From the Wikipedia article on Neil Armstrong, section "First Moon Walk"
Although the official NASA flight plan called for a crew rest period before extra-vehicular activity, Armstrong requested that the EVA be moved to earlier in the evening, Houston time. Once Armstrong and Aldrin were ready to go outside, Eagle was depressurized, the hatch was opened and Armstrong made his way down the ladder first.
Armstrong describes the lunar surface.
At the bottom of the ladder, Armstrong said "I'm going to step off the LEM now" (referring to the Apollo Lunar Module). He then turned and set his left boot on the surface at 2:56 UTC July 21, 1969, then spoke the famous words "That's one small step for [a] man, one giant leap for mankind."
Armstrong had decided on this statement following a train of thought that he had had after launch and during the hours after landing. The broadcast did not have the "a" before "man", rendering the phrase a contradiction (as man in such use is synonymous with mankind). NASA and Armstrong insisted for years that static had obscured the "a", with Armstrong stating he would never make such a mistake, but after repeated listenings to recordings, Armstrong admitted he must have dropped the "a". Armstrong later said he "would hope that history would grant me leeway for dropping the syllable and understand that it was certainly intended, even if it was not said – although it might actually have been".
Armstrong on the Moon
It has since been claimed that acoustic analysis of the recording reveals the presence of the missing "a"; Peter Shann Ford, an Australia-based computer programmer, conducted a digital audio analysis and claims that Armstrong did, in fact, say "a man", but the "a" was inaudible due to the limitations of communications technology of the time. Ford and James R. Hansen, Armstrong's authorized biographer, presented these findings to Armstrong and NASA representatives, who conducted their own analysis. The article by Ford, however, is published on Ford's own web site rather than in a peer-reviewed scientific journal, and linguists David Beaver and Mark Liberman wrote of their skepticism of Ford's claims on the blog Language Log. Although Armstrong found Ford's analysis "persuasive", he expressed his preference that written quotations include the "a" in parentheses.
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80. Goddard, Jacqui (October 2, 2006). "One small word is one giant sigh of relief for Armstrong". The Times (London). Retrieved August 28, 2007.
81. Ford, Peter Shann (September 17, 2006). "Electronic Evidence and Physiological Reasoning Identifying the Elusive Vowel "a" in Neil Armstrong's Statement on First Stepping onto the Lunar Surface" (reprint). CollectSpace.com. Retrieved August 28, 2007.
82. "Software finds missing 'a' in Armstrong's moon quote". CNN.com. Associated Press. October 1, 2006. Archived from the original on October 4, 2006. Retrieved August 28, 2007.
83. Smith, Veronica (October 2, 2006). "Armstrong's Moon landing speech rewritten". Cosmos Magazine. Agence France-Presse. Retrieved August 29, 2007.
Language Log. "One small step backwards". (including audio)
Language Log. "One 75-millisecond step before a "man"".
Language Log. "Armstrong's abbreviated article: the smoking gun?".
Language Log. "Armstrong's abbreviated article: notes from the expert".
Language Log. "First Korean on the moon!".
Language Log. "What Neil Armstrong said".
85. Carreau, Mark (September 29, 2006). "High-tech analysis may rewrite space history". Houston Chronicle. Retrieved September 30, 2006.
Y lo cierto es que yo no recuerdo bien qué es lo que oí en aquella madrugada de verano de 1969.... pero allí estaba, delante de la tele, pendiente de Armstrong y de Aldrin, como medio mundo.
Hasta siempre, Comandante.