In the old days when people invented a new function they had something useful in mind.

Hypotheses are what we lack the least.

The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognisable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile and vain.

It is far better to foresee even without certainty than not to foresee at all.

If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it.

All of mathematics is a tale about groups.

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.