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

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?

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.

Topology is precisely the mathematical discipline that allows the passage from local to global...

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

Catastrophe Theory is-quite likely-the first coherent attempt (since Aristotelian logic) to give a theory on analogy. When narrow-minded scientists object to Catastrophe Theory that it gives no more than analogies, or metaphors, they do not realise that they are stating the proper aim of Catastrophe Theory, which is to classify all possible types of analogous situations.

The importance of the "New Mathematics" lies mainly in the fact that it has taught us the difference between the disc and the circle.

Quantum mechanics, with its leap into statistics, has been a mere palliative for our ignorance

At a time when so many scholars in the world are calculating, is it not desirable that some, who can, dream ?

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

Algebra is rich in structure but weak in meaning.

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