Bernhard Riemann
Revolutionized geometry and complex analysis
Quotes by Bernhard Riemann
The most beautiful experience we can have is the mysterious.
The human condition is one of constant striving for understanding.
The purpose of life is to live a life of purpose.
Death is not the end, but a transformation.
The universe is a living organism, and we are its cells.
The concept of a space of higher dimensions is not an arbitrary construction, but a necessary consequence of the inherent properties of space itself.
The properties of space are not given a priori, but are determined by the distribution of matter and energy within it.
We must free ourselves from the prejudice that space is necessarily Euclidean.
The very nature of space could be different in different regions of the universe.
The metric of space is not fixed, but is a variable quantity that can be influenced by physical phenomena.
The axioms of geometry are not absolute truths, but rather empirical statements that can be tested and potentially falsified.
The concept of a straight line is only meaningful in a Euclidean space; in a curved space, the shortest path between two points is a geodesic.
The universe might be finite but unbounded, like the surface of a sphere.
The properties of space at infinitesimally small scales might be fundamentally different from those at macroscopic scales.
The question of whether space is infinite or finite cannot be answered by pure reason, but requires empirical observation.
The concept of a manifold allows us to generalize the notion of space beyond our intuitive three dimensions.
The curvature of space is a physical quantity, not merely a mathematical abstraction.
The laws of physics themselves might be dependent on the local geometry of space.
The idea of a 'flat' universe is just one possibility among many.
The geometry of space is not a static background, but an active participant in physical processes.