I turn away with fright and horror from the lamentable evil of functions which do not have derivatives.

Abel has left mathematicians something to keep them busy for five hundred years.

Analysis takes back with one hand what it gives with the other. I recoil in fear and loathing from that deplorable evil: continuous functions with no derivatives.

There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation.

I shall risk nothing on an attempt to prove the transcendence of p. If others undertake this enterprise, no one will be happier than I in their success. But believe me, it will not fail to cost them some effort.

I turn away with fright and horror from the lamentable evil of functions which do not have derivatives.

In mathematics our role is more that of servant than master.