Is Math Invented or Discovered?

Ponder with me the question: “Is math invented or discovered?” Math is the science and study of quantity, space, motion, etc. that was probably used to count the number of edible apples that Farmer John could sell. Some would say that math is invented, while others claim that math is discovered. But who is right and who is wrong? This article will delve deep into that topic, starting with a story.

Back in the day, mathematicians had to write “is equal to” every time they wrote an equation, producing whole pages where half of the ink was dedicated to phrases of “is equal to.” Soon, mathematicians got tired of this, and a Welsh mathematician by the name of Robert Recorde invented the equal sign. Yes, he invented the equal sign. 

Contradictorily, we have calculus, the study of motion and change that uses miniscule parts. It is used in engineering and physics for calculating motion. Similar to videos, which are like a series of photos played at high speeds, calculus is like a group of really small parts that approach zero, but aren’t zero, which creates motion or change (don’t take this as the literal definition of calculus because to be honest, I don't really understand calculus and you don’t need to either). Some might also know that Isaac Newton and Gottfried Wilhelm von Leibniz discovered calculus, and sources like Encyclopedia Britannica and National Geographic claim that calculus wasn’t invented, but discovered.

In addition, math is not about symbols, like equal and addition signs; it’s about concepts and patterns in numbers, like 1+1=2. If you haven’t noticed, 1 apple + 1 apple has always been 2 apples, even though we perhaps only formalized it a few hundred years ago. Also, 3 groups of 2 apples have always been 6 apples; that “rule” didn’t just pop into existence from the moment multiplication was conceptualized. So, math is discovered then, right?

Well, if math was a tool used to count apples, then when we didn’t count apples, math didn’t exist. Think about it: math was a tool for counting, but before counting, that tool didn’t exist. Therefore, math didn’t exist, hence we invented math when we needed to count apples. That must mean that math is invented!

However, math is full of concepts of numbers, space, change, etc. like the distributive property, the triangle sum theorem, and congruent supplements theorem. These have always existed, have always been true. We just didn’t know about them, which means that we discovered them. We didn’t invent them.

In conclusion, there are many reasons for both sides of this argument. Math could be invented as a tool for counting apples, then it could have evolved into something more concept-based. My opinion on this is that math is discovered and that it is a concept that was discovered. Just keep in mind that many sources, including universities, say that the answer to this question is both. So go ask your friends and see what they think! (But more importantly, go do some math. Trust me, whether it’s discovered or invented, it’s definitely fun!)