What is zero and why is it so important. Was there ever a time when there was no zero, and who discovered its importance? Any info greatly appreciated.
Yes, there was a time when zero wasn’t used as a number.
I believe the story goes that the man who originated the concept of zero was blind.
I’ll do more research and get back to you.
There’s no zero in Roman numerals.
If you’d gotten zero replies to your question, you’d probably feel sad, rejected, and suffer from low self-esteem. So I guess zero would have been pretty important to you.
The first folks to use a digit for zero in their number system were the Mayans. A little bit later, the Arabs independently got the same idea, and came up with essentially the same system that we use today. The main importance of the digit zero is it makes it possible to use a place-value number system. The number 42, four tens and two ones, is different than the number 402, four hundreds, zero tens, and two ones, but without a zero digit, you’d have a nard time expressing that difference.
Another use for zero is that it separates 1 and -1. For some reason, 1 AD follows 1 BC, and that’s caused all kinds of exasperating debates along the lines of “Noooo, the 21st century doesn’t start until 2001!”
no comment, but for a beevis moment I wanted to say hehe.
Its not that people didn’t have a concept of ‘none’ but as chronos says, its the use of zero as a place holder, that is a huge development. (my original intention was to link to Cecil’s column about that here , but either the search isn’t working, or I imagined the whole thing.)
I thought the Arabs borrowed the concept from India?
I think the importance of zero is merely as a fundamental improvement in the language of mathematics. The way the ancient Greeks wrote down their math is frightening–almost exclusively in lines and polygons. It’s like us being unable to use letters and forced to draw pictures for everything we wanted to say. And try finding simple rules to multiply two numbers expressed in roman numerals.
Well, of course. I just said that the Arabs got the idea, not whence they got it 
Zero is two different concepts, as wolfman pointed out.
It means “nothing,” of course. But it’s also a placeholder used to indicate orders of magnitude: 10, 100, 1000 etc.
It occurs to me that it’s just an accident of history that we use the same symbol, “0,” to serve both purposes. We could just as easily indicate orders of magnitude with “X” or “#” or “¿,” right?
Has there ever been a culture that used different symbols for the two concepts?
I think zero is very important as a ‘concept’ too, beyond numerics, to name the possibility of nothing. Like, what if there were no universe?
The Arabs themselves freely admit that they got their numerals from India. The name for the Arabic numerical system is al-arqâm al-hindîyah, meaning ‘the Indian numerals’.
“Zero” can be very significant, e.g. if you get a zero raise.
Oy oy oy, I knew the historian of mathematics was gonna have to step in and tidy up this thread. All righty, the following synopsis is taken mostly from R. C. Gupta’s article “Who Invented the Zero?” in Ganita Bharati 17 (1995):
-
No zero in Egyptian hieroglyphic or hieratic numerals. They weren’t place-value systems, so you didn’t need a zero place-holder. (Place-value systems are like our decimal (or binary) system where you have a limited number of digits each of which can represent a multiple of any power of the base. Non-place-value systems are like Roman numerals, where higher powers have different symbols, such as the powers of ten: I=1, X=10, C=100, M=1000, all of which we represent with the same symbol 1 followed by the necessary amount of zero place-holders. This is why, in response to Five’s question, we don’t see any place-value system (AFAIK) using one symbol for a zero place-holder to indicate an arbitrary missing digit and a different symbol to indicate the missing digits specifically in a power of the base. If you want to distinguish powers of the base specifically, you might as well be using a non-place-value system.)
-
No zero in Old-Babylonian (before 1500 BCE) sexagesimal (base-sixty) place-value cuneiform numerals. They did sometimes leave a blank space as a place-holder to indicate that there was a digit missing, but often they didn’t: so for example, if they wrote 63 (for which the cuneiform representation in our numerals would look like this: 1 3, that is, 60[sup]1[/sup] x 1 + 60[sup]0[/sup] x 3), only the context could tell you that it wasn’t supposed to be 3603 (that is, 60[sup]2[/sup] x 1 + 60[sup]1[/sup] x 0 + 60[sup]0[/sup] x 3). Like Chronos’s example with 42 and 402, this can be confusing (although it seems from their vast quantities of correct calculations that it didn’t really confuse them much in practice).
-
We don’t have a lot of cuneiform mathematical texts between the Old-Babylonian period and the Neo-Babylonian period in the last half of the first millennium BCE. But around 500–300 BCE we do see various zero-markers used as place-holders. So yes, zero is used in Babylonian texts beginning by 500 BCE at the latest.
-
No zero in the Greek alphanumeric system of numerals, which wasn’t place-value either (alpha=1, beta=2,…,iota=10, kappa=20, etc.) (psycho got a little carried away, however, in assuming that all Greek math was basically Euclidean geometry—not so! There was plenty of calculation using the alphanumeric numerals.) By at least the second century CE, however, Greeks were using a zero-symbol as a place-holder in sexagesimal sequences of numbers (like degrees, minutes, seconds). It looked like a little circle or Greek letter omicron (it’s been suggested that this stood for Greek “ouden”, meaning “nothing”) with a little dumbbell on top of it. The little circle by itself appears as a zero marker in manuscripts of the Byzantine period, from about 300 CE onwards. So the plain round zero is attested in Greek mathematics from around 300 CE.
-
No zero in ancient Chinese (non-place-value) numerals.
-
Zero symbol (like an eye or oval) developed independently in Mayan mathematics sometime in first millennium CE.
-
Our decimal place-value system was invented in India, where it replaced an earlier numeral system that wasn’t place-value; since very early examples of writing in India are hard to find (the climate is not as kind to writing materials as the dry sand of Egypt, and the materials themselves were not as sturdy as the clay tablets of Mesopotamia), it’s hard to pinpoint exactly when the changes took place. We see definite references to decimal place-value in texts dating at least as far back as the first century or so CE, and by the time we get mathematical texts explicitly about numerical calculations, a bit before 500 CE, the whole system is firmly in place, including the zero-symbol. AFAIK the Indian zero-symbol has always been the circle (“sunya”, “sky” or “void”) or else a filled-in dot. Its form may have been inspired by the well-attested use at the beginning of this era of clay counting-pits with pebbles in them to keep track of the ones and tens and hundreds etc., sort of like an abacus. Any place with a value of zero would be marked by an empty pit, just a round hole; so maybe this led to the apparently independent invention of the round zero.
-
The Arabs did take over the Indian place-value numerals in the seventh and eighth centuries, as Tom and ishmintingas point out, though they also adopted the alphanumeric system they found in Greek works. So the round zero or dot came along for the ride in both cases. And various forms of the Arabic numerals were eventually assimilated into the Latin West. Ta-da! Western decimal place-value system with round zero.
There, happy now?