German Mathematician Quotes

Carl Friedrich Gauss

Albrecht Dürer

Gottfried Wilhelm Leibniz

David Hilbert

Bernhard Riemann

Georg Cantor

Gottlob Frege

In the Theory of Numbers it happens rather frequently that, by some unexpected luck, the most elegant new truths spring up by induction.

Carl Friedrich Gauss

An advantage could consist not only in a single important advantage but also in a multitude of insignificant advantages.

The purely formal sciences, logic and mathematics, deal with those relations which are, or can be, independent of the particular content or the substance of objects. To mathematics in particular fall those relations between objects which involve the concepts of magnitude, of measure and of number.

It is indeed wonderful that so simple a figure as the triangle is so inexhaustible in properties. How many as yet unknown properties of other figures may there not be?"

August Leopold Crelle

The different branches of algebra and analysis which have been investigated are so numerous that it would be quite impossible to give an approximately exhaustive representation even only of the most important problems, within the limits of the time allowed to me. I, therefore, have confined myself to the minimum admissible number, namely one.

Heinrich Maschke

One cannot guess the real difficulties of a problem before having solved it.

Carl Ludwig Siegel

It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.

A mathematician who is not also something of a poet will never be a complete mathematician.

Karl Weierstrass

This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.

As a boy of six I could understand the proof of a mathematical theorem more readily than that meat had to be cut with one's knife, not one's fork.

Ferdinand Eisenstein

Mathematics is the science of the connection of magnitudes. Magnitude is anything that can be put equal or unequal to another thing. Two things are equal when in every assertion each may be replaced by the other.

Hermann Grassmann

In science nothing capable of proof ought to be accepted without proof.

Richard Dedekind

Mathematics exists solely for the honour of the human mind.

Carl Gustav Jacob Jacobi

The design of this Memoir is to deduce strictly from a few principles, obtained chiefly by experiment, the rationale of those electrical phenomena which are produced by the mutual contact of two or more bodies, and which have been termed galvanic; its aim is attained if by means of it the variety of facts be presented as unity to the mind.

The recognition of the fact that infinite series fall into two classes (according to whether the limit is independent of the ordering of the terms or not) constitutes a turning-point in the conceptualization of the infinite in mathematics.

Bernhard Riemann

Please forget whatever you've been studying at school; for you have not learned it.

I wonder what an astronomy would look like which has been rigorously demonstrated in every respect. It seems as if one can get to the truth only through a series of hypotheses, and that one has to reject each previous one to espouse the next and to abandon it again.

Johann Heinrich Lambert

It is widely believed that in our quantum world physical facts about occurrences in space time must be grounded in the wave function. There are several long recognized and much discussed difficulties with this view.

As far as I can see, all a priori statements in physics have their origin in symmetry.

The infinite, like no other problem, has always deeply moved the soul of men. The infinite, like no other idea, has had a stimulating and fertile influence upon the mind. But the infinite is also more than any other concept, in need of clarification.

From this hour on, space as such and time as such shall recede to the shadows and only a kind of union of the two retain significance.

Hermann Minkowski

Number theorists are like lotus-eaters — having once tasted of this food they can never give it up.

Leopold Kronecker

We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"

Alfred Pringsheim

Miracles are not to be multiplied beyond necessity.

Gottfried Wilhelm Leibniz

Mathematics is perfectly free in its development and is subject only to the obvious consideration, that its concepts must be free from contradictions in themselves, as well as definitely and orderly related by means of definitions to the previously existing and established concepts.