Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.
Interpretation
Creative mathematicians are driven by aesthetic values rather than practical applications.
In this quote, Eric Temple Bell highlights the intrinsic motivation of mathematicians who pursue the beauty and elegance of mathematics itself. He argues that their work is inspired more by artistic principles such as symmetry, simplicity, and generality than by the practical usefulness of their findings, suggesting that the joy of creation and discovery in mathematics parallels that in the arts.
In practice
In a lecture about the beauty of mathematics, this quote could be used to express the artistic nature of mathematical study.
In his wretched life of less than twenty-seven years Abel accomplished so much of the highest order that one of the leading mathematicians of the Nineteenth Century could say without exaggeration, "Abel has left mathematicians enough to keep them busy for five hundred years." Asked how he had done all this in the six or seven years of his working life, Abel replied, "By studying the masters, not the pupils."
The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.
If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.
Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.
Any impatient student of mathematics or science or engineering who is irked by having algebraic symbolism thrust upon him should try to get along without it for a week.
I'm not trying to be a poet on Twitter; I'm trying to be aware of the fact that a very simple sentence, well written, can have a very moving effect without that person knowing why. There's a deep genetic part of you that somehow, even without your permission, recognizes good language when it arrives.
The institutions of human society treat us as parts of a machine. They assign us ranks and place considerable pressure upon us to fulfill defined roles. We need something to help us restore our lost and distorted humanity. Each of us has feelings that have been suppressed and have built up inside. There is a voiceless cry resting in the depths of our souls, waiting for expression. Art gives the soul's feelings voice and form.
Whatever the thing you wish to say, there is but one word to express it, but one verb to give it movement, but one adjective to qualify it; you must seek until you find this noun, this verb, this adjective.
I ground matter to find the continuous line. And when I realized I could not find it, I stopped, as if an unseen someone had slapped my hands.
Artists are the people that no matter what, pick up the pen, pick up a paintbrush. They take the time to translate what is happening to create something that resonates deeply with the rest of the people that are caught in the middle of their own reality.
Although cover notes for classical music albums tend to say that the trill of flutes suggests mountain streams and so on, I don't think anybody listens to music with the expectation that they're going to be presented with a sort of landscape painting.
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