In an attempt to improve English, which was considered inferior to Latin, prescriptive grammarians devised rules for English grammar based on the model of Latin grammar. One of these rules is that it is wrong to split an infinitive.
Guess what. In Latin, the infinitive is a single word. It can't be split with anything short of an atom smasher. But in English, the infinitive form of the verb is usually accompanied by the particle "to": "to walk," "to run," "to think," "to feel," "to be." As a two-word unit, the infinitive in English almost begs to be split, at least sometimes. Think of the S. S. Enterprise and its mission "to boldly go where no man has gone before."
Usually, there is no need to split an infinitive, and to do so gratuitously is just asking for trouble from the grammar police. But if placing the infinitive's adverbial modifier either before or after the complete infinitive actually alters your intended meaning or makes it ambiguous, then by all means, go ahead and split the infinitive. Even the Oxford English Dictionary now recognizes the split infinitive as a grammatically valid structure.
But that warning about the grammar police should not be taken lightly. As a writer, you will be judged by many people who know only those inflexible rules of grammar and usage that they were taught, often by teachers who did not have a very solid grounding in grammar, and who therefore relied on lists of "rules" in teaching the subject to their students.
Whether they are "merely" readers, or whether--as is often the case--they are in a position to assign a grade to your writing or to accept or reject it for publication (or you for hiring) based on their perception of your competence as a writer, you should avoid giving them reason to doubt that competence.
This same caveat applies to my articles concerning the acceptability of ending a sentence with a preposition. (To read them, click here and here.) It far is better to split an infinitive or to end a sentence with a preposition than to write awkward or ambiguous sentences in an attempt to avoid breaking such supposed rules. But if you are careful, you won't often write yourself into a corner where you are forced to make such a choice.
If I am advising you generally not to break these "rules," then why do I bother to tell you that they aren't even really valid as general rules? Well, sometimes even the most careful writer will be in a position where his precise meaning is best conveyed in a sentence that raises the problem of splitting an infinitive or ending a sentence with a preposition. When that happens, I want the writer to know that he doesn't have to write a ridiculous sentence just to avoid violating some so-called rule.
And if the grammar police do come knocking at his door, at least he will be able to argue intelligently for the validity of his choice.