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What is the rule determinating whether or not we need to capitalize them?
Sometimes I see "Math" ; "Physics" in the middle of a sentence, and sometimes lower case is used.

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Check here:

Generally, you should capitalise the names of school subjects only when you refer to a specific course:

  • I am excited to study history this summer.

  • I'll be taking History 101 at the community college.

But you always capitalise the names of languages:

  • I am excited to study Russian this summer.
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    I think the rule is "Capitalize Proper Nouns ; Else use lower case". In the reference you give : In "study history" , history is not a Proper Noun ; In "History 101" , IT is a Proper Noun of a Subject ; In "study Russian" , It is always a Proper Noun. – Prem Feb 23 '16 at 14:32
  • @Prem I agree. It surely applies here too. – Vim Feb 23 '16 at 14:35

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