Is the following sentence grammatically correct?
1.) Oscar believed that the sum of two and two is four.
In this case it seems to make the most sense to mix the past tense "believed" with the present-tense "is." If the sentence were changed to,
2.) "Oscar believed that the sum of two and two was four,"
then the meaning of the sentence would be changed.
When the verb is was used, the sentence meant that Oscar had a belief about the present (relative to him). But when the verb was was used, the sentence meant that Oscar had a belief about the past (relative to him).
Consider this sentence that is structurally parallel:
3.) Oscar believed that the killer of J.F.K. was Lee Harvey Oswald.
In this case it seems to make the most sense to not mix verb tenses. Presumably this is because Lee Harvey Oswald's assassination of J.F.K. is an event solely in the past.
I find myself needing to write sentences of this form often, and it always puzzles me whether this mixing of verb tenses is acceptable.