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There is an astonishing amount of controversy over this subject, as evidenced recently in the year 2000 when many people all over the world celebrated what they thought was the beginning of a new millennium (a period of a thousand years), but many more did not so celebrate until 2001. This is because many people think that the Nineteenth Century started with the year 1801 and ended with the year 1900, and the Twentieth Century (recently concluded) therefore started in 1901 and ended with the year 2000. The Twenty First Century, and the New Millennium, by that reckoning did not begin until the year 2001. Confused yet? Yep. So is everyone else. Personally, I'm a the-21st-century-started-with-2001 man, but hey, that's just me.
The controversy originally arose because there was never a year zero. The commonly used (Gregorian) calendar is supposed to begin with the year of Jesus of Nazareth's birth, considered to be the year one. In fact, this is controversial since no one knows exactly when Jesus was born, and Christian scholars of all denominations have been cudgeling each other over this since, well, the year one. Or zero. Depending.
For centuries everyone used a calendar called the Julian Calendar, after Julius Caesar who approved it. That calendar was a 46 BC (Before Christ) reform of the old Roman Calendar, and it declared every fourth year to be a leap year, adding one full day. This was because the smarty Romans had figured out that the sidereal or "star" year is actually 365 + 1/4 days long. Sort of. So every four years you just added a day and, presto, you were back in synch with the stars. This worked great for a while until it was discovered around 1582 (Common Era) that the extra quarter day wasn't really a whole quarter day, but just a hair and a squeak shorter, so by 1582 the calendar was out of synch with the sidereal year by ten days and was lousing up the celebration of Easter. Not good.
The Pope at the time, Gregory XIII, went, "eek," and fixed it by dropping the ten extra days and decreeing that henceforth every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 was not a leap year; the year 2000 was a leap year.
Still confused? It gets worse. In the first place, almost everybody went, "yay," and adopted the cool new Gregorian calendar because it was much more accurate. Except some of the fellows in the old Orthodox Church and a few others, who thought the old Julian Calendar worked just fine (some of them are still using it to this day, which is why the Orthodox Church celebrates Christmas on what most of the rest of us think of as January 7th). The other problem is that as technology has improved and we now have atomic clocks and orbiting telescopes, the actually really truly sidereal year has been much more refined -- down to the nanoseconds, so every so often they have to tinker with the calendar anyway to bring it into phase with the sidereal year. Oh, and the earth is slowing down in its orbit, too, just to louse things up further. (And you thought you had problems?)
All of this is just to determine just exactly when the earth reaches that point in its orbit where it was at exactly this time last year, and the year before that and so on. But the Gregorian calendar that most of us use is pretty accurate for most purposes, since humans need to be able to tell time in order for us to know when to do stuff, like go to work -- or not. The funny thing is, none of the other animals have watches or calendars and they muddle along just fine.
Humans are weird.
Comments: Yes this can get people confused.
Also, it does attract a lot of pedants as well as "anti-pedants"
I think the "New Millennium" celebrations at the start of 2000 were a bit of a disaster for "logic".
Also, there are some complications as discussed above.
However, it's generally agreed by authoritative sources that the 20th Century did indeed end at the end of the year 2000 and the 21st
Century began at the start of 2001.
Certainly things would be different if we used "year zero", as astronomers do.
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