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."
Interpretation
Abel emphasizes the importance of learning from the best instead of focusing on lesser influences.
This quote reflects the profound insight of mathematician Niels Henrik Abel, who accomplished remarkable feats in mathematics in a short life. By advocating for studying the masters, Abel underscores that true mastery and innovation come from learning from those at the pinnacle of their field rather than from those still developing their skills.
In practice
This quote can be used in a speech about the importance of mentorship in academic success.
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.
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.
We should take care not to make the intellect our god; it has, of course, powerful muscles, but no personality.
Certainly, possessions, money, and power can give a momentary thrill, the illusion of being happy, but they end up possessing us and making us always want to have more, never satisfied. ‘Put on Christ’ in your life, place your trust in him, and you will never be disappointed!
If we are ever going to develop an ability to hear from God and be led by His Spirit, we have to start making our own decisions and trust the wisdom God has deposited in our own heart.
That which does not kill us makes us stronger.
Creativity is intelligence having fun.
I’ve never been certain whether the moral of the Icarus story should only be, as is generally accepted, ‘don’t try to fly too high,’ or whether it might also be thought of as ‘forget the wax and feathers, and do a better job on the wings.
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