Riemann …

• Bernhard Riemann lived from 1826 to 1866.
• He took mathematics courses from Gauss.
• He was a very intuitive thinker.
• Gauss described him as having "a gloriously fertile originality".
• For a while, only Gauss appreciated Riemann.
• Riemann came up with a new geometry - one where you have a curved surface for a plane, instead of the flat surface in Euclidean Geometry. It was called Elliptic Geometry.
• But at an address given by Riemann, Einstein attended and heard what he needed - a new geometry for his ideas on Relativity.
• Riemann read Euclid's Second Postulate: "A piece of straight line may be extended indefinitely". He reacted to the idea of 'indefinite' and said, "... we must distinguish between unboundedness and infinite extent ... The unboundedness of space possesses ... a greater empirical certainty than any external experience. But its infinite extent by no means follows from this." He changes Euclid's second postulate to "A straight line is boundless." Thus Riemann has provided for curved or circular or spherical lines that boundlessly come around.