If you're an historian, 1 AD was preceded by the year 1 BC, and 1000 AD was 1999 years after 1000 BC.
If you're an astronomer (or, I submit, any sensible human being), the year +1 was preceded by the year 0, and the year 1000 was 2000 years after the year -1000. The solar eclipse that occurred (according to astronomers) on Oct 13 -982 also occurred (according to historians) on 13 Oct 983 BC. Both are accepted schemes within their disciplines, and fortunately, there's not much room for confusion. If you enter a year as -982 or 983 BC in the astronomy software I wrote, the code can figure out which year you "really" meant without ambiguity.
I can grudgingly accept the idea that the 20th century ran from 1901 Jan 1 to 2000 Dec 31, but only if you will accept the idea that the 1900s span from 1900 Jan 1 to 1999 Dec 31. Or that a date in 1980 would be both at the start of the '80s and at the end of the 198th decade.