Bernhard Riemann

The true measure of a theory is not its simplicity, but its ability to explain the inexplicable.

If only I had the theorems! Then I would have the proofs.

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.

The value of a problem is not so much in coming to the answer, but in the process of thought it induces.

We must know, we will know.

The ideas of space and time are not given to us by experience, but are forms of intuition, which are prior to all experience.

The properties of space are not given a priori, but are determined by the matter which fills it.

The question of the ultimate nature of space is a question that can only be decided by experiment.

The concept of a manifold of n dimensions is a generalization of the concept of a surface.

The infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to.

Mathematics is the queen of the sciences and arithmetic the queen of mathematics.

The greatest mathematicians, like poets and musicians, are creators of patterns.

The true method of discovery is to have no method.

What we know is a drop, what we don't know is an ocean.

The universe is not only stranger than we imagine, it is stranger than we can imagine.

The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way.

The object of mathematics is to understand the universe.

The human mind is not a vessel to be filled, but a fire to be kindled.

To understand is to perceive patterns.

The essence of mathematics lies in its freedom.