Unraveling the Catastrophe Theory Controversy in the USA

 Renee Thom coined the term CATASTROPHE THEORY, and that may have been a poor choice of words.  Apparently the tempestuous moods of the sixties were a factor. The names mathematicians come up with often do not stand the test of time. Examples:  COMPLEX ANALYSIS, IMAGINARY NUMBERS,  IRRATIONAL NUMBERS,  LIE GROUPS, and CHAOS THEORY,  

Never mind that without these concepts we might be living in potentially unsanitary conditions. 

Never mind also that an evolving language is necessary to formulate new concepts. Every somewhat educated person at least should have a rudimentary understanding of the distinctions between:  possibility, probability, statistics. This was not the case 100 years ago when some of these topics were in their infancy, riddled with inconsistencies and puzzles.

During the 70s publications  on the topic of Catastrophe Theory and Bifurcation Theory  were  produced (at an alarming rate) on the topic of  Catastrophe Theory ( see ).  We mention the early paper by John Guckenheimer: Bifurcation and Catastrophe , and the one by Ian Stewart: Catastrophe Theory in Physics     These presented a great many interesting  applications to mathematics (dynamical systems, On the Nature of Turbulence, the Lorenz Attractor, Universality and Renormalization), the emerging  Chaos Theory in physics and  Bifurcation Analysis with applications in engineering. For an explicit engineering example we mention a classic example initiated by Leonhard Euler:  The stability of Ships. Capsizing is indeed then catastrophic. 

 Chrisopher Zeeman in particular was also pushing applications to social sciences, prison disturbance, fight or flight, etc, etc. Catastrophe Theory in the hands of the holy men and women at the RAND Corporation must have scared some also, and perhaps rightly so given the Zeitgeist.

An ultimately very effective counterattack was launched by Hector Sussman and Raphael Zahler in a number of publications, for example in Nature: Claims and Accomplishments of applied catastrophe theory ". This issue was taken up also by Gina Kolata in her famous 1977 Science Magazine article: Catastrophe Theory: The Emperor Has No Clothes.  For this article she interviewed a great many experts on the topic.  Finally, Steve Smale's review of Zeeman's big book made clear that the advertized impact of Catastrophe Theory on the social sciences was somewhat simple minded,  

Exit Zeeman

We think that the current consensus is that the response may have been overblown. But the damage was done and the topic is now largely forgotten, but maybe not by everybody in the USA.  We refer here also to the 2007 paper by J. Barkley Rosser Jr: The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater?