myths ...

Certain myths really raise my ire. The picture of Newton under an apple tree, getting bonked on the head, and suddenly having the notion of universal gravity is one of the major ones, but there are many. Pretty much any history of science you might remember from high school probably qualifies.

One that has popped-up in several conversation in the last few months, annunciated by different quite intelligent individuals, deals with the history of the number zero. There seems to be this notion that out number zero as we use it came exclusively from Arabic Islam. Unlike Newton, at least there is some truth to the statement, but i have trouble understanding where the blanket claim arises.
I do recall myself hearing the claim as an undergrad, but within a limited context (of commercial history) in which the claim is most correct.

I want to talk a little about the history of zero, but first i need to cover some history of mathematical systems, and also there must be a quick discussion on the number zero itself as we use the term. We'll do that last piece first.

There are at least 3 mutually exclusive uses we have for zero: the natural number or null set, the placeholder in writing numbers such as "103" so we can tell it from "13", and as a tool in base 10 arithmetic. You can have the earlier notions without having the latter notion, and indeed that is the case in the history of the use of zero.
It is that last notion, as a tool for arithmetic, that the Arabic world brought us the concept of zero.

We also want to consider mathematical practices real quick. The western history (Greek and Rome) is geometry based, not arithmetic based. Well ... let me restate that ... commerce used a form of simple arithmetic, but the fields we would call math and natural science were geometry based. Even as late as Galileo, Descartes and Newton the main work is done in geometry ... pick up and thumb through a copy of Newton's "Principia" ... you'll not see algebraic "flute music", you'll see geometric proofs.
Newton knew algebra, and used if for quick calculations, but he did the proofs in geometry so that they would be trusted (at least until the birth of differentials ... but that is another story).
The Indo-Arabic world, however, was arithmetic based. Still, the areas of commerce, math and astrology did not quite use the same arithmatic methods, but they at least similar ... unlike ancient Greece where the merchants would have no clue as to what the mathmeticians math meant. (Okay, that is probably stated too strongly.)
Anyway ... so the main notion here is that the concept of zero as placeholder and later as arithmatic tool was only invented in the Indo-Arabic world because it was imbedded in the math system of the Greco-Roman world, that is, it did not have to be invented, it was always there.

So ...
... the three uses of zero.

First, as a natural number representing the null set, all cultures had the concept. Many non-primate creatures even easily demonstate that they understand that taking one thing away when you have one thing means there is no thing left. It is hard to say when the notion was first unnunciated, but it seems strongly imbedded in all cultures we have uncovered.

Second, and here we can actually talk about some real history, is the use of zero as a placeholder in writing down numbers. The Sumerians used no such concept, but the Babylonians did. Those in commerce did not, and, a little suprsingly, the mathemeticians did not. It was the astrologers that started the trend. Of course ... they had to predict things and so they needed precision and without placeholders the meanings of the number columns before you was ambiguous. So first they used spaces to mark the place holders, but due to hand writing that was still ambiguous, and later they used a symbol to represent a placeholder just like we do. They were still calculating like merchants, they were not using zero to calculate, but it was in their math. The invention of zero in this sense occured in Babylon before 700 BC and was standerdized around 400 BC.
They were still using base-6 math, i suppose that should be noted.

The use of zero in arithmatic, that is, modern arithmetic, probably started in Hindu India by around 650 AD. The Islamic Arab conquest of that culture later brought the notion and system to the Arab world, and it was eventually transfered to the western world from our contacts with Islam. Zero, in this sense, is almost a short-hand way of saying that we got the base-10 column arithmetic that we use from the Arabic world ... and that is much closer to being correct.

I don't know exactly where the column arithmetic started, though apparently the Hindus used it by 650 AD and it was standard fair in India and the Arab world two to four hundred years later.


That is what i know.


I think it would be interesting to know two more pieces of information ... maybe i'll do some research on it.

1) When and where did merchants, mathemeticians and scientists all begin using the same number system ... or at least sometimes all used it. I would imagine it started in the Arab world and spread to Europe. The invention of algebra would have to be a big part of this. One had to use geometry to mimic the physical world for science up until algebra was "trusted" for this task, which is as late as Leibniz/Newton and the next couple generations.
In short, the notion of "one math" for all these disparate activities ... where/when did it begin?

The proof of the equivalency of algebrai and geometry is a 1700s phenomenon.


2) When/where did arithmetic gain the powers of algebrai as we think of algebrai? The left to right notation "3 + 4 = ?" IS algebrai, sure, but the concept of actually using "x" and the like as constants in an equation ... i do not know when that started.