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The 52 pages that link to Bernhard Riemann, each with the reason it gives.

• Carl Friedrich GaussRelated: Riemann extended geometric questions raised by Gauss into a broader theory of curved spaces.

• Differential geometryRelated: His 1854 lecture developed the foundations of geometry on curved spaces.

• Non-Euclidean geometryRelated: His framework extended non-Euclidean ideas beyond constant-curvature surfaces.

• Algebraic geometryRelated: His surfaces linked algebraic functions to geometric spaces.

• Prime number theoremRelated: His 1859 memoir supplied the analytic framework that led toward the theorem.

• Metric tensorRelated: His 1854 lecture introduced the broader framework of geometry defined by a metric.

• Riemann zeta functionRelated: His 1859 memoir connected zeta zeros with the distribution of primes.

• Analytic continuationRelated: His theory of multivalued functions and surfaces gave continuation a geometric framework.

• Prime-counting functionRelated: His 1859 paper linked prime-counting errors to zeta-function zeros.

• Riemann hypothesisRelated: His 1859 memoir introduced the zeta-function framework and stated the hypothesis.

• Richard DedekindRelated: Dedekind edited and published Riemann’s collected works after his death.

• Riemann curvature tensorRelated: His 1854 habilitation lecture introduced the geometric framework from which the tensor developed.

• Elliptic partial differential equationRelated: Riemannian geometry supplies the setting for many elliptic operators.

• Modular formRelated: Riemann surfaces and period lattices underpin the geometric setting of classical modular forms.

• Karl WeierstrassCompared with: Riemann's influential approach to complex analysis differed from Weierstrass's emphasis on power series and rigor.

• Riemann mapping theoremRelated: His 1851 dissertation introduced the theorem and its influential existence argument.

• Analytic number theoryRelated: His 1859 memoir connected zeta-function zeros with the distribution of primes.

• Cauchy–Riemann equationsRelated: His complex-function theory made the equations central to the study of analytic functions.

• Uniformization theoremRelated: Riemann introduced the surfaces and mapping problems that led to uniformization.

• Jacques HadamardRelated: Riemann supplied the zeta-function framework that Hadamard later used to prove the prime number theorem.

• Potential theoryRelated: His ideas helped extend potential methods into geometric and complex-analytic settings.

• Elliptic functionRelated: His surface viewpoint connects doubly periodic functions with meromorphic functions on tori.

• Elliptic geometryRelated: His 1854 lecture introduced a systematic geometric setting for positive curvature.

• Levi-Civita connectionRelated: Riemannian metrics created the geometric setting in which this canonical connection is defined.

• Cauchy's integral theoremRelated: Riemann developed influential approaches to complex integration and the theorem’s consequences.

• Nikolai LobachevskyRelated: Riemann’s later geometry broadened the transformation of geometric thought that Lobachevsky helped initiate.

• Prime number theorem for arithmetic progressionsRelated: His ideas about analytic continuation and zeros informed later prime-distribution methods.

• Riemann–Roch theoremRelated: His ideas on functions and surfaces gave rise to the theorem’s analytic form.

• Weierstrass functionRelated: A related nowhere-differentiable function had been attributed to Riemann before Weierstrass's example.

• Weierstrass factorization theoremRelated: His approach to analytic functions formed part of the mathematical setting Weierstrass helped formalize.

• Generalized Stokes theoremRelated: Riemannian integration and manifold ideas helped set the geometric stage for the theorem.

• Abelian varietyRelated: His theory of Riemann surfaces supplied foundational ideas behind Jacobians and abelian functions.

• János BolyaiRelated: Riemann later extended the transformation of geometry that Bolyai and Lobachevsky began.

• Peter Gustav Lejeune DirichletRelated: Riemann studied under Dirichlet and developed methods that extended his analytic approach.

• Theta functionRelated: Riemann extended theta functions to higher-genus surfaces and connected them to their geometry.

• Erlangen programRelated: Riemannian geometry helped expand the range of geometries Klein sought to organize.

• History of geometryRelated: His 1854 lecture recast geometry around manifolds and curvature.

• Hurwitz's theoremRelated: Hurwitz's function theory developed within the analytic framework established by Riemann.

• Algebraic functionRelated: His surface-based view made multivalued algebraic functions geometrically coherent.

• Hirzebruch–Riemann–Roch theoremRelated: The theorem generalizes the curve-level dimension formula associated with Riemann.

• Riemann series theoremRelated: His name is attached to the theorem on rearranging conditionally convergent series.

• Grothendieck–Riemann–Roch theoremRelated: His work on surfaces supplied the historical setting for the classical formula generalized here.

• Riemann–Hurwitz formulaRelated: Riemann’s theory of surfaces supplied the setting for the genus relation.

• Abel’s theoremRelated: Riemann’s framework of surfaces and periods made Abel’s integral relations geometrically explicit.

• Class number formulaRelated: The analytic methods behind zeta functions grew from his work on the Riemann zeta function.

• Morera's theoremRelated: Morera's theorem is often used in proving that continuous functions satisfying the Cauchy–Riemann equations are holomorphic.

• Riemann–Roch theorem for surfacesRelated: The theorem’s name traces to Riemann’s original result for curves.

• Riemann–Siegel formulaRelated: Riemann's zeta-function investigations supplied the problem the formula addresses.

• Riemann–von Mangoldt formulaRelated: His 1859 paper introduced the zeta-function framework behind the zero count.

• Harnack's principleRelated: His theory of harmonic functions and surfaces formed essential background for later convergence principles.