Mathematicians are born, not made. - Henri Poincaré

La logique parfois engendre des monstres. Depuis un demi-siècle on a vu surgir une foule de fonctions bizarres qui semblent s’efforcer de ressembler aussi peu que possible aux honnêtes fonctions qui servent à quelque chose. Plus de continuité, ou bien de la continuité, mais pas de dérivées, etc. Bien plus, au point de vue logique, ce sont ces fonctions étranges qui sont les plus générales, celles qu’on rencontre sans les avoir cherchées n’apparaissent plus que comme un cas particulier. Il ne leur reste qu’un tout petit coin.

if the contrary takes place, if these two muscular sensations vary independently of one another, we shall have to take account of one more independent variable, and 'complete visual space' will appear to us as a physical continuum of four dimensions.

One need only open the eyes to see that the conquests of industry which have enriched so many practical men would never have seen the light, if these practical men alone had existed and if they had not been preceded by unselfish devotees who died poor, who never thought of utility, and yet had a guide far other than caprice.
As Mach says, these devotees have spared their successors the trouble of thinking.