Sentence Correction: Subject–Verb Agreement: A Plural Subject Consisting of Singular Nouns that are Connected by "and"

Although mathematical physics are not the same as physical mathematics, the differences between the two are quite subtle and vague.

Incorrect.

This answer choice is grammatically incorrect. The singular subject physics does not agree with the plural verb are.

[[snippet]]

Physics is a confusing subject. It ends with -s, which might make us think of it as a plural subject, but it is, in fact, singular.

Excellent!

This answer choice corrects the original Subject Verb Agreement mistake by changing the order of the sentence so that the new subject is the plural "Mathematical physics and physical mathematics".

Although each of the individual subjects is a singular noun, connecting both physics and mathematics with "and' creates a plural subject made of singular nouns, and this subject correctly agrees with the plural verb are

While this answer choice changes the wording and structure of the original sentence, the original meaning does not change. Both Although and but are opposition words, and stating that X is not the same as Y equals stating that X and Y are not the same.  

Incorrect.

This answer choice is grammatically incorrect. The singular subject mathematics does not agree with the plural verb are.

[[snippet]]

Mathematics is a confusing subject. It ends with -s, which might make us think of it as a plural subject, but it is, in fact, singular.

Incorrect.

While this answer choice corrects the original Subject Verb Agreement mistake, removing the subordinate counjunction although creates a comma splice error. Remember that two independent clauses cannot be connected by just a comma. It changes the meaning of the original sentence as a result of removing the opposition word Although.

Incorrect.

While this answer choice corrects the original Subject Verb  Agreement mistake, it changes the meaning of the original sentence as a result of replacing the opposition word Although with the addition word and. The result is an illogical sentence because the two parts of the sentence are opposed to each other, a relation that was correctly expressed by Although but which the word and fails to express. 

In addition, this answer choice changes the meaning of the original sentence by omitting the word the. There is a difference between the differences (=specific, known differences) and differences (any, unspecified differences). 

Although mathematical physics are not the same as physical mathematics, the

Mathematical physics and physical mathematics are not the same, but the

While physical mathematics are not the same as mathematical physics, the

Mathematical physics is not the same as physical mathematics, the

Mathematical physics is not the same as physical mathematics, and

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