I'm facing a difficulty about referring to previously mentioned words. It's something that bothers me a lot about the English language. Please consider
Mathematicians can use these theorems to their advantage.
Mathematicians can, to their advantage, use these theorems.
Which is more correct? The first sounds more natural and most people would probably say it's correct.
However, I would think that technically the first is wrong and the second is correct, even though the second is a bit more unnatural. Why? Because in the first, their is referring to the last thing mentioned, namely these theorems, which is absurd. In the second, their actually refers to the mathematicians, as it should.
What do you think? If the first is (also) correct, my question is simply this: Since when can sentences be counted as being correct just because they happen to make sense from the context?