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.
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", p. 113, 1957.
