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  1. Number theory | Definition, Topics, & History | Britannica

    Nov 20, 2025 · Number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Modern number theory is a broad subject that is classified into …

  2. Mathematics - Number Theory, Algorithms, Equations | Britannica

    Nov 11, 2025 · Mathematics - Number Theory, Algorithms, Equations: Although Euclid handed down a precedent for number theory in Books VII–IX of the Elements, later writers made no …

  3. Riemann hypothesis | Prime Numbers, Zeta Function & Complex …

    Nov 6, 2025 · number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the oldest and most …

  4. Set theory | Symbols, Examples, & Formulas | Britannica

    Oct 30, 2025 · Set theory, branch of mathematics that deals with the properties of well-defined collections of objects such as numbers or functions. The theory is valuable as a basis for …

  5. Euclidean algorithm | Algorithm, Division & GCD | Britannica

    Sep 16, 2025 · number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the oldest and most …

  6. Probability theory | Definition, Examples, & Facts | Britannica

    Oct 16, 2025 · Probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it …

  7. Joseph Liouville | French Mathematician & Analytical Number …

    number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the oldest and most natural of …

  8. Algebra - Group Theory, Applications, Math | Britannica

    Oct 24, 2025 · Number theory The notion of a group also started to appear prominently in number theory in the 19th century, especially in Gauss’s work on modular arithmetic.

  9. Algebra - Equations, Polynomials, Groups | Britannica

    Oct 24, 2025 · Some other fundamental concepts of modern algebra also had their origin in 19th-century work on number theory, particularly in connection with attempts to generalize the …

  10. Pafnuty Chebyshev | Number Theory, Probability Theory

    Dec 4, 2025 · number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the oldest and most …