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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.
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.
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.
Fashion as king is sometimes a very stupid ruler.
Science makes no pretension to eternal truth or absolute truth; some of its rivals do. That science is in some respects inhuman may be the secret of its success in alleviating human misery and mitigating human stupidity.
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.
The so-called obvious was repeatedly scrutinized from every angle and was frequently found to be not obvious but false. 'Obvious' is the most dangerous word in mathematics.
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