Was Mathematics invented or discovered?

👋 Hey Friends,

the concept of mathematics or the act of doing math has a vast and complex historical time span, spanning from the earliest evidence of written mathematics dating back to the ancient Sumerians from 3000 BC. It includes the discovery or invention of the number pi, the twisting thought of graphically representing algebraic equations on the cartesian plane, invented by the French philosopher Rene Descartes. And still today, the importance of mathematics is only growing with time since all sciences, daily products and so much more would not work without mathematics.

Babylonian tablet listing Pythagorean triples. (Dated back to 3000 BC.)

The question often asked by many students, including me, is the most obvious and reasonable question someone studying math should ask: Was mathematics invented or discovered? Is the highly effective usage and the general importance of math a magnificent coincidence or where we determined to find something just like it? There is no right or wrong answer and there hasn’t been found a fundamental consensus among mathematicians and scientists about whether or not math is actually invented or discovered. We, for ourselves, have to explore different viewpoints to understand the evidently proven effectiveness of mathematics in all sciences. What does make math so special and why does it seem to be so fundamental?

"It is what the physicist Eugene Wigner had in mind when he wrote of “the unreasonable effectiveness of mathematics in the natural sciences.“"

-Strogatz, Steven H. The Joy Of X .

The rational answer

The short and most rational answer to the question is as obvious as asking the question itself. Without the existing coherence of Earth and human civilisation, the concept of mathematics would have never been created and this evidence might show us that math is a concept of the human mind and not a discoverable property of the universe we live in.

The reason why mathematics is admirably suited to describing the physical world is that we have invented it to do just that. Since math is, for this reason, a product of the human mind, we construct its own nature to follow the reasoning of the universe we see around us.

If the universe disappeared, there would be no mathematics in the same way that there would be no football, tennis, chess or any other set of rules with relational structures that we contrived.

Following this reasoning, mathematics is only existing as long as we can think about it. It is similar to what Rene Descartes wrote about the existence of ourselves: "Cogito, ergo sum.", "I think, therefore I am." In the case of mathematics, it would rather be something like: "I think about math, therefore it is existing." And without the condition of thinking about the concept of math, the part with existence has no logical reason to be true. So why should there be mathematics, when there is nobody to think about mathematics?

Math as a fundamental product of the universe

Contrary to what we have said before we can also go with the other argumentative approach and we could say that math is actually innate. The reason mathematics is the natural language of science is that the universe is underpinned by the same order.

The structures of mathematics are intrinsic to nature. Moreover, if the universe disappeared tomorrow, our eternal mathematical truths would still exist, as a concept outside of the human mind. Algebraic rules wouldn't change just because we are not around any more.

The addition of the variable \( a\) with itself for example could still be represented as \( a+a\) but also as \( 2a\). It would not be equal to \( 4a\) just because we cannot think about the variable \( a\) anymore.

From this standpoint, mathematics is a concept outside of our pure imagination and it doesn't follow the definition of existence from Descartes, which we have discovered before.

It is up to us to discover mathematics and its workings--this will then assist us in building models that will give us predictive power and an understanding of the physical phenomena we seek to control. This rather romantic position is what I loosely call mathematical Platonism.

Conclusion

So, what are we left with?

The question of whether mathematics is invented or discovered remains a subject of debate among mathematicians and scientists. While there is no definitive answer, exploring different viewpoints allows us to appreciate the remarkable effectiveness of mathematics in describing the natural world. On one hand, mathematics appears to be a product of the human mind, created to explain and navigate the complexities of our environment.

It exists as long as we think about it, much like other human-contrived systems and concepts. On the other hand, there is a perspective that mathematics is inherent in the fabric of the universe, with mathematical structures being intrinsic to nature itself. If the universe were to disappear, mathematical truths would still exist independently. This viewpoint suggests that mathematics is a concept beyond our imagination, existing outside of our subjective experience.

Ultimately, the nature of mathematics may lie somewhere between these two perspectives, with elements of both invention and discovery. Regardless of the answer, the importance and significance of mathematics in our lives, from scientific advancements to everyday applications, cannot be denied. Mathematics remains a fundamental tool for understanding the world around us and pushing the boundaries of human knowledge.

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Thanks again and I'll see you soon.

xoxo

Victor 👋 :) (@observethecosmos)