Cassius Jackson Keyser Quotes

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The rigor of mathematics is not absolute - absolute rigor is an ideal, to be, like other ideals, aspired unto, forever approached, but never quite attained, for such attainment would mean that every possibility of error or indetermination, however slight, had been eliminated from idea, from symbol, and from argumentation.

Cassius Jackson Keyser
Mathematics, like any other cardinal activity of the human spirit, has an individuality of its own.

Cassius Jackson Keyser
It is commonly, but erroneously, believed that it is easy to ask questions. A fool, it is said, can ask questions that a wise man cannot answer. The fact is that a wise man can answer many questions that a fool cannot ask.

Cassius Jackson Keyser
There are many infinites of many orders... infinites are surpassed by other infinites... infinites, like the stars, differ in glory. This is not rhetoric, it is naked fact.

Cassius Jackson Keyser
Knowledge - a kind of proliferating sphere, expanding along divergent lines by the outward-seeking of an inner life of wonder.

Cassius Jackson Keyser
It seems indeed as if the entire surface of the world of human consciousness were predestined to be covered over, in varying degrees of luxuriance, by the flora of mathematic science.

Cassius Jackson Keyser
What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an "ever flying perfect" as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration.

Cassius Jackson Keyser
To think the thinkable — that is the mathematician's aim.

Cassius Jackson Keyser
The Modern Theory of Functions — that stateliest of all the pure creations of the human intellect.

Cassius Jackson Keyser
Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite and eternal.

Cassius Jackson Keyser
Intelligibility is alike the first and the last demand of the understanding.

Cassius Jackson Keyser
Projective Geometry: a boundless domain of countless fields where reals and imaginaries, finites and infinites, enter on equal terms, where the spirit delights in the artistic balance and symmetric interplay of a kind of conceptual and logical counterpoint - an enchanted realm where thought is double and flows throughout in parallel streams.

Cassius Jackson Keyser
If people would stop objectifying abstractions (which they probably never will), or if they would stop objectifying the abstractions they make consciously (which they might learn to do), at least half the pseudo-questions befuddling the world today - as they have befuddled it since time immemorial - would vanish. And that would be a very, very great gain.

Cassius Jackson Keyser
Unlike man the individual, a university is, like man the race, immortal.

Cassius Jackson Keyser
To facilitate eyeless observation of his sense-transcending world, the mathematician invokes the aid of physical diagrams and physical symbols in endless variety and combination...

Cassius Jackson Keyser
Mathematics is, in a word, the study of Fate. Let me hasten to say that the Fate is not physical, it is spiritual - the unbreakable binding thread of destiny runs through the universum of rigorous Thought: the fate is logical Fate.

Cassius Jackson Keyser
Mathematics may be legitimately pursued for its own sake or for the sake of its applications or with a view to understanding its logical foundations and internal structure or in the interest of magnanimity or for the sake of its bearings upon the supreme concerns of man as man or from two or more of these motives combined.

Cassius Jackson Keyser
The average pupil's interest in mathematics is but slight, is a matter of common knowledge. His lack of interest is, in my opinion, due, not to a lack of the appropriate faculty in him, but to the circumstance that he is a human being, whilst mathematics, though it teems with human interest, is not presented to him in its human guise.

Cassius Jackson Keyser
In the whole universe of events, none is more wonderful than the birth of wonder, none more curious than the nascence of curiosity itself, nothing to compare with the dawning of consciousness in the ancient dark and the gradual extension of psychic life and illumination throughout a cosmos that before had only been.

Cassius Jackson Keyser
The present is no more exempt from the sneer of the future than the past has been.

Cassius Jackson Keyser
Curiosity is the aspect of the universe seeking to realise itself, and the fruit of such activity is new reality, stimulating to new research.

Cassius Jackson Keyser
My conviction is, that hope of improvement in mathematics teaching, whether in secondary schools or in colleges, lies mainly in the possibility of humanizing it.

Cassius Jackson Keyser
But for the unattainable ideal of perfect conquest of Nature, we should not have the marvels of modern Invention and Empirical Science.

Cassius Jackson Keyser
Mathematics has been often praised by the scientifically incompetent; it has not, so far as I am aware, been dispraised, or its worth challenged or denied, by the scientifically competent.

Cassius Jackson Keyser
Every major concern among the intellectual concerns of man is a concern of mathematics.

Cassius Jackson Keyser