Quotes from René Thom

The essential point of view advanced here is this: the stability of every living being, as of every structurally stable form, rests, in the last analysis, on a for- mal structure—in fact, a geometrical object—whose biochemical realization is the living being.

At a time where so many scholars are calculating, is it not desirable that some, who can, dream?

The subjects mentioned in his title, Structural Stability and Morphogenesis, have a much wider reference; and he relates his topological system of thought to physical and indeed to general philosophical problems.

There seems to be a time scale in all natural processes beyond which structural stability and calculability become incompatible. In planetary mechanics this scale is of such an extent that the incompatibility is not evident, whereas in quantum mechanics it is so short that the incompatibility is immediately felt, and today the physicist sacrifices structural stability for computability. I hope that he will not have cause to regret this choice.

The problem of stability is then: Is the collection of structurally stable vector fields everywhere dense in the space B of all vector fields? A partial answer has been obtained recently: yes, when dimension m is less than or equal to 2 (Peixoto[18]), no when dimension m is greater than or equal to 4(Smale[22]), or 3 (Smale and Williams[24]).

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