page_title: History of group theory
section_title: Appearance of groups in number theory
hierarchical_section_title: History of group theory / Early 19th century / Appearance of groups in number theory
caption_attribution_description: English: German mathematician Ernst Kummer (1810–1893)
context_page_description: The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry. Joseph Louis Lagrange, Niels Henrik Abel and Évariste Galois were early researchers in the field of group theory.
context_section_description: The third root of group theory was number theory. Certain abelian group structures had been implicitly used in number-theoretical work by Carl Friedrich Gauss, and more explicitly by Leopold Kronecker. Early attempts to prove Fermat's last theorem were led to a climax by Ernst Kummer by introducing groups describing factorization into prime numbers.
caption: Ernst Kummer
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