Die Religion ist der Seufzer der bedrängten Kreatur, das Gemüt einer herzlosen Welt, wie sie der Geist geistloser Zustände ist. Sie ist das Opium des Volks. Die Aufhebung der Religion als des illusorischen Glücks des Volks ist die Forderung seines wirklichen Glücks.
Religion is the sigh of the oppressed creature, the heart of a heartless world, just as it is the spirit of spiritless conditions. It is the opium of the people. To abolish religion as the illusory happiness of the people is to demand their real happiness.

Descartes constructed as noble a road of science, from the point at which he found geometry to that to which he carried it, as Newton himself did after him. ... He carried this spirit of geometry and invention into optics, which under him became a completely new art.

Fermentation is the exhalation of a substance through the admixture of a ferment which, by virtue of its spirit, penetrates the mass and transforms it into its own nature.

I like the scientific spirit—the holding off, the being sure but not too sure, the willingness to surrender ideas when the evidence is against them: this is ultimately fine—it always keeps the way beyond open.

I see with much pleasure that you are working on a large work on the integral Calculus [ ... ] The reconciliation of the methods which you are planning to make, serves to clarify them mutually, and what they have in common contains very often their true metaphysics; this is why that metaphysics is almost the last thing that one discovers. The spirit arrives at the results as if by instinct; it is only on reflecting upon the route that it and others have followed that it succeeds in generalising the methods and in discovering its metaphysics.

Science is not the enemy of humanity but one of the deepest expressions of the human desire to realize that vision of infinite knowledge. Science shows us that the visible world is neither matter nor spirit; the visible world is the invisible organization of energy.

Science is teaching man to know and reverence truth, and to believe that only so far as he knows and loves it can he live worthily on earth, and vindicate the dignity of his spirit.

There is no thing as a man who does not create mathematics and yet is a fine mathematics teacher. Textbooks, course material—these do not approach in importance the communication of what mathematics is really about, of where it is going, and of where it currently stands with respect to the specific branch of it being taught. What really matters is the communication of the spirit of mathematics. It is a spirit that is active rather than contemplative—a spirit of disciplined search for adventures of the intellect. Only as adventurer can really tell of adventures.

We find that one of the most rewarding features of being scientists these days ... is the common bond which the search for truth provides to scholars of many tongues and many heritages. In the long run, that spirit will inevitably have a constructive effect on the benefits which man can derive from knowledge of himself and his environment.