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.
Perhaps our originality manifests itself most strikingly in what we do with that which we did not originate. To discover something wholly new can be a matter of chance, of idle tinkering, or even of the chronic dissatisfaction of the untalented.
You may look through the streets of heaven, asking each how they came to b there, and you will look in vain everywhere for a person who is morally and spiritually strong, whose strength did not come to him in struggle. There is no exception anywhere. Every true strength is gained in struggle.
Gaze into the fire, into the clouds, and as soon as the inner voices begin to speak... surrender to them. Don't ask first whether it's permitted, or would please your teachers or father or some god. You will ruin yourself if you do that.
If you do not wish a man to do a thing, you had better get him to talk about it; for the more men talk, the more likely they are to do nothing else.
In my tradition, one must wait until one has learned a lot of Bible and Talmud and the Prophets to handle mysticism. This isn't instant coffee. There is no instant mysticism.
When we ask for advice, we are usually looking for an accomplice.
Subscribe for the occasional hand-picked quote. No noise.