Unless the subject is capitalized for other reasons. Usually, that means because it is the name of a language. "This semester, I am taking English, history, geometry, Spanish, and biology." It would always be wrong to write, "... taking english, history, geometry, spanish, and biology," because the names of languages are always capitalized.
Proper adjectives are also capitalized in the names of uncapitalized subjects: "I am going to Oxford to study British history, molecular biology, and Russian literature." It would always be wrong to write, "... to study british history, molecular biology, and russian literature."
"euclidean geometry" is a situation where a proper name (it would be incorrect to refer to the Greek mathematician as "euclid") has become a common, non-capitalized adjectives.