Rudolf Steiner Quotes

The science [geometry] is pursued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes.

Mathematics is a body of knowledge, but it contains no truths.

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?

As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable.

Projective geometry is all geometry.

We have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.

I maintain that two and two would continue to make four, in spite of the whine of the amateur for three, or the cry of the critic for five.

That sometimes clear ... and sometimes vague stuff ... which is ... mathematics.

The pretence that numbers are not the humble creation of man, but are the exacting language of the Universe and therefore possess the secret of all things, is comforting, terrifying and mesmeric.

Euclid alone Has looked on Beauty bare. Fortunate they Who, though once only and then but far away, Have heard her massive sandal set on stone.

Geometry is the only science that it hath pleased God hitherto to bestow on mankind.

Mathematics is not only real, but it is the only reality.

Geometry in every proposition speaks a language which experience never dares to utter; and indeed of which she but halfway comprehends the meaning.

At the beginning of the new millennium, we still do not know why mathematics is true and whether it is certain. But we know what we do not know in an immeasurably richer way than we did. And learning this has been a remarkable achievement-among the greatest and least-known of the modern era.

We cannot ... prove geometrical truths by arithmetic.

Do mathematics have a relation to reality or are they only a mathematical symbol?

Geometry is to the plastic arts what grammar is to the art of the writer.

Truth is more than a mental exercise.

Our ideas must agree with realities, be such realities concrete or abstract, be they facts or be they principles, under penalty of endless inconsistency and frustration.

Strange! I don't understand how it is that we can write mathematical expressions and calculate what the thing is going to do without being able to picture it.

The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.

Geometry enlightlens the intellect and sets one's mind right