I noted in an earlier post that in 1893, Milne used “are” as a casual speech reading of the equality sign, rather than the “is” that I’m used to. Adam Liss notes that “are” is also used in Danny Kaye’s 1952 movie Hans Christian Andersen. On the other hand, by the early 1960s, the Beatles were using “is”. Assuming there wasn’t a radical grammatical shift in the intervening decade, I assume that there was some period of transition, and also that there are still “are” speakers today.
Thinking about this, I’m also led to reflect on the shift from “the data are” to “the data is” (and I’m aware there are still plenty of people who insist on “the data are”). In the case of “data”, the argument for “are” relies on the fact that “data” is the plural of “datum”; the argument for “is” relies on the assumption that “data” has become a count noun and, as such, ought to behave like “spaghetti”. Nobody would say “the spaghetti are very tasty!” A further argument would be that “opera” (once a plural) has become a firmly singular count noun with a plural of its own. But then, the rebuttal is that “datum” is still an active enough word in English, with a clear semantic tie to its plural, while “spaghetto” is not English at all and “opus” has lost its immediate semantic tie to “opera”.
With regards to “one and one are two” vs “one and one is two”: Milne uses “are” because he’s relating groups of things (“The sign + means and, and the sign = means are” [p. 12]). Two apples are two apples. Five books are five books. Using “are” reinforces that even when the unit is abstract (e.g., “two and two”), we’re adding numbers of objects. Using “is” further abstracts numbers away from this notion. Logically, and from a teacher’s perspective, I prefer “are”.
However, when Milne introduces the mathematically rigorous terms, he uses “equals” instead of “equal”: “3 + 2 = 5 is read 3 plus 2 equals 5” (p. 89). The use of the singular puts the emphasis on the operation rather than on the objects. The result of adding three and two is five. Three apples and two apples are five apples.
This shift indicates that Milne is still at least tacitly acknowledging the shift from the concrete (object-oriented) mathematics to the abstract (operator-oriented) mathematics, he’s just doing it later than the current norm.