Definition

1. Proper noun:
   • Georg Friedrich Bernhard Riemann: A 19th-century German mathematician renowned for his foundational contributions to analysis, differential geometry, and number theory. He is a pioneer of non-Euclidean geometry, which studies spaces where Euclid's parallel postulate does not hold.

Usage Examples

• Proper noun:
  • The theorems of Bernhard Riemann underpin much of modern physics.
  • Our class studied the Bernhard Riemann hypothesis in number theory.

Advanced Usage

• "in the tradition of Riemann": Referring to work or ideas that follow the mathematical approaches established by Bernhard Riemann.
  • The physicist's work on manifold theory is firmly in the tradition of Riemann.
• "Riemannian": An adjective derived from his name, used to describe concepts from his geometric work.
  • The concept of a Riemannian manifold is central to general relativity.

Variants and Related Words

• Riemannian (adj): Pertaining to the geometry developed by Bernhard Riemann, especially Riemannian geometry.
  • Einstein's theory uses Riemannian geometry to describe spacetime.
• Riemann surface (n): A one-dimensional complex manifold, a key concept he introduced.
  • The topology of a Riemann surface can be very complex.

Synonyms

• Georg Friedrich Bernhard Riemann: The full name.
• Riemann: The common shortened reference.

Related Phrases and Concepts

• Riemann integral: A classical definition of the integral, though largely superseded by the Lebesgue integral.
  • The Riemann integral is taught in introductory calculus courses.
• Riemann hypothesis: A famous, unproven conjecture in number theory concerning the zeros of the Riemann zeta function.
  • Solving the Riemann hypothesis is one of the great unsolved problems in mathematics.
• Riemann curvature tensor: A fundamental object in Riemannian geometry that quantifies curvature.
  • The Riemann curvature tensor vanishes in flat space.

Related Idioms

• • It's not Riemann, but it's a clever piece of geometry. (Implies the work is not of the groundbreaking caliber associated with Riemann).

Noun

1. pioneer of non-Euclidean geometry (1826-1866)