# Your question – why is math discovered not invented?

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Math is discovered, not invented, because mathematical concepts and relationships already exist in the universe, and humans simply uncover and describe them through a process of exploration and deduction.

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Mathematics is a fundamental aspect of human knowledge and understanding, but its origins and development have been a subject of debate for centuries. One perspective is that math is a human invention, created to serve specific purposes and practical applications. However, another perspective, embraced by many mathematicians and scholars, is that math is discovered, not invented.

This view sees mathematics as a natural and universal language that humans have accessed and refined over time. Mathematical concepts and relationships are considered to exist independently of human thought or activity, waiting for humans to discover and describe them through reasoning and observation. In the words of acclaimed mathematician and philosopher Bertrand Russell, “Mathematics, rightly viewed, possesses not only truth but supreme beauty, a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.”

There are many interesting facts and examples that support the idea of math as a discovery rather than an invention. For instance, the concept of pi, or the ratio of a circle’s circumference to its diameter, is a universal constant that exists within the geometry of circles regardless of human culture or civilization. Similarly, the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, is applicable to any right triangle and is not dependent on human development or innovation.

Another example is the Fibonacci sequence, which appears in many natural phenomena, such as the spiral patterns of shells and flowers. This sequence, where each number is the sum of the two preceding numbers, is not a product of human invention, but a pattern that emerges naturally in the growth and structure of various organisms. As mathematician Marcus du Sautoy writes, “Mathematics allows us to access the universal patterns that define our physical world. These patterns are not inventions but discoveries.”

The following table summarizes the main differences between math as invention versus math as discovery:

Math as Invention Math as Discovery
Created by humans for practical purposes Exists independently of human thought or activity
Can vary depending on cultural or historical context Universal and unchanging
Can be replaced or improved over time Has always existed and will always exist
Emerges from human imagination and creativity Emerges from natural and logical patterns in the universe
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In conclusion, while the debate between math as invention versus discovery may continue, there is a compelling case to be made for math as a discovery. Mathematical concepts and relationships are fundamental to the natural world, waiting for humans to uncover and explore them. As Galileo Galilei famously said, “The book of nature is written in the language of mathematics.”

This video discusses the debate between those who believe that mathematics is discovered, and those who believe that it is invented. The video provides examples of how mathematics has been used to solve problems in the real world.

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Some people argue that, unlike the light bulb, mathematics wasn’t an invention, but a discovery. The idea behind it is that mathematics exists in the mind of God or the Platonic world of ideas, and all we do is discover it—a position known as Platonism.

There is no definitive answer to whether math is discovered or invented, as different philosophical views have different arguments. One view is that math is universal, objective and certain, and that mathematical truths are discovered by intuition and proof. This is the Platonist position. Another view is that math is incomplete, revisable and changing, and that mathematical truths are invented or emerge as by-products of inventions. This is the non-Platonist position.

The absolute nature of mathematics is universal, objective and certain, with mathematical truths being discovered through the intuition of the mathematician and then being established by proof while the fallible nature of mathematics is an incomplete and everlasting work-in-progress, and is corrigible, revisable, changing, with new mathematical truths, being invented, or emerging as the by-products of inventions, rather than…

Mathematics is not discovered, it is invented. This is the non-Platonist position.

I am far from an expert on this subject, but it might be illuminating to consider what happens when a dog catches a ball. Neglecting air resistance and other secondary effects, the ball follows a predictable trajectory that is shaped by gravity, and math allows us to predict where it will land. Astonishingly, a dog can _also_ predict where the ball will land almost immediately after the throw, and some dogs can even run and leap to catch the ball before it touches the ground. When you consider that the dog has far less visual acuity than we do and that it is estimating the three-dimensional geometry of the world and position of the ball in real time from imperfect two-dimensional signals bouncing on its retinas as it runs, you might be tempted to award the dog a degree in Applied Mathematics!

So does the dog that successfully locks the ball in its jaws in mid-air invent math, discover it, or neither?

One perspective would be that the dog discovers math: through life experience, it ob…

## In addition, people are interested

Why is math invented and not discovered?
As an answer to this: 2) Math is a human construct.
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. Mathematics is not discovered, it is invented.
Is math discovered if it is not invented?
The response is: This is true for all right-angled triangles on a level surface, so it’s a discovery. Showing it is true, however, requires the invention of a proof. And over the centuries, mathematicians have devised hundreds of different techniques capable of proving the theorem. In short, maths is both invented and discovered.
Why was math discovered?
Answer will be: Throughout history, different cultures have discovered the maths needed for tasks like understanding groups and relationships, sharing food, looking at astronomical and seasonal patterns, and more. There are probably forms of mathematics that were understood by people we don’t even know existed.
Is math a humanly created subject?
Answer: Maths is a human construct
Maths is a product of the conscious mind: both a tool and a language used to make sense of the designs and functions of our universe – quenching humans’ instinctual thirst for rationalisation.
Is mathematics invented or discovered?
Some mathematics, I think, is definitely invented, not discovered. That tends to be trivial mathematics — papers that fill in much-needed gaps because somebody has to publish. So you take some problem, you change the wording of the mathematical problem a little bit, then you solve it, and then you write a paper.
Why do some people oppose the idea that math was discovered?
Some people oppose the idea that math was discovered. They belong to the anti-Platonic school of thought, which believes that mathematics was invented. They consider math to be a human invention designed in a way that suitably describes the physical world. To suit our needs, the human mind continually makes up new mathematical concepts.
Does mathematics exist within us?
As a response to this: Some believe that mathematics exists within us, and that the objects of mathematics were therefore our creation. Other philosophers thought that mathematics exist independent of our thoughts, outside of us. However, does the truth lie somewhere between the stark choice of being invented or discovered?
Is math beyond that which fits the world invented?
The answer is: Well, there is none. It is a desire at best. It a false desire, too. For here is the simple proof that the proposition “Math beyond that which fits the world is invented” is false. In math, we have the simple proof (using “successor functions”) that the natural numbers run 1, 2, 3, … and so on, all the way up.
Is mathematics invented or discovered?
Some mathematics, I think, is definitely invented, not discovered. That tends to be trivial mathematics — papers that fill in much-needed gaps because somebody has to publish. So you take some problem, you change the wording of the mathematical problem a little bit, then you solve it, and then you write a paper.
Is math beyond that which fits the world invented?
Well, there is none. It is a desire at best. It a false desire, too. For here is the simple proof that the proposition “Math beyond that which fits the world is invented” is false. In math, we have the simple proof (using “successor functions”) that the natural numbers run 1, 2, 3, … and so on, all the way up.
Where can I find a history of mathematics?
Answer will be: The Story of Maths. MacTutor History of Mathematics archive (John J. O’Connor and Edmund F. Robertson; University of St Andrews, Scotland). An award-winning website containing detailed biographies on many historical and contemporary mathematicians, as well as information on notable curves and various topics in the history of mathematics.
Why was Archimedes considered the father of mathematics?
The answer is: Archimedesis considered the father of mathematics because of his notable inventions in mathematics and science. He was in the service of King Hiero II of Syracuse. At that time, he developed many inventions. Archimedes made out a pulley system designed to help the sailors move objects up and down that are weighty.

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