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Although mathematical physics are not the same as physical mathematics, the differences between the two are quite subtle and vague.
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.
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.
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.
While this answer choice corrects the original Subject Verb Agreement mistake, it does not fit into the original sentence: the word Although that connected the two parts of the original sentence is omitted.
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).