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Math, a discovery or invention?

By Naomi Hannah

"How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?" ~Albert Einstein




According to Wikipedia, most mathematical activity consists of discovering and proving (by pure reasoning) properties of abstract objects. Sometimes scientists create methods specifically for quantifying real-world phenomena. These equations could be the explanation to everything, even to the most natural phenomena on this earth. So, is math just merely discovered?


Newton’s view

Here is the story that led to the creation of calculus: Newton started by trying to describe the speed of a falling object. When he did this, he found that the speed of a falling object increases every second, but that there was no existing mathematical explanation for this. The issue of movement and the rate of change had not yet been explored to any significant degree in the field of mathematics, so Newton saw a void that needed to be filled. Today, calculus is the language of engineers, scientists, and economists. The work of these professionals has a huge impact on our daily life – from microwaves, cell phones, TV, and cars to medicine, economy, and national defense.


Natural existence

The Fibonacci numbers seem to come up often in nature such as in pineapple scales, sunflowers, shells, the list goes on. There are also animals who can identify mathematical concepts. A university studied lemurs, which they believe are similar to humans. Through experimentation, they observed that these animals can easily recognize numbers, specifically quantity. The university concluded from this trial that even without mathematical education we still have the primitive number sense.


Numbers Systems

Anthropologist Caleb Everett writes in his book, Numbers and the Making of Us, “Mathematical concepts are not wired into the human condition. They are learned, acquired through cultural and linguistic transmission. And if they are learned rather than inherited genetically, then it follows that they are not a component of the human mental hardware but are very much a part of our mental software- the feature of an app we ourselves have developed.”

Various cultures in history came up with their own number systems, some of which we follow even now. There are still more being developed. Numbers have always been there, waiting to be discovered and so were different ways of organizing them. And over time humans developed mathematical systems around number patterns.


The Verdict

So is Mathematics a discovery or an invention? Popular scientists and personalities in the field of physics and arithmetic have a variety of dogmas on this question. Many great mathematicians including David Hilbert, Georg Cantor and the group known as Nicolas Bourbaki have shared Einstein's view- i.e. Mathematics is a discovery. Illustrious thinkers, among them Godfrey Harold Hardy, Roger Penrose and Kurt Göde think otherwise. Issac Newton seems to stand on the neutral side of this argument.

Mathematics could stand as humanity's greatest invention. It composes a vital part of our neural architecture and continues to empower us beyond the mental limits we were born with, even as we struggle to fathom its limits.


By asking simply whether mathematics is invented or discovered, the possibility of a more convoluted answer is overlooked: mathematics is both an invention and a discovery. I hypothesize that together they account for why math works so well.