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 |
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.”
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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…
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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.
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.