Should I use the singular or plural verb in mathematical formulae ("Two and two make/makes four")?

Solution 1:

Singular and plural are both correct.

The singular form is also used because "two and two" is an arithmetic formula. The verb agreement in that case is with the formula as a single entity.

• Two and two makes four.

• Two plus two is four.

• Four times four divided by two is
  eight.

In your example in particular, Google indicates that the plural form occurs more often:

"two plus two make four" = 353K results
"two plus two makes four" = 77K results

And while Google hit counts are notoriously, the result is supported by Google Ngrams.

Solution 2:

"I know that two and two make four—& should be glad to prove it too if I could—though I must say if by any sort of process I could convert 2 & 2 into five it would give me much greater pleasure."
– George Gordon Noel Byron.

"When speculation has done its worst, two and two still make four."
– Samuel Johnson.

"Freedom is the freedom to say that two plus two make four. If that is granted, all else follows."
– George Orwell.

Both "make" and "makes" are correct usages; I prefer saying "two and two make four" — I find it more natural because when I use this idiom in a sentence, I am not talking math!
(When I'm talking math, I prefer using the term "plus": "two plus two is three point one four".)

And I love patterns (when they make sense)!

Observe the pattern:

• John makes money.
• Jane makes money.
• John and Jane make money.
• Two and two make four.