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.
Rene ThomTopology is precisely the mathematical discipline that allows the passage from local to global.
Rene ThomAt a time when so many scholars in the world are calculating, is it not desirable that some, who can, dream ?
Rene ThomThe 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?
Rene Thom