Solution of/to/for equation

Question

A recent question to when to use of and when for/to for solution suggested that of appears only in context of chemistry, and the word means something very different then. But I recalled almost universally finding

-2 and 2 are the solutions of the equation x^2 = 4

I consulted the dictionary and to my surprise I found:

2. Mathematics A value or values which, when substituted for a variable in an equation, make the equation true. For example, the solutions to the equation x^2 = 4 are 2 and -2.

I consulted the ngram and it made me even more confused than before.

It seems like solution to the equation is a relatively new trend, but picking up.

So, what's the official stance on correctness of the preposition to go with solution in mathematics?

Answer 1

Prepositions are versitile words with overlapping meanings. There are several usages in English where more than one preposition could be used, with little or no change in meaning. Let me reiterate that: There are several usages in English where more than one preposition could be used, with little or no change of meaning.

The Ngram is interesting, but hardly surprising. There's no "official" correct preposition here.

Answer 2

I think there is a slight difference in meaning: solution of indicates that some set of solutions is known to exist, while solution to reflects no such knowledge. Consider these examples:

A. I have not found any solutions of this equation.

B. I have not found any solutions to this equation.

My intuition is that in (A), the speaker is treating it as a given that the equation has solutions, and just can't find them; in (B), however, it is possible that there are no solutions.

This intuition maybe comes from the fact that only mathematical systems can be said to definitively possess solutions. Solution to is much more common than solution of when the word is used in the context of real-world issues: a solution to the debt crisis.