It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils.
Interpretation
To advance in mathematics, it's more beneficial to learn from the greats than from those still learning.
Niels Henrik Abel emphasizes the importance of studying the works and methods of accomplished mathematicians rather than those of learners or novices. By focusing on the masters, one gains insight into advanced concepts and techniques that have been proven valuable, thus facilitating a deeper understanding and accelerated progress in the field of mathematics.
In practice
During a math seminar, one could use this quote to highlight the importance of studying significant mathematicians.
Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.
With the exception of the geometrical series, there does not exist in all of mathematics a single infinite series the sum of which has been rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation.
I had a lot of really terrible advice early in my writing career, and I cheesed off people without even knowing it, all the while thinking I was implementing good advice. Well, what can you do about it? Next.
Publicity, publicity, PUBLICITY is the greatest moral factor and force in our public life.
Cheating in school is a form of self-deception. We go to school to learn. We cheat ourselves when we coast on the efforts and scholarship of someone else.
I never let schooling interfere with my education.
Voters inclined to loathe and fear elite Ivy League schools rarely make fine distinctions between Yale and Harvard. All they know is that both are full of rich, fancy, stuck-up and possibly dangerous intellectuals who never sit down to supper in their undershirt no matter how hot the weather gets.
A child is not a vase to be filled, but a fire to be lit.
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