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Niels Henrik Abel Quotes

By studying the masters and not their pupils Picture Quote #1
He is like the fox, who effaces his tracks in the sand with his tail Picture Quote #1
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 Picture Quote #1
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 Picture Quote #1
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils Picture Quote #1
The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may draw any conclusion he pleases and that is why these series have produced so many fallacies and so many paradoxes Picture Quote #1
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By studying the masters and not their pupils  (Niels Henrik Abel Quotes) He is like the fox, who effaces his tracks in the sand with his tail  (Niels Henrik Abel Quotes) 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  (Niels Henrik Abel Quotes) 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  (Niels Henrik Abel Quotes) It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils  (Niels Henrik Abel Quotes) The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may draw any conclusion he pleases and that is why these series have produced so many fallacies and so many paradoxes  (Niels Henrik Abel Quotes)