This is of course, just my opinion. You don't have to agree, and I would happily welcome a debate, but this is how I feel.
I would highly disagree that Stanley Kubrick is, "easily..." the greatest filmmaker of all time. His first three films are really bad, and his last six films show almost no signs of life from his cast, or show a character so devoid of any humanity you lose any emotional connection with them. Three truly great films do not make him easily the greatest filmmaker by any stretch of the imagination.
I would say 2001 would be his best film. It is a marvelous work, except that there is absolutely no emotional connection to any character in the film, which means that Kubrick's message at the end of the film is almost lost because one is constantly asking, "Why do I care?" Oh, and Andrei Tarkovsky outmatched Kubrick just four years after this film with Solaris.
Clockwork Orange claims to be a dark portrait against totalitarianism, but Kubrick makes his character so lacking in any fundamental human emotion that the film seems to support the things it does to him much more than it ever seems to be against them. An ambitious work that fails miserably, unfortunately.
His last three films suffer from this same fundamental problem. An inability on the audiences part to care for the people in Kubrick's films.
His greatest achievement is Paths of Glory. It has a deep understanding of man's relationship to death, and an ever deeper, and more pessimistic of portrait of the nature of power, and the inevitability of corruption.
Lolita, and Dr. Strangelove are great, also.