A brief history of the invention of "zero" can be found here. Meaning "worthless person" is recorded from 1813. As an adjective from 1810. Zero tolerance first recorded 1972, originally U.S. political language. Zero-sum in game theory is from 1944 (von Neumann), indicating that if one player wins X amount the other or others must lose X amount.
late 14c., "arithmetical symbol for zero," from Old French cifre "nought, zero," Medieval Latin cifra, which, with Spanish and Italian cifra, ultimately is from Arabic sifr "zero," literally "empty, nothing," from safara "to be empty;" a loan-translation of Sanskrit sunya-s "empty." Klein says Modern French chiffre is from Italian cifra.
The word came to Europe with Arabic numerals. From "zero," it came to mean "any numeral" (early 15c.), then (first in French and Italian) "secret way of writing; coded message" (a sense first attested in English 1520s), because early codes often substituted numbers for letters. Meaning "the key to a cipher or secret writing" is by 1885, short for cipher key (by 1835).
Figurative sense of "something or someone of no value, consequence, or power" is from 1570s.
"against, over against, opposite, on the opposite side; on the contrary, contrariwise," mid-14c., from Latin contra (prep. and adv.) "against," originally "in comparison with," ablative singular feminine of *com-teros, from Old Latin com "with, together" (see com-) + -tr, zero-degree form of the comparative suffix -ter-.
Middle English, from Old English nowiht "nothing," variant of nawiht (see naught). Meaning "zero, cipher" is from early 15c. Expression for nought "in vain" is from c. 1200. To come to nought is from early 15c. (become to naught, ycome to naught are from c. 1300).
also count-down, "the counting down of numerals in reverse order to zero before a significant event," also the preparations made during this time, 1953, American English, in early use especially of launches of rockets or missiles, from the verbal phrase (attested by 1954); see count (v.) + down (adv.).