How zero gave us mathematical and philosophical power | Talithia Williams

• Before zero was a part of mathematics, we really didn't have a need to quantify nothing. Numbers were really just used as a measure of exchange: "I'm gonna give you this number of cattle in exchange for your wheat."

And with the introduction of zero, we went from a very tangible way of thinking about the amount of something to an abstract way. And so, by giving ourselves permission to sit and ponder about nothingness and to give it structure, to give it a value, we also give ourselves permission as a society to think about hard things and complex things and sit in them and define them and change them to solutions that then benefit us all.

Part of what was revolutionary in this transition to numbers being actual objects that we manipulate is that mathematics really became a universal language. Previously, numbers were really just used as placeholders. The way that four pens would be represented would be by some symbol, and five pencils might be represented by a different symbol, but there was no way to take those two symbols and compare them to someone who had, say, five goats or four sheep. This was what was so unique.

Now, I can take the number four and apply it to anything, and it represents the same amount. When you add zero to that, that then gives you the power to think about, well, if I've got zero, can I have less than zero? What does less than zero mean? And so, so much was gained when we were able to harness the power of numerals and then use that to really expand and build on the field of mathematics.

Thinking about zero gives us a framework to think about the absence of things, and it allows us a way to quantify that. It's now allowed us to build mathematical equations like E equals MC squared, for example, in physics that represent the world around us. It represents what we see in nature in a way that everyone understands.

Any time we think about concepts like dark matter or dark energy or black holes, we've never been there. No, we observe the magnetic fields that are happening in space, and through our models, we're able to see that there's a gravitational force that we can't quite explain, but we can quantify through equations and through mathematics.

And so, to sit in void and understand emptiness in zero, mathematics is able to elucidate a world that we would never visit in person. It allows us to understand what's happening at the far reaches of our universe without ever having gone there.