For a "PL" or "smooth" homotopy n-sphere, in 1960 Stephen Smale proved for formula_1 that it was homeomorphic to the "n"-sphere and subsequently extended his proof to formula_2; he received a Fields Medal for his work in 1966. Shortly after Smale's announcement of a proof, John Stallings gave a different proof for dimensions at least 7 that a PL homotopy "n"-sphere was homeomorphic to the "n"-sphere using the notion of "engulfing". E. C. Zeeman modified Stalling's construction to work in dimensions 5 and 6. In 1962, Smale proved a PL homotopy "n"-sphere was PL-isomorphic to the standard PL "n"-sphere for "n" at least 5. In 1966, M. H. A. Newman extended PL engulfing to the topological situation and proved that for formula_3 a "topological" homotopy "n"-sphere is homeomorphic to the "n"-sphere.