> Moreover, he added, “When you look at the history of mathematics, it turns out that [zero] is an extreme latecomer in our culture as well.” Historical research finds that human societies didn’t begin to use zero as a number in their mathematical calculations until around the seventh century.
There are huge differences between zero as the concept of "none" (I had five cows and someone took them all away, how many do I have?), zero as a more formal integer value (e.g. solution to 2 + 7 - 4 + x = 5), zero as unit placeholder (e.g. 101 dalmations), and zero as a real number (on the continuum from positive to negative rationals and irrationals).
When people make claims about "zero" they're essentially meaningless unless they specify which meaning of zero they're talking about.
I really wonder how zero came to be, was it a need to homogenize the algebraic tools (we have nice operations and want to reify the 'nothing' dead end into something that can be kept chugging along) or something else /
The ancient Greeks understood division and reciprocals from the perspective of inverting multiplication.
I have to imagine that the multiplicative identity (1) and additive identity (0) were also known at that time. They really figured out everything else there is to integer-based math.
They failed at irrational numbers (like sqrt(2)). But their mastery of integers was outstanding. Perhaps 0 wasn't used on the number-representation yet, but the concept had to have been known.
There's a whole book on this history of zero you may enjoy called "Zero: The Biography of a Dangerous Idea" that goes into the whole story of how it came to be including problems and resistance along the way
(mods I promise I'm not here to shill this book but people keep wondering about the history and that's a great resource that I like XD)
I think most such research don't delve upon ancient India wherein use of zero with a proper modern like numerals have been extensively observed at least since thousands of years [0].
> Hindu units of time are described in Hindu texts ranging from microseconds to trillions of years, including cycles of cosmic time that repeat general events in Hindu cosmology.
You don't appreciate zero until you try to invent a positional number system. In the past, when they used positional system they would often just leave a blank spot in the place of zero. This inevitably leads to errors. Is that two numbers or one number with zero between? How do you distinguish between 1 and 10?
Source:
A popular science book
"The history of numbers or the history of a great discovery" (Georges Ifrah)
Contains some fun chapters like "How to count if you can't count". For example if natives in a stereotypical jungle want to count numbers to a holiday. They memorize a sequence of items, for example body parts: little finger of one hand, palm, wrist, forearm, arm, shoulder, neck.... then they measure once and conclude one needs to wait as many days as there are from the little finger on left hand to, say, navel.
> Moreover, he added, “When you look at the history of mathematics, it turns out that [zero] is an extreme latecomer in our culture as well.” Historical research finds that human societies didn’t begin to use zero as a number in their mathematical calculations until around the seventh century.