Just what are infinitives and why should you care?
An infinitive is a fundamental form of the verb, commonly preceded by to: to go, to work, to wish. The to is not a preposition but is a kind of prefix. You split an infinitive when you place an adverb between to and the rest of the infinitive.
For example, when we put another word between "to" and the verb, we're said to have "split" the infinitive, as in "to unsteadily run," "to boldly go," or "to quietly laugh." (This editor would avoid splitting infinitives in the preceding examples.) However, formerly outlawed, a split infinitive now is accepted if the sentence would lose clearness, smoothness, or force by avoiding the split.
Because a split infinitive raises many readers' hackles and is so easy to spot, however, good writers, at least in academic and technical prose, tend to avoid the split infinitive. Instead of writing "She expected her grandparents to not stay," then, we would write "She expected her grandparents not to stay."
It comes to this: if you split an infinitive wisely and judiciously, or, as in the case of author Gene Roddenberry, successfully, use it with care. This editor just can't tamper with such (successful) sentences as the following:
"Its five-year mission is to explore new worlds, seek out new life and new civilizations, and to boldly go where no man has gone before."
His first thought, when something went wrong, was to immediately hit the escape key—even when he was nowhere near a computer.
Rather than concern yourself about such matters, why not concentrate on writing? Then, simply hire The Word Lab, formerly Infinitives, split and otherwise,and let us worry about it.