Cassius Jackson Keyser Quotes

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

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

Cassius Jackson Keyser
What is mathematics? I inquire, not about the word, but about the thing. Many have been the answers of former years, but none has approved itself as final. All of them, by nature belonging to the "literature of knowledge," have fallen under its law and "perished by supersession."

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
Who is so unfortunate as not to know something of the religious awe, the solace and the peace that come from cloistral contemplation of the purity and everlastingness of mathematical truth?

Cassius Jackson Keyser
Next to the peaceful pleasure of meeting genuine curiosity, half-way, upon its own ground, comes the joy of combat when an attack upon some valued right or precious interest of the human spirit requires to be repelled.

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
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
Science does not seek emancipation in order to become a drudge, she consents to serve indeed but her service aims at freedom as an end.

Cassius Jackson Keyser
But while mathematics may spring up and flourish in any and all experimental and observational fields, it is by no means to be expected that 'experiment and' observation will ever thus be superseded.

Cassius Jackson Keyser
The domain of mathematics is the sole domain of certainty.

Cassius Jackson Keyser
Their [mathematics and science] combined scope is the two-fold world of the Actual and the logically Possible.

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
Mathematics is no more the art of reckoning and computation than architecture is the art of making bricks or hewing wood, no more than painting is the art of mixing colors on a palette, no more than the science of geology is the art of breaking rocks, or the science of anatomy the art of butchering.

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
Absolute certainty is a privilege of uneducated minds and fanatics. - It is, for scientific folk, an unattainable ideal.

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
To assume that nature is thinkable, an incarnate rational logos, and to seek the thought supposed incarnate there - these are at once the principle and the hope of the nature student.

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
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
To humanize the teaching of mathematics means so to present the subject, so to interpret its ideas and doctrines, that they shall appeal, not merely to the computatory faculty or to the logical faculty but to all the great powers and interests of the human mind.

Cassius Jackson Keyser
The characteristic marks of the great engineer will be four: Magnanimity — Scientific Intelligence — Humanity — Action.

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