Some people oppose the idea that math was discovered because they believe it was invented by humans and is therefore a human construct.

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Some people oppose the idea that math was discovered because they believe it was invented by humans and is therefore a human construct. They argue that math concepts, such as numbers and geometry, are not inherent in the universe and were created by humans to help us understand and manipulate the world around us.

One famous person who believed that math is a human invention is the philosopher, Immanuel Kant. He argued that math is a product of the human mind and that it does not describe the world as it is, but rather as we see it.

Despite this belief, there are several interesting facts that support the idea that math was discovered rather than invented. For example:

- Math concepts such as pi and the Fibonacci sequence appear in nature and were not created by humans.
- Different cultures and civilizations throughout history independently discovered the same math concepts, suggesting that they exist independent of human influence.
- Math is often used to accurately predict natural phenomena and events, such as eclipses and tides, which suggests that it is describing underlying rules and patterns in the universe.

Here is a table summarizing the arguments for and against the idea that math was discovered:

Argument For the Idea That Math was Discovered Argument Against the Idea That Math was Discovered

Math concepts appear in nature, suggesting they were discovered by observing the world around us. Math concepts are a product of human invention and are not inherent in the universe.

Different cultures and civilizations independently discovered the same math concepts, suggesting they exist independent of human influence. Math is a product of the human mind and does not exist outside our understanding of it.

Math is often used to accurately predict natural phenomena, suggesting it describes underlying patterns and rules in the universe. Math is a tool for humans to understand and manipulate the world around us, but does not necessarily describe it as it is.

**Video answer to “Why do some people oppose the idea that math was discovered?”**

This video discusses the fundamental flaw in mathematics – that there are some statements that cannot be proven. This was discovered by mathematician Kurt Gödel, and Hilbert and the formalists were about to discover this too. However, the dream of a formal system of proof was already crumbling by the time Hilbert gave this speech. The video goes on to discuss Turing’s theory of computing, and how his ideas about computability came from thinking about Hilbert’s question: is math decidable? There is a hole at the bottom of math, a hole that means we will never know everything with certainty. However, thinking about this problem transformed the world of mathematics, and led to the development of modern computers.

## There are alternative points of view

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.

I’ve spent a long time, perhaps too long, thinking about what is discovered and what is invented.

I thought that, at first, constructivism and Homotopy Type Theory answered that question, and I think that after spending a long time there, I realize that the answer was actually forthright and available long before I even started down that path. However, learning these concepts helped point me in this direction.

Some fundamental concepts in mathematics are relations and types (or even as simple as models). What I can now state with confidence is that types are constructed (invented), but that relations are discovered.

This fits with much of what we think of with theorems being a discovery, but the proofs of the theorems being an invention.

Furthermore, it helps us dig deeper, for when we say that two definitions are different, they are defined (as in constructed) by people. However, when we find that they are two equivalent ways to represent the same concept, then they are the same t…

## You will probably be interested

Also asked, **Do you believe that mathematics is discovered or invented?**

The response is: *Mathematicians invent math all the time*, formalizing observations they make about the mathematical world into rules. To understand what that might be like, take for example the famous paradox of infinite sums first proposed by the Greek philosopher Zeno.

Keeping this in consideration, **Why do realists believe that mathematics is discovered?**

As the realist sees it, mathematics is the study of a body of necessary and unchanging facts, which it is the mathematician’s task to discover, not to create. These form the subject matter of mathematical discourse: a mathematical statement is true just in case it accurately describes the mathematical facts.

**Why was math discovered?** As an answer to this: 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.

Then, **Is math discovered if it is not invented?** As an answer to this: 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*.

In this regard, **What if we didn’t discover mathematical ideas?**

Some mathematical ideas are so fundamental that even if you didn’t discover them, *someone else would have*. Mathematics is the language of science and its structures are innate to nature. Even if the universe were to disappear tomorrow, the eternal mathematical truths would still exist.

**Is mathematics a human invention?**

As a response to this: Many people think that mathematics is a human invention. To this way of thinking, mathematics is like a language: it may describe real things in the world, but it doesn’t ‘exist’ outside the minds of the people who use it. But the Pythagorean school of thought in ancient Greece held a different view.

In respect to this, **What if mathematics explains so many things we see around US?** The response is: If mathematics explains so many things we see around us, then *it is unlikely that mathematics is something we’ve created*. The alternative is that mathematical facts are discovered: not just by humans, but by insects, soap bubbles, combustion engines, and planets. What did Plato think? But if we are discovering something, what is it?

Accordingly, **What did Plato think about mathematics?** The ancient Greek philosopher Plato had an answer. He thought mathematics describes objects that really exist. For Plato, these objects included numbers and geometric shapes. Today, we might add more complicated mathematical objects such as groups, categories, functions, fields, and rings to the list.

**What if we didn’t discover mathematical ideas?** The answer is: Some mathematical ideas are so fundamental that even if you didn’t discover them, *someone else would have*. Mathematics is the language of science and its structures are innate to nature. Even if the universe were to disappear tomorrow, the eternal mathematical truths would still exist.

**Was mathematics invented?** *The word mathematics might have been invented*, the language in which the mathematics are written might have been invented but the abstraction movement from the real word, the structured synthesis that it undertakes, all that give thickness to mathematics themselves (it depends what you call mathematics) are part of mankind.

Similarly one may ask, **Is mathematics discovery or creation?** The answer is: The fact that two cultures independently come up with the same logic sets establishes that mathematics is discovery, not creation. I like your reasoning here, but it only works for very simple kinds of mathematics.

Additionally, **What did Plato think about mathematics?**

As a response to this: The ancient Greek philosopher Plato had an answer. He thought *mathematics describes objects that really exist*. For Plato, these objects included numbers and geometric shapes. Today, we might add more complicated mathematical objects such as groups, categories, functions, fields, and rings to the list.