In the first section it is argued that Catastrophe Theory is not a true "Theory" in the classical sense, rather it looks like a "paradigm" in Kuhn's sense. The proof consists in analysing the sociological (better social) and the philosophical (better ideological) aspects of the controversy about Thom's and Zeeman's works. Thus in the second section it is showed that Thom's views are greatly unconventional and opposed to the usual opinions and scientific pratice shared by mathematicians, mainly regarding the indipendence of mathematics from the natural science. Moreover the paradigm of catastrophe implies major modifications in biology, linguistics and mathematical physics.In the third section the historical process of the algebraization of mathematics, recalling also the birth of quantum mechanics, is presented to stress the resemblance between Thom and Poincarè, Volterra, Weyl, Eistain, Schrodinger. However Thom cannot be confined in the image of mathematicians out of date, rather he should remember to us that it is necessary to criticize now again and to supersede the main results of the recasting of science between the wars.

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