. [17] Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics.

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