For many years, students were taught to never split infinitives, as I have just done, despite the split infinitive breaking no grammatical rule. Some now deride the rule as an example of how English teachers liked to torture students for no good reason, but few pity the poor teacher who used this and other guidelines to encourage students to study their own writing with a critical, curious eye rather than to rely on easy, colloquial, or poor habits. Yes, splitting an infinitive is grammatically acceptable, but that does not mean you always want to split your infinitives.
To split an infinitive is to place an adverb between the to and the root verb. Using everyone’s favorite example, the unsplit infinitive to go can be split into to boldly go. To split an infinitive is thus to shift the rhythm and remove emphasis from the verb and place it on the adverb—often a weak, unemphatic, and superfluous word form overused by insecure writers; many adverb-verb combinations can be replaced with a more specific and succinct verb. However, a split infinitive can, at times, form a more approachable voice. An example from The Elements of Style captures this well: “I cannot bring myself to really like the fellow” would sound unbalanced and lightly formal if the infinitive were not split: “I cannot bring myself really to like the fellow.”
Keep your infinitives unsplit unless voice, rhythm, or emphasis convinces otherwise. It requires a practiced ear to recognize when a split infinitive improves on an unsplit infinitive (or a more specific verb); if you’re unsure, do not split the infinitive.