Англичане выводят из магистра, а далее из meg-.
Т.е. Megal-великий.

"master (n.)
late Old English mægester "one having control or authority," from Latin magister (n.) "chief, head, director, teacher" (source of Old French maistre, French maître, Spanish and Italian maestro, Portuguese mestre, Dutch meester, German Meister), contrastive adjective ("he who is greater") from magis (adv.) "more," from PIE *mag-yos-, comparative of root *meg- "great" (see mickle). Form influenced in Middle English by Old French cognate maistre. Meaning "original of a recording" is from 1904. In academic senses (from Medieval Latin magister) it is attested from late 14c., originally a degree conveying authority to teach in the universities. As an adjective from late 12c."

Вроде очевидно, что и МАГ (magic) должно быть отсюда.
Но явно не сказано:
"magic (n.)
late 14c., "art of influencing events and producing marvels using hidden natural forces," from Old French magique "magic, magical," from Late Latin magice "sorcery, magic," from Greek magike (presumably with tekhne "art"), fem. of magikos "magical," from magos "one of the members of the learned and priestly class," from Old Persian magush, possibly from PIE *magh- (1) "to be able, to have power" (see machine). Transferred sense of "legerdemain, optical illusion, etc." is from 1811. Displaced Old English wiccecræft (see witch); also drycræft, from dry "magician," from Irish drui "priest, magician" (see druid)."

Тоже гипотеза.

Корень MAG
"Greek megas "great, large;" Latin magnus "great, large, much, abundant," major "greater," maximus "greatest;" Middle Irish mag, maignech "great, large;" M.Welsh meith "long, great""

Заметим, что сюда же MAX. А мы помним, что X могло быть славянским Ж.

Получается, что-то типа Ж, З, ЖД (?)? СТ (?).
Может быть МАЖ, МАЗ МАЖД и пр.

МАЖ можно получить из ВАЖный (отвага, уважение) переходом В-М.
Как переход ВЕД-МЕД.

Но ВАЖный Фасмер выходит из нем. WAGA =весы, тяжесть.
"ВАЖный" это отдельное интересное непонятное слово, так как наши весы вроде как не от ВАГи, а от ВЕШАТЬ, ВИСеть, может быть ВЕСло (как рычаг).