[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.

[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.

It may happen that small differences in the initial conditions produce very great ones in the final phenomena.

If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living

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.

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know

. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.