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.
Cinema, radio, television, magazines are a school of inattention: people look without seeing, listen in without hearing.
Honest criticism and sensitive appreciation are directed not upon the poet but upon the poetry.
Radio... force-feeds us music... everywhere and all the time... sewage-water music in which music is dying.
Poetry should... should strike the reader as a wording of his own highest thoughts, and appear almost a remembrance.
Any artist should be grateful for a naive grace which puts him beyond the need to reason elaborately.
While photography is the easiest medium in which to be competent, it is the hardest in which to develop an idiosyncratic personal vision.
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