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Which one is correct:
"A popular approach is the so-called immersed interface methods."
"A popular approach are the so-called immersed interface methods."
In Portuguese, the second one would be correct, because the verb "to be" sometimes agrees with the object instead of the subject. I was wondering if in English such exception also exists, of if the verb "to be" always agrees with the subject no matter what.
It depends on the meaning of "immersed interface methods." If it is to be considered a a whole, a single thing, then singular is correct, if it represents many different methods consider individually, then the subject should be plural.
Let me give you an example that might help clarify. I live in the USA. I might say:
a popular country is the United States.
"States" is technically plural, so this doesn't seem to fit, but "United States" is considered idiomatically a single entity.
To give another example:
On the football squad, a popular topic of conversation is girls.
Again "girls" is plural, but it is considered just one thing for the subject of this sentence.
So for you, you have two options:
A popular approach is the so-called "immersed interface methods."
To emphasize the unified nature of the methods, I have quoted it, which helps a lot in understanding. The qualifier "so-called" adds to this a lot, indicating that it is called that as a common idiomatic construction. Or alternatively:
Popular approaches are the the so-called immersed interface methods.
A modification of the first option:
A popular approach is the so-called immersed interface method.
English does not have any exception to the rule that to be should agree with the subject. Furthermore, idiomatic English would use the singular method rather than methods in this sentence, so the problem doesn't even apply.
You can't say 'A popular approach' (singular), and then use 'methods' (plural). So both are incorrect.
You can have either:
A popular approach is the so-called immersed interface method.
Popular approaches are the so-called immersed interface methods.
Singular and plural respectively, if there are more than one 'so-called immersed interface methods', then use the latter.
It is awkward to define a single thing as being multiple things regardless of language. There is a logical gap here.
Consider that you are describing a single approach but the approach admits multiple facets. Then you need more to the approach than the methods themselves. You need additionally to chose between them or integrate them.
The best solution is to admit this, and mediate the problem away by inserting 'to use'.
"A popular approach is to use ... methods"
