Does a perfect circle exist without a human brain to see it? Or is the circle just a useful concept we use to make sense of space?
The Big Question: Is Mathematics Discovered or Invented?
Does the number three exist in the woods? Imagine a world without any humans. Would circles still follow the same geometrical rules? This is the core of The Big Question. We must ask if mathematics is invented or discovered. At the present time, this topic divides the greatest scientific minds. This debate shapes how we understand the structure of reality.
Mathematics Discovered or Invented?
Case 1: Mathematics as a Discovery
At first, look at the patterns in the natural world. The Fibonacci sequence appears in the seeds of sunflowers. It also appears in the curves of seashells. To illustrate, these numerical patterns existed long before humans named them. Platonists believe that mathematics is a part of the universe. It is a fixed structure waiting for us to find it. Prior to our civilization, the prime numbers were already prime.
To point out, we do not decide that two plus two equals four.
We simply notice that this is a universal truth. As a matter of fact, astronomy uses math to predict the paths of planets. If math were just a human game, it would not work so well for physics.
Are Numbers Part of External Reality?
In reality, mathematical objects feel as real as physical things. Scientists find new formulas through logic and careful observation. For the purpose of exploration, we use calculus to land on the moon. Seeing that math describes gravity perfectly, it seems built into the stars. To enumerate, we have constants like pi, e, and imaginary units. We observe these concepts throughout the physical world. Because of this, many think math is a discovery of eternal truths.
Case 2: Mathematics as an Invention
In contrast, many thinkers view math as a brilliant human creation. We built the language of numbers to help us survive. Prior to human language, there were no formal equations. We made the rules for geometry ourselves. To explain, think about the game of chess. We invented the pieces and the legal moves. Mathematics might be a very complex logical game. In light of this, we use abstract symbols to organize our thoughts. While this may be true, math changes as our biological brain evolves. After all, different ancient cultures used different counting systems. To put it another way, math is a mental map of the world. It is not the physical world itself.
Mathematics as an Invented Tool of Logic
At this point, we should look at the use of axioms. These are the starting points we choose to believe. Together with rules of logic, we build large mathematical systems from these points. In essence, we are the architects of a logical world. While it may be true that the math works, we are the ones who designed the tools. At any rate, the symbols like “x+x” or “x=x” are clearly human inventions.
Mathematics Discovered or Invented: Weighing the Evidence
All things considered, the final answer remains elusive. Is it possible that we do both?
We might invent the symbols but discover the logical consequences. To that end, mathematics acts as a bridge. It connects the human mind to the outer world.
At this instant, you must look at the evidence yourself. Does a perfect circle exist without a human brain to see it? Or is the circle just a useful concept we use to make sense of space?
In either case, your perspective changes how you view science and truth.
Ultimately, The Big Question stays open for you to answer. Mathematics: Discovered or Invented?
We see the beauty of complex equations everywhere. All in all, mathematics remains our most powerful language. Whether we found it or made it, the logic holds firm. To sum up, the choice is yours. Think deeply about the numbers you use every day.
“Mathematics is the language in which God has written the universe.”
~ Galileo Galilei
Additionally, to stay updated with the latest developments in STEM research, visit ENTECH Online. Basically, this is our digital magazine for science, technology, engineering, and mathematics. Further, at ENTECH Online, you’ll find a wealth of information.
Reference:
- Fine, K. (2012). MATHEMATICS: DISCOVERY OR INVENTION? Think, 11(32), 11–27. doi:10.1017/S1477175612000188
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I am a Master’s qualified in Science with focus on Zoology and Entomology and am a passionate, curiosity-driven science enthusiast aiming to transform complex scientific ideas in a manner that are easy to understand hence, educate, and inspire.
I have an experience of working on the projects in the field of Entomology which has provided me hands-on experience with various research techniques. Besides, I have also gained experience of lab work as well as developed communication skills during the course of my bachelors and masters.
With a strong foundation in life sciences and a growing interest in Medical and Biological research, I have cultivated a writing style that merges scientific facts with creativity.
My experience in teaching has also taught me to develop an understanding of what are the interests of people and how to communicate them effectively.
I am committed to lifelong learning, actively engaging in Interdisciplinary learning, so as to broaden my perspective.
