Why did the 3rd Millennium and the 21st Century start on 1 Jan 2001?
A millennium is an interval of 1000 years and a century is an interval of 100 years. Because there is no year zero, an interval of 1 year has only elapsed since the start of the era, at the end of the year named 1AD. By a similar argument 100 years will only have elapsed at the end of the year 100AD. It is therefore clear that 2000 years had not elapsed until midnight on 31 December 2000. So the 3rd Millennium and the 21st Century began at the same moment, namely zero hours on January 1st 2001.