Mezue ahịrịokwu na-esonụ: Nchịkọta ahụ malitere na 1957, na-ewepu "Egwuregwu nke Narị Afọ" a ma ama megide Donald Byrne na 1956 (egwuregwu a gụnyere na obere ọrụ, nke a na-akpọ "Egwuregwu Chess nke Bobby Fischer", nke e bipụtara na 1959). Ọnwụ atọ ahụ bụ Tal na asọmpi ndị Candidates 1959, Spassky na Mar del Plata 1960, na Geller na Skopje 1967. N'etiti ihe ndị a na-eme bụ naanị nzute ya na onye mmeri ụwa bụ Mikhail Botvinnik, na 1962 Varna
Egwuregwu Olimpik. Egwuregwu a nwere mpempe nyocha kachasị ogologo n'akwụkwọ ahụ, ebe Fischer kwubiri na ọ tụfuru mmeri na njedebe. Botvinnik mechara gbaghaa nke a, site n'aka otu n'ime ụmụ akwụkwọ ụlọ akwụkwọ chess ya, Garry Kasparov dị afọ iri na atọ. Nke a bụ otu n'ime ihe atụ ole na ole nke nyocha Fischer nke a na-enyo enyo. N'ime mmeri ndị ahụ bụ mmeri mbụ ya nke onye isi Soviet, Paul Keres na Zurich 1959, na mmeri ya dị ka Black na Robert Byrne na 1963/64 US Championship. Enwere egwuregwu asaa site na asọmpi Candidates mbụ ya na 1959, mana naanị abụọ site na nke abụọ ya na Curaçao 1962. Egwuregwu niile na-egwuri egwu n'okpuru ọnọdụ asọmpi ma e wezụga egwuregwu enyi na ụlọ nke Reuben Fine na 1963 na mmeri site na njem ngosi ngosi nke Fischer na 1964 nke US.