The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

First Day of the 21st Century

Date: 12/01/1999 at 12:04:15
From: Rob Prejean
Subject: 1st day of 21st century??

What is the true date of the first day of the 21st century? From what 
day are we counting 2000 years?

Date: 12/01/1999 at 12:28:38
From: Doctor Rick
Subject: Re: 1st day of 21st century??

Hi, Rob.

A millennium is by definition "a period of 1000 years." The question, 
therefore, is, What span of years was covered by the first millennium? 
... the second millennium? etc.

If the first millennium began with the year 0 AD, then you could 
count: 0, 1, 2, ..., 98, 99 would be 100 years. Those 100 years would 
be the first century ("period of 100 years"). The second century would 
begin on January 1, AD 100. Similarly, the second millennium would 
begin on January 1, 1000, and the third millennium on January 1, 2000.

However, it's an historical fact that THERE WAS NO YEAR AD 0. The 
first century began on January 1, AD 1. You can follow the same logic 
as above to see that the first century encompassed the years 1, 2, 
..., 100, and the second century began on Jan. 1, AD 101. Likewise, 
the next millennium will begin on Jan. 1, 2001.

Here is where the history of math comes into the picture. If it were 
not for what follows, I would not care a bit when people want to say 
the millennium begins - it's just an arbitrary day with no deep 
significance. But I am fascinated by the history of math, and here we 
have one occasion when math history has a significant impact on things 
that are happening now. I have told others that I would like to see 
the year 2000 celebrated in schools as the Year of the Zero.

Here's why. The calendar was developed around AD 525, by Dionysius 
Exiguus. At that time in Europe, numbers were written in Roman 
numerals. Our Hindu-Arabic number system had not been invented. There 
was no such thing as zero; the earliest known use of a zero was in 
India 350 years later.

Using Roman numerals, Dionysius had no choice: numbers started with I. 
The year after I BC was AD I in his reckoning. There was no number to 
give to a year in between.

This seems very strange to us, who are accustomed to a number line of 
integers: -4, -3, -2, -1, 0, 1, 2, 3, 4, ... But Dionysius and his 
contemporaries had no concept of negative numbers either, at least not 
as a continuous progression from negative through zero to positive. 
"Negative" quantities were treated separately from positive 
quantities. It did not seem strange to them that the number of years 
from AD 10 to AD 40 is 30 - 10 = 20, but the number of years from 10 
BC to AD 10 is 10 + 10 - 1 = 19. The problems are different, and you 
solve them differently; that's the way it works.

If we had it to do over again, we would probably have used the number 
0 for the year in which Jesus Christ was born. Then his first birthday 
would have been in the year 1.

As it is, it would be a lot of work to renumber the years so that 
there is a year 0. Either we would have to rename AD 1 to AD 0, and 
likewise with all the years after - so that this is 1998, and the 
millennium is still a year away - or we would rename 1 BC to 0 AD, 
and every BC date would change, so all the ancient history books would 
need to be altered.

(By the way, if we were going to renumber the years, we'd probably 
want to correct Dionysius' other problem: his date for the birth of 
Jesus Christ was most likely 5 or 6 years late. This year really 
should be AD 2004; we missed the millennium.)

The best way is to keep things as they are, and make the year 2000 
"the Year of the Zero," an opportunity to remind ourselves what it 
used to be like before people had the brilliant idea of zero. 
"Nothing" has had quite an impact on the world!

- Doctor Rick, The Math Forum   
Associated Topics:
High School History/Biography
Middle School History/Biography

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.