Algebraic number theory

Inventor of ideal numbers, who proved Fermat's Last Theorem for regular primes and found the quartic surface with sixteen nodes.

algebraic number theory, analysis, algebraic geometry

Creator of ideal theory, Dedekind cuts and the set-theoretic foundations of the natural numbers.

algebraic number theory, foundations of mathematics, abstract algebra

Leader of Göttingen mathematics whose basis theorem, Zahlbericht, axioms of geometry, Hilbert space, Paris problems and proof theory shaped twentieth-century mathematics.

invariant theory, algebraic number theory, foundations of geometry

Founder of modern Japanese mathematics who proved that the abelian extensions of a number field are exactly its class fields.

algebraic number theory, class field theory, analysis

Number theorist who proved the functional equation of Dedekind zeta functions, introduced Grössencharaktere and their L-functions, and created the theory of Hecke operators linking modular forms to Euler products.

number theory, modular forms, l-functions

Algebraist and number theorist who proved the general reciprocity law, introduced Artin L-functions and the braid group, and solved Hilbert's seventeenth problem.

algebraic number theory, class field theory, abstract algebra

Number theorist who introduced the local-global principle, shaped class field theory and proved the Riemann hypothesis for elliptic curves over finite fields, and who directed the Göttingen institute under National Socialism.

algebraic number theory, class field theory, arithmetic of quadratic forms

Algebraist who introduced the Brauer group, founded modular representation theory and set the strategy that led to the classification of finite simple groups.

representation theory, finite group theory, algebra

Number theorist and matrix theorist who linked class field theory, integral matrices and eigenvalue localization, and made linear algebra a research field in its own right.

algebraic number theory, matrix theory, group theory