It depends on the discipline.
People often think there is a typo on my “About Grammar Girl” Web page because it says I have an undergraduate degree in English (capitalized) and a graduate degree in biology (lowercased).
Although I’ve never claimed to be perfect, that isn’t a typo.
Degree Names from Proper Nouns Are Capitalized
"English" is capitalized because it's derived from a proper noun ("England"), and biology is lowercased because it is not derived from a proper noun. Similarly, "Spanish," "Italian," and "German" are capitalized because they are derived from the country names "Spain," "Italy," and "Germany."
Degree Names from Common Nouns are Lowercased
Subject names such as "chemistry," "math," and "visual arts" are not capitalized because they don't come from proper nouns.
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