The expression is non-unique: the manipulation of handlebody decompositions is an essential ingredient of the proof of the Smale h-cobordism theorem, and its generalization to the s-cobordism theorem.
Assuming smoothness the existence of a Heegaard splitting also follows from the work of Smale about handle decompositions from Morse theory.
Smale's paradox can be done using isometric embedding of .
The solution by Smale, in 1961, of the Poincaré conjecture in higher dimensions made dimensions three and four seem the hardest; and indeed they required new methods, while the freedom of higher dimensions meant that questions could be reduced to computational methods available in surgery theory.
In computation theory, the Blum–Shub–Smale machine, or BSS machine, is a model of computation introduced by Lenore Blum, Michael Shub and Stephen Smale, intended to describe computations over the real numbers.
Since 2002 Smale is a Professor at the Toyota Technological Institute at Chicago; starting August 1, 2009, he is also a Distinguished University Professor at the City University of Hong Kong.
With integration high up on the agenda, the now 18-month-old website was updated by Jack Smale and Julian Farmer with even greater core presence on Facebook and Twitter.