Zero came on the scene around 200 C.E. and was used merely as a placeholder for other numbers. For example, zero was used in numbering systems to differentiate between 1 and 10 and 22 and 202. Thus, it was a form of mathematical punctuation. It took hundreds of years until it was used as a number in its own right (i.e. as the average of 1 and -1).
The use of zero fully as a number occurred in India in the fifth century C.E. and the concept of zero didn’t arrive in the Western world until about 1200, most famously delivered by Italian mathematician Fibonacci (aka Leonardo of Pisa), who brought it, along with the rest of the Hindu-Arabic numerals, back from his travels to north Africa.
In the 7th century, Indian mathematician Brahmagupta recorded the earliest known statement of exactly how zero works: “When zero is added to a number or subtracted from a number, the number remains unchanged. A number multiplied by zero becomes zero.”
It is shocking to me that the concept of zero came into existence so late, many centuries after the great Classical Greek Period and also long after many of the mathematical achievements of mathematicians in the Middle East. It had not occurred to earlier civilizations, even to the Greeks, that it would be useful to have a number which represents the absence of any objects.
Connected with the delay in developing the concept of zero is the fact that zero must be distinguished from nothingness (null). It is possible that it was the inability of earlier peoples to perceive this distinction which accounts for their failure to discover the zero. This was very understandable because the difference is very subtle. You can see the distinction of zero and nothing by considering the following examples from David Foster Wallace (of all people – the talented fiction writer): “Imagine there’s a certain math class, and in this class there’s a fiendishly difficult 100-point midterm, and imagine that neither you nor I get even one point out of 100 on this exam. Except there’s a difference: you are not in the class and didn’t even take the exam, whereas I am and did. The fact that you received 0 points on the exam was thus irrelevant—your 0 means N/A, nothing—whereas my 0 is an actual zero. Or if you don’t like that one, imagine that you and I are respectively female and male, both healthy 20-40 years of age, and we’re both at the doctor’s, and neither of us has had a menstrual period in the past ten weeks, in which case my total number of periods is nothing, whereas yours here is 0—and significant. End examples.”
You’ve always loved the number zero.
I see the difference.