I had an interesting discussion with several students the other day about whether numbers exist. My argument was that numbers themselves don’t exist, they are a concept. They only exist once they are attached to objects.

This led me to think about one of my other courses where we discuss the history of Risk. One of the things I mention there is that the concept of zero, which appeared after other numbers. People didn’t have zero animals, they had some animals. However, without it (and the ability to write numbers down as we do now) then the mathematics we do today not to mention our digital world wouldn’t function quite as well.

I thought this article presented quite a nice brief history of zero but other course quick google search will bring up others.