How did the concept of zero originate and why is it important to mathematics?

In: Mathematics

Scientific American has [a good history of the development of zero](https://www.scientificamerican.com/article/history-of-zero/). The short version is that zero-as-placeholder is documented as far back as Ancient Mesopotamia, from whence it traveled to India and was developed into zero-as-number. Probably (it’s a bit fuzzy). The Maya also developed the concept of zero independently.

It was invented by Indian mathematicians but became popular in the West after a guy named Al Gorithm (which is Arabic for, roughly, “The Uzbekistani”), living in Baghdad around 820 CE, used them in his super popular math book called *Al Gebra* (which is Arabic for “The Reunion”, as in when you solve an equation such as 2x=x+5 by subtracting x from both sides to get x=5; you’ve reunited the x’s).

Its main importance is as a placeholder for use in the “Arabic” numeral system (we call it “Arabic” because *Al Gebra* was written in Arabic). Calculating something like “409+101=510” is a *lot* easier than computing “CDIX+CI=DX”. And the easier it is to do simple calculations, the more hope you have of eventually figuring out how to do complex calculations.

We know that the concept of zero as a placeholder digit has been around for at least 5000 years. There are records from ancient Mesopotamia that use a version of zero in counting to help represent a number (eg 10, 101, 1001).

If you mean how did it originate as a number in & of itself (ie signifying nothing or an empty set), again it’s not known exactly but the concept is at least 1500 years old.

In terms of its importance to maths, hopefully there’s a mathematician on here who can give a more technical answer but in broad the concept of zero is fundamental in maths because every other number, positive & negative, is derived from it and all infinite processes relate to the concept of zero in some way. Look up Robert Kaplan if you want to read about it properly, he wrote a whole book on the idea of zero & why it’s important.

>Why is it important to mathematics?

Cause it’s sitting smack dab in the middle of all the numbers.

As I recall, numbers (numerals) are associated with collections of objects into what we call sets. The number 5 would indicate a collection of objects with 5 things. But what do you call a collection with no objects? Like if you had a set of 5 and I took them all away. You’d have nothing aka the empty set. The number we associate with the empty set is 0.