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.
To a clear eye the smallest fact is a window through which the infinite may be seen.
Ambition is a drug that makes its addicts potential madmen.
When you practice gratefulness, there is a sense of respect toward others.
To be honest, I've never been interested in how many games I've done and seen. It doesn't mean anything to anybody. All I know is I'm eternally grateful for having been allowed to work so many games.
Cultivating care and concern for others gives rise to a kind of inner strength. No matter what difficulties or problems you face, in this wider context they’ll seem less significant and troubling to you. The inner strength, self-confidence and courage you gain by focussing on others’ needs instead of your own, brings with it a deep, calm sense of satisfaction.
The world is full of people who have stopped listening to themselves or have listened only to their neighbors to learn what they ought to do, how they ought to behave, and what the values are they should be living for.
Subscribe for the occasional hand-picked quote. No noise.