A Quote by Cassius Jackson Keyser
Mathematics, even in its present and most abstract state, is not detached from life. It is just the ideal handling of the problems of life.
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People who have never had an ideal may hope to find one; they are in a better state than the people who allow the circumstances of life to break their ideal. To fall beneath one's ideal is to lose one's track in life; then confusion rises in the mind, and that light which one should hold high becomes covered and obscured, so that it cannot shine out to light one's path.
An immoderate fondness for dress, for pleasure, and for sway, are the passions of savages; the passions that occupy those uncivilized beings who have not yet extended the dominion of the mind, or even learned to think with the energy necessary to concatenate that abstract train of thought which produces principles.... that women from their education and the present state of civilized life, are in the same condition, cannotbe controverted.
It is impossible to overstate the imporance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps... Every new discovery in mathematics, results from an attempt to solve some problem.
The State is not the nation, and the State can be modified and even abolished in its present form, without harming the nation. On the contrary, with the passing of the dominance of the State, the genuine life-enhancing forces of the nation will be liberated.
The spirit of an age may be best expressed in the abstract ideal arts, for the spirit itself is abstract and ideal.
For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed.
If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
Mathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and state of present-day mathematics is hardly possible.
Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.
Life is short, and therefore, one thing being certain, death, let us take up a great ideal, and give up the whole life to it. For what is the value of life, this vegetating little low life of man? Subordinating it to one high ideal is the only value that life has.
It is sometimes said that the tragedy of an artist's life is that he cannot realise his ideal. But the true tragedy that dogs the steps of most artists is that they realise their ideal too absolutely. For, when the ideal is realised, it is robbed of its wonder and its mystery, and becomes simply a new starting-point for an ideal that is other than itself.
At present, when the prevailing forms of society have become hindrances to the free expression of human powers, it is precisely the abstract branches of science, mathematics and theoretical physics, which ... offer a less distorted form of knowledge than other branches of science which are interwoven with the pattern of daily life, and the practicality of which seemingly testifies to their realistic character.
Just because you have superpowers, that doesn't mean your love life would be perfect. I don't think superpowers automatically means there won't be any personality problems, family problems or even money problems. I just tried to write characters who are human beings who also have superpowers.
Across a range of inferences involving not just language but mathematics, logic problems, and spatial reasoning, sleep has been shown to enhance the formation and understanding of abstract relations, so much so that people often wake having solved a problem that was unsolvable the night before.
There is no ideal in observation. When you have an ideal, you cease to observe, you are then merely approximating the present to the idea, and therefore there is duality, conflict, and all the rest of it. The mind has to be in the state when it can see, observe. The experience of the observation is really an astonishing state. In that there is no duality. The mind is simply - aware.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
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