Does the new millennium begin on January 1st, 2000? Or must we wait another year, until New Year's Day, 2001?
The year 2000 has such a grip on the popular imagination that it seems futile to worry about the answer, but here it is:
Because the year 1 B.C. was followed immediately by A.D. 1. There was no "year zero", and so A.D. 1 was the first year of the Christian era. The first century of that era was complete after one hundred years, at the end of A.D. 100. The second century began with the year A.D. 101 and ended with A.D. 200.
The 19th century ran from 1801 to 1900 inclusive, and the 20th century from 1901 to 2000. The year 2000 is the last year of the 20th century and of the second millennium.
Calendar pedants will celebrate the beginning of the year 2000 (with the rest of humanity!) and the year 2001.