The English-speaking world may be divided into (1) those who neither know nor care what a split infinitive is; (2) those who do not know, but care very much; (3) those who know and condemn; (4) those who know and approve; and (5) those who know and distinguish.
1. Those who neither know nor care are the vast majority, and are a happy folk, to be envied by most of the minority classes. “To really understand” comes readier to their lips and pens than “really to understand”; they see no reason why they should not say it (small blame to them, seeing that reasons are not their critics’ strong point), and they do say it, to the discomfort of some among us, but not to their own…
4. Just as those who know and condemn the split infinitive include many who are not recognizable, since only the clumsier performers give positive proof of resistance to temptation, so too those who know and approve are not distinguishable with certainty. When a man splits an infinitive, he may be doing it unconsciously as a member of our class 1, or he may be deliberately rejecting the trammels of convention and announcing that he means to do as he will with his own infinitives.
—Henry Watson Fowler
A Dictionary of Modern English Usage