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.
Maturity is often more absurd than youth and very frequently is most unjust to youth.
Patience serves us against insults precisely as clothes do against the cold. For if you multiply your garments as the cold increases, that cold cannot hurt you; in the same way increase your patience under great offenses, and they cannot hurt your feelings.
Meditation is the way in which we come to feel our basic inseparability from the whole universe, and what that requires is that we shut up.
No wise combatant underestimates their antagonist.
Man can be stimulated by hope or driven by fear, but the hope and the fear must be vivid and immediate if they are to be effective without producing weariness.
...and I confess that, like a child, I cry. Ah, self-pity; I think we are at our most honest and sincere when we feel sorry for ourselves.
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