23 quotes
In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.
Hermann. Invariants. Duke Math. J. 5 (1939)
Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect.
Symmetry (1952)
Time is the primitive form of the stream of consciousness.
Space—Time—Matter (1952)
It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship.
Space—Time—Matter (1952)
Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means.
The Open World: Three Lectures on the Metaphysical Implications of Science (1932)
Consciousness spreads out its web, in the form of time, over reality.
Space—Time—Matter (1952)
Above all, the ominous clouds of those phenomena that we are with varying success seeking to explain by means of the quantum of action, are throwing their shadows over the sphere of physical knowledge, threatening no one knows what new revolution.
Space—Time—Matter (1952)
This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind.
Symmetry (1952)
We cannot hope to give here a final clarification of the essence of fact, judgement, object, property; this task leads into metaphysical abysses; about these one has to seek advice from men whose name cannot be stated without earning a compassionate smile—e.g. Fichte.
Das Kontinuum. Kritische Untersuchungen uber die Grundlagen der Analysis (1918)
Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it as history, that is, as a process that is going forward in time and takes place in space.
Space—Time—Matter (1952)
Cartan developed a general scheme of infinitesimal geometry in which Klein's notions were applied to the tangent plane and not to the n-dimensional manifold M itself.
On the foundations of general infinitesimal geometry. Bull. Amer. Math. Soc. 35 (1929)
With Mie's view of matter there is contrasted another, according to which matter is a limiting singularity of the field, but charges and masses are force-fluxes in the field. This entails a new and more cautious attitude towards the whole problem of matter.
Space—Time—Matter (1952)
And now, in our time, there has been unloosed a cataclysm which has swept away space, time, and matter hitherto regarded as the firmest pillars of natural science, but only to make place for a view of things of wider scope, and entailing a deeper vision.
Space—Time—Matter (1922)
In my work, I have always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful.
It is the nature of a real thing to be inexhaustible in content; we can get an ever deeper insight into this content by the continual addition of new experiences, partly in apparent contradiction, by bringing them into harmony with one another.
Space—Time—Matter (1952)
The rapid development of science... has, as it were, burst its old shell, now become too narrow.
Space—Time—Matter (1952)
To gaze up from the ruins of the oppressive present towards the stars is to recognise the indestructible world of laws, to strengthen faith in reason, to realise the "harmonia mundi" that transfuses all phenomena, and that never has been, nor will be, disturbed.
Space—Time—Matter (1952)
Recognition of the subjectivity of the qualities of sense is found in Galilei (and also in Descartes and Hobbes) in a form closely related to the principle underlying the constructive mathematical method of our modern physics which repudiates" qualities".
Space—Time—Matter (1952)
It seems clear that [set theory] violates against the essence of the continuum, which, by its very nature, cannot at all be battered into a single set of elements. Not the relationship of an element to a set, but of a part to a whole ought to be taken as a basis for the analysis of a continuum.
We now come to a decisive step of mathematical abstraction: we forget about what the symbols stand for... [The mathematician] need not be idle; there are many operations which he may carry out with these symbols, without ever having to look at the things they stand for.
The Mathematical Way of Thinking (1941)