I did try to tell people at the time, but most people didn't listen. Prince has a lot to answer for, if you ask me. However, if the first year of the century was 2001, as it was, then this is the 21st year of the 21st century.
Shall I lay it out? In simple terms?
How long is a century? 100...
The last day of last century before we went from BC to AD was 31st December 1BC. The first day of the first year of the first century started on 1st January 1 AD. There was no 0AD. Therefore, the 21st century started on 1st January 2001. That's all you need to know.