I shall devote all my efforts to bring light into the immense obscurity that today reigns in Analysis. It so lacks any plan or system, that one is really astonished that there are so many people who devote themselves to it - and, still worse, it is absolutely devoid of any rigor.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils.

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.

By studying the masters and not their pupils.