"His proof in the early 1960s of the Poincaré Conjecture for dimensions bigger or equal to 5 is one of the great mathematical achievements of the 20th century." 
"... four decades of pioneering work on basic research questions which have led to major advances in pure and applied mathematics."

"... for his contributions to various aspects of differential topology." 

The NCB thanks Lenore Blum for her photograph of Smale taken at the City University of Hong Kong for the cover of the Mathematical Intelligencer, Spring, 1998.  The cover story featured Smale's list of the "Problems for the Next Century" inspired in part by Hilbert's list of 1900.