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Bernhard Riemann Quotes

1826–1866 Germany

Georg Friedrich Bernhard Riemann (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting and revolutionary contributions to analysis, number theory, and differential geometry.

Germany
Academics
Mathematicians

Also known as: Riemann

Random Bernhard Riemann quote

21 quotes

Natural science is the attempt to comprehend nature by precise concepts.

Gesammelte Mathematische Werke (1876)

There remains only the assumption that the ponderable masses within the rigid earth-crust are supporters of the soul-life of the earth.

Gesammelte Mathematische Werke (1876)

Every entering mind-mass excites all related mind-masses and this excitation is the more powerful the more insignificant the diversity of their inner states (quality).

Gesammelte Mathematische Werke (1876)

Newton was far from the crude thought that explanation of phenomena could be attained by abstraction.

Gesammelte Mathematische Werke (1876)

With every simple act of thinking, something permanent, substantial, enters our soul.

Gesammelte Mathematische Werke (1876)

There are no degrees of being, a gradual difference of only states or relations being thinkable. Accordingly, if an agent strives to preserve or to restore itself, then it must be a state or relation.

Gesammelte Mathematische Werke (1876)

All thinking is, accordingly, formation of new mind masses.

Gesammelte Mathematische Werke (1876)

The substratum of mental activity must be sought only in ponderable matter.

Gesammelte Mathematische Werke (1876)

The soul is a compact of mind-masses combined in a most intimate and manifold manner. It grows constantly by accession of mind-masses, and upon these depend its development.

Gesammelte Mathematische Werke (1876)

II. Thesis. Freedom, i.e., not the power absolutely to originate, but to pass judgement between two or more possibilities. Antithesis. Determinism.

Gesammelte Mathematische Werke (1876)

IV. Thesis. Immortality. Antithesis. A thing in and by itself endowed with transcendental freedom, radical evil, intelligible character and lying at the basis of our temporal appearance.

Gesammelte Mathematische Werke (1876)

I. Thesis. Finite elements of Space and Time. Antithesis. Continuity.

Gesammelte Mathematische Werke (1876)

III. Thesis. A God working in Time. (Government of the world). Antithesis. A timeless, personal, omniscient, al-mighty, all-benevolent God (Providence).

Gesammelte Mathematische Werke (1876)

Mind-masses... are imperishable, their combinations are indissoluble; only the relative strength of these combinations is altered by the incoming of new mind masses.

Gesammelte Mathematische Werke (1876)

If... part of the related mind-masses hang together among themselves, then these are not only immediately excited but also mediately and consequently in proportion more powerfully than the rest.

Gesammelte Mathematische Werke (1876)

Mind-masses entering the soul appear to us as ideas, the quality of the... [ideas] depending on the inner state of the... [soul].

Gesammelte Mathematische Werke (1876)

I have... set myself the task of constructing the notion of a multiply extended magnitude out of general notions of magnitude.

On the Hypotheses which lie at the Bases of Geometry (1873)

Thesis. Finite, Representable. Antithesis. Infinite, System of Notions lying at the limit of the representable.

Gesammelte Mathematische Werke (1876)

"When the body of the lower soul dies," says Fechner, "the higher soul takes it up out of its life of contemplation into its life of reminiscence." The souls of perished creatures shall, therefore, form the elements of the soul-life of the earth.

Gesammelte Mathematische Werke (1876)

We now apply these laws of mental processes, to which the explanation of our own inner consciousness leads, to explain the order and adaptation observed on the earth, i.e., to explain Being and historical development.

Gesammelte Mathematische Werke (1876)

Attribution

Quotes and notes from Wikiquote: Bernhard Riemann (page history), available under CC BY-SA 4.0.