Students sometimes find the phrase 'split inf.' in the feedback on their assignments. (It is short for split infinitive.) Probably the best-known 'split infinitive' is "To boldly go where no man has been before," the opening line from the credits of the television series Star Trek (and Hollywood films). It is often derided by British academics and schoolteachers of a certain age who would rather it said 'To go boldly'. (This would be less striking, if more correct.) The Split Infinitive is an area in which formal academic English is stricter than 'ordinary' English. (It also seems to be true that British academic English seems to be stricter than American academic English.) Here is an explanation of their pedantry.
The infinitive is the form of the verb which is usually used to put that verb in its alphabetical place in dictionaries, or similar word-lists. It is usually written in English as "to do": in dictionaries, it is usually simply do, v.
In most European languages, the infinitive is expressed in just one word - the English "to go" is ire in Latin, ἰέναι in Greek, andare in Italian, aller in French, and gehen in German. This is one main reason why it is said that in English we should treat the infinitive essentially as one word, and not split it by putting another word or phrase between "to" and the verb it introduces. There is another, more important, reason. Splitting the infinitive sometimes leads to ambiguity, or to clumsiness, or to lack of precision.
Consider, for example, the difference between "the argument is difficult to conclusively demonstrate" and "the argument is difficult to demonstrate conclusively". In the second version the emphasis is properly on the word "conclusively" (it might contrariwise be possible to demonstrate the argument in such a way that it did not provide a final compelling demonstration). In the first version, there is no demonstrable emphasis: the adverb feels, to a careful reader, to be floating, not clearly attached to any particular word.
"To clearly write an essay" does not mean the same as "To write an essay clearly". The first version actually makes matters less clear by putting the focus on the noun (the essay), and taking it away from the adverb (the clarity of the essay). The second, preferable, version applies the adverb 'clearly' with better relevance to the Verb + Object combination 'write an essay'.
On the other hand, Burchfield's Fowler's advice is that the split infinitive has its uses. Editors of AWE agree: it allows English a flexibility and shades of meaning that other languages lack, so why deny yourself the use of it and tie one hand behind your back? Consider, for example, the difference between "our aim is not to affect passengers" and "our aim is to not affect passengers". The second states with absolute clarity that 'what we are trying to do' is the negative aim: our efforts are to make sure that passengers are not affected. The first says very nearly the same thing, but more as a secondary or incidental goal: it implies that 'our main aim is to do [something else], but we will, while doing that, try not to let it cause trouble to the passengers'. Nevertheless, some academics will still feel distaste at such a sentence: as always, good writers are sensitive to their readers, and a student who knows that the teacher marking the essay dislikes split infinitives is unwise to split them.
- Historical note: It appears that the rule was first stated in English about 1670, by John Dryden, and is an echo of Latin - the language of scholarship in those days. In English, it is just a fussiness invented by a writer who wanted to give himself grounds for feeling superior to others. You may judge its value by the fact that when Dryden had stated it, he then produced a second edition of his own poems in which all split infinitives were removed.
When tempted to split an infinitive it would be appropriate to remember the apothegm of the Latin writer Quintilian - "aim not at being possible to understand, but at being impossible to misunderstand."