Georg Friedrich Bernhard Riemann Quotes

Nash's genius was of that mysterious variety more often associated with music and art than with the oldest of all sciences. It wasn't merely that his mind worked faster, that his memory was more retentive, or that his power of concentration was greater. The flashes of intuition were non-rational. Like other great mathematical intuitionists - Georg Friedrich Bernhard Riemann, Jules Henri Poincaré, Srinivasa Ramanujan - Nash saw the vision first, constructing the laborious proofs long afterward. ~ Sylvia Nasar

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane. ~ Richard Hamming

The Catholics had been in the position of oppressors, and the Protestants of the oppressed ~ Georg Wilhelm Friedrich Hegel

The person must give himself an external sphere of freedom in order to have being as Idea. ~ Georg Wilhelm Friedrich Hegel

If you want to love you must serve, if you want freedom you must die. ~ Georg Wilhelm Friedrich Hegel

I have the courage to be mistaken. ~ Georg Wilhelm Friedrich Hegel

Nothing great in the world was accomplished without passion. ~ Georg Wilhelm Friedrich Hegel

We stand at the gates of an important epoch, a time of ferment, when spirit moves forward in a leap, transcends its previous shape and takes on a new one ... A new phase of the spirit is preparing itself. Philosophy especially has to welcome its appearance and acknowledge it, while others, who oppose it impotently, cling the past. ~ Georg Wilhelm Friedrich Hegel

No man is a hero to his valet de chamber ~ Georg Wilhelm Friedrich Hegel

If we are in a general way permitted to regard human activity in the realm of the beautiful as a liberation of the soul, as a release from constraint and restriction, in short to consider that art does actually alleviate the most overpowering and tragic catastrophes by means of the creations it offers to our contemplation and enjoyment, it is the art of music which conducts us to the final summit of that ascent to freedom. ~ Georg Wilhelm Friedrich Hegel

The Beautiful is the expression of the absolute Spirit, which is truth itself. This region of Divine truth as artistically presented to perception and feeling, forms the center of the whole world of Art. It is a self-contained, free, divine formation which has completely appropriated the elements of external form as material, and which employs them only as the means of manifesting itself. ~ Georg Wilhelm Friedrich Hegel

Because of its concrete content, sense-certainty immediately appears as the richest kind of knowledge, indeed a knowledge of infinite wealth for which no bounds can be found, either when we reach out into space and time in which it is dispersed, or when we take a bit of this wealth, and by division enter into it. Moreover, sense-certainty appears to be the truest knowledge ... but, in the event, this very certainty proves itself to be the most abstract and poorest truth. All that it says about what it knows is just that it is; and its truth contains nothing but the sheer being of the thing. ~ Georg Wilhelm Friedrich Hegel

Science and knowledge, especially that of philosophy, came from the Arabs into the West. ~ Georg Wilhelm Friedrich Hegel

Thinking is, indeed, essentially the negation of that which is before us. ~ Georg Wilhelm Friedrich Hegel

In history an additional result is commonly produced by human actions beyond that which they aim at and obtain
that which they immediately recognize and desire. They gratify their own interest; but something further is thereby accomplished, latent in the actions in question, though not present to their consciousness, and not included in their design. ~ Georg Wilhelm Friedrich Hegel

The life of God - the life which the mind apprehends and enjoys as it rises to the absolute unity of all things - may be described as a play of love with itself; but this idea sinks to an edifying truism, or even to a platitude, when it does not embrace in it the earnestness, the pain, the patience, and labor, involved in the negative aspect of things. ~ Georg Wilhelm Friedrich Hegel

Education is the art of making man ethical ~ Georg Wilhelm Friedrich Hegel

History teaches us that man learns nothing from history ~ Georg Wilhelm Friedrich Hegel

Beauty and art, no doubt, pervade all business of life like a kindly genius, and form the bright adornment of all our surroundings, both mental and material, soothing the sadness of our condition and the embarrassments of real life, killing time in entertaining fashion, and where there's nothing to be achieved, occupying the place of what is vicious, better, at any rate, than vice. ~ Georg Wilhelm Friedrich Hegel

