Split infinitives are, after passive voice, a grammatical construct that calls for the most pissed off responses from either side of the argument. A split infinitive means to literally split the infinitive (the verb form preceded with to) and stuff another word or phrase inside. Take to triple. That's an infinitive verb. Now let's murder that son of a bitch: Apple stocks are expected to more than triple in profits. Doesn't that feel fine? And, since every article that discusses split infinitives uses the next example, so will I: To boldly go where no man has gone before.
The craze against split infinitives started when someone decided that English should follow Latin grammar; Latin infinitives are one word (e.g. videre = to see). It would be stupid to split a word in two and stuff something else inside, wouldn't it? But if you do, call it tmesis, and it becomes a literary device. I leave it to the reader to decide whether it makes sense to place the grammar of an old language upon a modern language. But if you say yes we better also love passive voice, because Vergil and those poetic Latin authors used it every chance they had. (When it comes to passive voice, English classes teach bugger all, but Latin clears it up good.)
If I need even more support, I'll call into play The New Yorker, which some hail as the epitome of professional writing and grammar. The New Yorker accepts split infinitives, or so claims Mary Norris, the magazine's copy editor.
Before we split our infinitives with sharpened axes, let's see what really bothers people about them. To charmingly cut an infinitive is to gaspingly call attention to the word stuffed in the hole. That word needs to be perfect and flow well with the rhythm of the sentence. If we stuff any word we like, as I did, the result is juvenile at best. Split your infinitives all you want, but do so with careful intent: if you mess up, we will know.