I am bad at writing concisely. I am not great at writing to a deadline. In order to practice both skills I make this pledge: 400 words researched and written in half an hour on a mathematical topic, weekly. I may not keep this up but we will see. It is for my benefit but if you also enjoy reading it that is good. I make no promises about the content except that it will be related to mathematics, so expect some variety and no pattern. I will think of a topic outside of the half hour, and sometimes I may have some prior knowledge of it, but generally I will research and write each piece very quickly. Corrections welcome in the comments. For the first entry, let’s begin where things begin, from zero.

When you don’t have any apples you have zero apples, right? Zero is a natural concept and easy to understand. However, zero is a relative newcomer to the mathematical world and its introduction caused a shake-up in what mathematics can do.
In ancient Babylonian mathematics, the lack of a numeral in expressing a number was indicated at first by a blank space and later by a punctuation mark between numerals. This would be like us writing 2011 as “2\11”. However, this was not our zero because it was not used alone.
All over the world – notably in Greece, China and South America – different cultures used symbols for zero. Some, like the Babylonians, used this as a placeholder but others began to understand zero as a number itself.
In 9th century India, decimal zero was used as we might use it today in practical calculations. The symbol for zero was incorporated in Hindu-Arabic numeral system, which comes to us through the Islamic mathematician al-Khwārizmī. This system of numbers was brought to Europe in the 12th century, particularly by Fibonacci, and so zero was brought into modern mathematics.
But why is zero important?
Zero plays one role in helping to distinguish numbers. Take the number 101: this means one hundred, zero tens and one unit. Without the zero, we would struggle to use this shorthand to represent 101, 1001 and 11.
Apart from this, zero serves as a number in its own right. If you subtract any number from itself, you get zero. This opens up all sorts of possibilities. For example, if rather than just having nothing you can consider yourself to have zero of an item then this opens up the possibility of being owed items as debt. If you allow zero you then get on to negative numbers, and the idea that you can have, say, -3 apples. This means that if someone gives you 3 apples, you will return to the default state of having zero apples again. This idea is very important in trade and economics.
In mathematics, zero plays an important role as an identity element for addition. This means that when you add zero to any number, you get the number itself. This fact is important in group theory, which underpins much of mathematics and must be left for another time.

Performance: not great first time out. 393 words in 38 minutes. At 30 minutes I was about 70 words over.