My work in the future must be devoted entirely to pure mathematics in its abstract meaning. I shall apply all my strength to bring more light into the tremendous obscurity which one unquestionably finds in analysis. It lacks so completely all plan and system that it is peculiar that so many can have studied it. The worst of it is, it has never been treated stringently. There are very few theorems in advanced analysis which have been demonstrated in a logically tenable manner. Everywhere one finds this miserable way of concluding from the special to the general, and it is extremely peculiar that such a procedure has led to so few of the so-called paradoxes. It is really interesting to seek the cause.
Niels Henrik Abel, Letter to Professor Christoffer Hansteen (1826) Oeuvres Complètes de N. H. Abel, mathematician, Nouvelle edition (1881) ed., Peter Ludwig Mejdell Sylow & Sophus Lie, Vol. 2, pp. 263-265, as quoted by Øystein Ore, Niels Henrik Abel: Mathematician Extraordinary (1957) p. 113.