On Feb 8, 2005, at 2:25 AM, Marco Cimarosti wrote:

> IMHO, a mathematics which does not have zero is a mathematics which
> does not
> have subtraction. I.e., hardly a "mathematics" at all.

Remember, there are two things going on here. One is the concept of
zero and the other is the ability to represent it in numerals. The
concept is certainly very old and generally predates the ability of
mathematicians to represent it as a quantity.

Indeed, the history of mathematics is rife with instances where the
lack of a proper notation hindered the development of a concept.

>> [...]
>> Like "discovery of America," the phrase "invention of zero"
>> describes an undeniably important event of history in very
>> misleading words.
> You are comparing a well-documented historical event and an
> undocumented
> hypothesis.
> America was "discovered" on the 12th of October of AD 1492, when a
> trans-oceanic expedition led by Cristobal Colón (or Cristoforo Colombo,
> Christopher Columbus), a Spanish explorer of Italian origin, arrived
> in the
> American islands now called Bahamas.
> Now, can you provide similar details about when, where and by whom
> zero was
> "invented"?
>

BTW, mathematicians do tend to be platonists (or, at least, act as if
they were) in that they treat the things they talk about as if they
were real and can therefore be "discovered" because they exist prior to
their discovery. But that's as may be...

Zero as a *concept* is very old. A notation for zero is not and stems
from the development of our modern numeral system in India. (The
Chinese had an earlier notation for zero but did not use it in a fully
systematic way.)

> Or, as a minimum, can you cite any evidence of an early *documented*
> mathematics which lacks the concept of zero and a way to express it (a
> symbol, a blank cell, the phrase "Sorry, no more of it")?

If you're willing to allow people to resort to words, then it's always
been possible. That's different from being fully integrated into the
numerical system (e.g., Roman numerals have no symbol for zero) or, for
that matter, the philosophical system of the mathematics.