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.
Taking trains and trams in Berlin, I noticed people reading. Books, I mean - not pocket-size devices that bleep as if censorious, on which even Shakespeare scans like a spreadsheet.
Whenever I start a book, I swear it's going to be a short one. But then it's, 'Who was his grandfather? And how did he get there in the first place? And what kind of animals is he chasing?'
I never had a black teacher or lecturer, I never once met a black British person who held any sort of professional or managerial role.
Tis the good reader that makes the good book; a good head cannot read amiss: in every book he finds passages which seem confidences or asides hidden from all else and unmistakeably meant for his ear.
I've seen schools in Detroit where the windows are broken, where there's no heat, and children are sitting with their coats on in class in the middle of a snowstorm. I've also seen schools in California with Olympic-sized swimming pools and cafeterias like five-star restaurants.
You know that I don't believe that anyone has ever taught anything to anyone. I question that efficacy of teaching. The only thing that I know is that anyone who wants to learn will learn. And maybe a teacher is a facilitator, a person who puts things down and shows people how exciting and wonderful it is and asks them to eat.
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