Prompt: “Is math invented or discovered?”
Excellent question! The short answer is both—which is why the question is so thought-provoking. Mathematics rests at the intersection of human cognition and absolute reality, which is why the essence of invention and discovery pertaining to the subject remains a contested topic.
The Discovered View
This view of mathematics stipulates that the universe adheres by a rigid framework of countless rules. In other words, mathematical truths exist independently of human inquiry. Below are some examples that corroborate this view of mathematics.
- Prime numbers are inherently indivisible by any number other than 1 and itself
- The Pythagorean theorem was true before Pythagoras, on any surface, and in any place in the universe
- Given two rocks sequentially, both a human and a relatively sentient alien would surmise that there would be more stones in their possession (concept of addition)
Essentially, this view treats mathematical notions as timeless and abstract parts that serve as the scaffolding of the universe.
The Invented View
On the contrary, this view of mathematics refers to the field as something humans have miraculously created. Below are some examples that not only support this view of mathematics but also refute the corporeal view of mathematics mentioned previously.
- Isaac Newton “invented” calculus to complement his research on gravitational forces
- Mathematical notations synthesize abstract concepts into rudimentary steps
- Cartesian and polar coordinates both succinctly model and describe the world
From this perspective, math becomes even more powerful and consistent. However, it’s important to recognize that these “invented” tools of mathematics are still made from the very basic scraps that humanity needed to discover.
The bottom line is this—mathematics is both an invention and discovery, and these two aspects simultaneously work in equilibrium to enhance humanity’s understanding of the universe.