FRACTURE

As a kid, I was asked a question by my father. The question sounded simple, but it had, I should say, a little twist that made my young mind spin: “What’s the difference between Invention and Discovery?”

Of course I couldn’t answer that. If you thought I knew the answer, then thank you for having a little faith in me. My father already presumed that I would fail to answer as it came up casually during a conversation. But if it was a question from my curriculum, my father, and my mother sitting next to me, wouldn’t have looked at me so softly.

Invention is something that never existed, but we humans created it by our own hands—from individual intellect, creativity, imagination, and hard work. And to create this, we had to use the resources available on Earth, and convert those into whatever shape or appearance we preferred.

Discovery is something we never created—it was already there waiting for a curious human mind to figure it out. Sometimes we needed to use a technology that was already invented, or sometimes we just had to use our creative thinking and logical approaches—in order to “discover” the truth behind the mystery.

For example, we can think of a “chair". Is a chair invented or discovered?

First we need to find some big durable trees, cut them down, extract pieces of flat wood from them, and shape those however we like. Then we need a few nails to attach those pieces all together. This is how we make something to sit on. (I don’t know the exact process of making a chair. So I kept it as simple as possible.)

So a chair is invented—since it never existed, and we had to use the available materials to make it ourselves. Computers, cellphones, light bulbs, frying pans, pens or pencils, bed sheets, dresses, bags, etc. are all human inventions. These never existed before, we created them.

Is the planet Mars invented or discovered? Well, we never created planets, stars, black holes, or whatever is out there. So Mars isn’t invented, we humans discovered its existence with the help of our own invented technologies. But the name “Mars” was invented for sure (created by humans).

But the reason I’m writing today isn’t just to tell you the difference between invention and discovery. Most of you probably knew it already. Everything I mentioned was just for this one question, “Is Mathematics invented or discovered?”

In my opinion, mathematics is something that’s both invented and discovered. Let me explain it clearly:

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics...
— Galileo Galilei, Il Saggiatore (The Assayer), 1623

Mathematics is the language we use to describe patterns in the universe. We sometimes see glimpses of new information in the universe, and we need to decode those “glimpses” in a way our brains can capture them meaningfully. And mathematics became the tool for decoding those natural events.

It all started with philosophical thinking. After the era of agriculture, humans quickly felt the necessity to keep records of how “many” cattle they had, or how “many” trees they owned, etc. They started using sticks or small stones as tools for what we today call “counting". Each stick or stone represented one object they wanted to “count” (keep record of).

Soon they realized that sticks weren’t efficient enough for keeping track of larger “amounts". They started visualizing, and began to develop new symbols to represent different amounts.

The oldest known written numbers to represent quantities were the Tally Symbols. The tally system was the simplest way humans first represented numbers visually. Each mark stood for one object or unit. To make counting easier, groups of five marks were often bundled together, with the fifth line drawn diagonally across the previous four.

After getting tired of drawing lines for years, they realized this still wasn’t effective enough for larger “numbers". Then humans came up with drawings known as Pictographs. They were simple drawings or symbols that represented objects, ideas, or quantities. Unlike tally marks, which counted one mark per object, pictographs could stand for a specific thing or group of things—making it easier to track larger numbers or more complex information.

Today, we use Positional Number System. The most common one—taught to children in their first math classes—is the Decimal Number System.

The Decimal Number System is a Positional Number System that uses ten symbols (0–9) to represent infinitely many numbers—each symbol is called a “digit". In this system, the value of each digit depends on its position in the number. For example, in the number 352, the 2 represents “2 ones", the 5 represents “5 tens", and the 3 represents “3 hundreds".

So, Mathematics was already there, as the building block of this universe. But to understand how the universe reacts, we created our own methods to measure, calculate, and describe its patterns.

Mathematics itself—the structure behind reality—is discovered. But the symbols we use to express it are invented.