In the phrase, "all ready," the word "all" acts as an adverb meaning "entirely" or "completely." "Already" is an adverb meaning "previously" or "so soon." In your example, you would use "All ready.": "(Having been) all ready for the university by the age of ten, John Stuart Mill waited until his mid-teens to enter Oxford." You could also say: "(Having been) entirely ready for the university by the age of ten, John Stuart Mill waited until his mid-teens to enter Oxford." Note: the (Having been) is optional, but provides a little bit more of a gramatical context for the first clause. Some more examples: "already" "I already did that." = "I previously did that." (The first sounds more common) "Oh, you're done already?" = "Oh, you're done so soon?" "all ready" "I am all ready to go." = "I am completely ready to go."