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Common experience teaches us that continual, varying change is the order of nature. As the old hymn has it, 'Change and decay in all around I see,' which seems a needlessly pessimistic paraphrase of the dictum of Heraclitus, 'All things flow'.
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I trust that this explanation has illuminated an obscure matter, but I have my doubts.
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Sooner or later the cold plunge into pure abstraction must be taken if one is to learn to swim in mathematics and to reason as rational, thinking human beings do.
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The toughminded suggest that the theory of the infinite elaborated by the great mathematicians of the Nineteenth and Twentieth Centuries, without which mathematical analysis as it is actually used today is impossible, has been committing suicide in an unnecessarily prolonged and complicated manner for the past half century.
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Even stranger things have happened; and perhaps the strangest of all is the marvel that mathematics should be possible to a race akin to the apes.
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The distinction between the mathematical method and the scientific is seen in the agonies of very young children to do what their teachers sometimes tell them is mathematics. Anyone who was subjected to elementary geometry when his infantile brain was as unripe as a green walnut will recall the protracted misery he endured.
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The statistical method is social mathematics par excellence.
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The tensor calculus that cost Einstein an effort to master is now a regular part of an undergraduate course in the better technical schools. The subject has been so thoroughly emulsified that even an eighteen-year-old can swallow it without regurgitating. But this does not prove that wither his brain or his stomach is stronger than Einstein's was.
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This would appear to put at least part of the Theory of Demonstration in a category with the efforts of beginners in Geometry: To prove that A equals B: let A equal B; therefore A equals B.
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The algebraic numbers are spotted over the plane like stars against a black sky; the dense blackness is the firmament of the transcendentals.
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A circle no doubt has a certain appealing simplicity at the first glance, but one look at a healthy ellipse should have convinced even the most mystical of astronomers that that the perfect simplicity of the circle is akin to the vacant smile of complete idiocy. Compared to what an ellipse can tell us, a circle has nothing to say.
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The task of cleaning up mathematics and salvaging whatever can be saved from the wreckage of the past twenty years will probably be enough to occupy one generation.
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Daniel Bernoulli has been called the father of mathematical physics.
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Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.
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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."
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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.
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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.
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Some of his deepest discoveries were reasoned out verbally with very few if any symbols, and those for the most part mere abbreviations of words. Any impatient student of mathematics or science or engineering who is irked by having algebraic symbolism thrust on him should try to get on without it for a week.
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This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven.
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Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. Then, in the alleged proof, be alert for inexplicit assumptions. Euclid's notorious oversights drove this lesson home.
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Perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth — whatever that may be, if anything.
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The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so also can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular.
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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.
Eric Temple Bell
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The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry.
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Experiment as scientists understand it is admittedly an indispensable adjunct to the progress of civilization and its probable destruction.
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Quote of the day
It ain't as bad as you think. It will look better in the morning.
Colin Powell
Eric Temple Bell
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Born:
February 7, 1883
Died:
December 21, 1960
(aged 77)
Bio:
Eric Temple Bell was a Scottish-born mathematician and science fiction writer who lived in the United States for most of his life. He published non-fiction using his given name and fiction as John Taine.
Known for:
Men of Mathematics (1937)
The magic of numbers (1946)
The last problem
Mathematics, queen and servant of science (1951)
The development of mathematics (1940)
Most used words:
mathematics
science
obvious
mathematicians
abel
human
truth
years
assumptions
Eric Temple Bell on Wikipedia
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