Is it farther or further?
"associate, fellow, comrade," mid-14c., also "companion" (late 14c.), from Middle Low German mate, gemate "one eating at the same table, messmate," from Proto-Germanic *ga-maton "having food (*matiz) together (*ga-)," which is etymologically identical with companion. Cognate with Danish and Swedish mat, German Maat "mate," Dutch maat, from German. Meaning "one of a wedded pair" is attested from 1540s. Used as a form of address by sailors, laborers, etc., since at least mid-15c. Meaning "officer on a merchant vessel is from late 15c.
in chess, "a condition of checkmate," c.1300, mat, from Middle French mat, from Old French mater (see mate (v.2)).
c.1500, "to equal, rival," 1590s as "to match, couple, marry, join in marriage," from mate (n.1). Also, of animals, "to pair for the purpose of breeding." Related: Mated; mating.
"checkmate," c.1300, from Old French mater "to checkmate, defeat, overcome," from mat "checkmated" (see checkmate (v.)).
mate 1 (māt)
Either of a pair of animals or birds that associate in order to propagate.
Either of a pair of animals brought together for breeding.
To become joined in marriage.
To be paired for reproducing; breed.
A friend of the same sex; a friend or companion: Give me a hand, mate (1380+)