Would you reference the years between 3000 and 3999 as the fourth millennium?
I assume so because the first millenium would be the years 0-999, the second 1000-1999, the third 2000-2999 et al.
However I want to make sure this is fairly common knowledge and that when I reference the year 3000 as the fourth millenium in my story, I won't confuse readers.
While technically it may be correct that 2001 was the beginning of the new millenium, I don't think anyone's going to quibble with you if you say 3000 is the first year of your fictional new millenium--mostly because we, as a society, are so entrenched in the idea that 1999 is the end of the old and 2000 is the beginning of the new. Largely because it's easier that way--years in the fourth millenium start with the digit 3, years in the fifth century start with the digit 4, etc.
[This message has been edited by djvdakota (edited October 03, 2004).]