2.  German Mathematician  Born on Sept. 17, 1826, in Breselenz, Hanover (now part of Germany).  Studied at the universities of Berlin and Gottingen  Earned a doctor’s degree in 1851.  Became a professor at Gottingen in 1859.  He died on July 20, 1866.

3. Developed a branch of advanced geometry Did important work in other areas of advanced mathematics: Calculus Mathematical Analysis Mathematical Physics

4. The Riemann integral is a generalization he uses on the definite integral, giving it a firmer basis. In 1851 Riemann invented a new way to show functions of complex numbers on a plane and developed fundamental ideas of topology to handle such representations. In 1854 Riemann suggested a new form of non- Euclidean geometry, addressed the foundations of geometry in spaces of n dimensions. In 1859 Riemann made a conjecture, that remains among the main unresolved issues of mathematics, about a complex function called the zeta function.

5. “Riemann pioneered the view of geometry as the general study of "curved spaces." His work later enabled the German-born physicist Albert Einstein to develop his theory of general relativity, which holds that gravity results from the curvature (bending) of space and time.” World Book Encyclopedia

6. “On the Hypothesis Which Lie at the Foundation of Geometry.”

7.  Became one of the most famous presentations in the history of mathematics.  It dealt with a type of non-Euclidian geometry  Replaces a famous postulate (basic statement) developed by the ancient Greek mathematician Euclid.  This system has become known as elliptic geometry or Riemannian geometry

8. GREEK Through a point not on a given line, only one line can be drawn parallel to the given line. RIEMANN Through a point not on a given line, no lines can be drawn that are parallel to the given line.

9. The Greek postulate says that exactly one line through the point will be parallel to the blue line. Riemann’s postulate says that no line through the point will be parallel to the blue line.

10. A main unresolved issues of mathematics

11. Bibliography Bernhard Riemann. (2009). Retrieved May 18, 2009, from Answers.com: http://www.answers.com/topic/bernhard-riemann Patterson, B. E. (2009). Riemann, Georg Friedrich Bernhard. Retrieved May 18, 2009, from World Book Student: http://www.worldbookonline.com/student/article?id=ar469400 Sandow, J. (2009). Riemann Zeta Function. Retrieved May 19, 2009, from Mathworld: http://mathworld.wolfram.com/RiemannZetaFunction.html