Algebra is rich in structure but weak in meaning.

Algebra is rich in structure but weak in meaning.

The world of ideas is not revealed to us in one stroke; we must both permanently and unceasingly recreate it in our consciousness.

I believe that proving is not a natural activity for mathematicians.

If one must choose between rigour and meaning, I shall unhesitatingly choose the latter.

All models divide naturally...into two a priori parts: one is kinematics, whose aim is to parameterize the forms of the states of the process under consideration, and the other is dynamics, describing the evolution in time of these forms.

The purely formal language of geometry describes adequately the reality of space. We might say, in this sense, that geometry is successful magic. I should like to state a converse: is not all magic, to the extent that it is successful, geometry?