When we say, "God is love," we are saying something very great and true. But it would be senseless to grasp this saying in a simple-minded way as a simple definition, without analyzing what love is. For love is a distinguishing of two, who nevertheless are absolutely not distinguished for each other. The consciousness or feeling of the identity of the two - to be outside of myself and in the other - this is love. I have my self-consciousness not in myself but in the other. I am satisfied and have peace with myself only in this other - and I am only because I have peace with myself; if I did not have it, then I would be a contradiction that falls to pieces. This other, because it likewise exists outside itself, has its self-consciousness only in me, and both the other and I are only this consciousness of being-outside-ourselves and of our identity; we are only this intuition, feeling, and knowledge of our unity. This is love, and without knowing that love is both a distinguishing and the sublation of the distinction, one speaks emptily of it. This is the simple, eternal idea. ~ Georg Wilhelm Friedrich Hegel

Animals are in possession of themselves; their soul is in possession of their body. But they have no right to their life, because they do not will it. ~ Georg Wilhelm Friedrich Hegel

It is manifest that behind the so-called curtain which is supposed to conceal the inner world, there is nothing to be seen unless we go behind it ourselves, as much in order that we may see, as that there may be something behind there which can be seen. ~ Georg Wilhelm Friedrich Hegel

Everything that from eternity has happened in heaven and earth, the life of God and all the deeds of time simply are the struggles for Spirit to know Itself, to find Itself, be for Itself, and finally unite itself to Itself; it is alienated and divided, but only so as to be able thus to find itself and return to Itself ... As existing in an individual form, this liberation is called 'I'; as developed to its totality, it is free Spirit; as feeling, it is Love; and as enjoyment, it is Blessedness. ~ Georg Wilhelm Friedrich Hegel

America is therefore the land of the future, where, in the ages that lie before us, the burden of the World's History shall reveal itself. ~ Georg Wilhelm Friedrich Hegel

The learner always begins by finding fault, but the scholar sees the positive merit in everything. ~ Georg Wilhelm Friedrich Hegel

War is progress, peace is stagnation ~ Georg Wilhelm Friedrich Hegel

Only one man ever understood me, and he didn't understand me. ~ Georg Wilhelm Friedrich Hegel

The true is thus the bacchanalian whirl in which no member is not drunken; and because each, as soon as it detaches itself, dissolves immediately - the whirl is just as much transparent and simple repose. ~ Georg Wilhelm Friedrich Hegel

Consequently, the sensuous aspect of art is related only to the two theoretical sensesof sight and hearing, while smell, taste, and touch remain excluded. ~ Georg Wilhelm Friedrich Hegel

But even regarding History as the slaughter-bench at which the happiness of peoples, the wisdom of States, and the virtue of individuals have been victimised - the question involuntarily arises - to what principle, to what final aim these enormous sacrifices have been offered. ~ Georg Wilhelm Friedrich Hegel

The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. The ceaseless activity of their own inherent nature makes these stages moments of an organic unity, where they not merely do not contradict one another, but where one is as necessary as the other; and constitutes thereby the life of the whole. ~ Georg Wilhelm Friedrich Hegel

All the worth which the human being possesses, all spiritual reality, he possesses only through the State ... For Truth is the unity of the universal and subjective will; and the Universal is to be found in the State, in its laws, its universal and rational arrangements. The State is the Divine Idea as it exists on earth. We have in it, therefore, the object of history in a more definite shape than before; that in which Freedom obtains objectivity. ~ Georg Wilhelm Friedrich Hegel

The beginning of religion, more precisely its content, is the concept of religion itself, that God is the absolute truth, the truth of all things, and subjectively that religion alone is the absolutely true knoweldge. ~ Georg Wilhelm Friedrich Hegel

The courage of the truth is the first condition of philosophic study. ~ Georg Wilhelm Friedrich Hegel

The ignorant man is not free, because what confronts him is an alien world, something outside him and in the offing, on which he depends, without his having made this foreign world for himself and therefore without being at home in it by himself as in something his own. The impulse of curiosity, the pressure for knowledge, from the lowest level up to the highest rung of philosophical insight arises only from the struggle to cancel this situation of unfreedom and to make the world one's own in one's ideas and thought. ~ Georg Wilhelm Friedrich Hegel