Is math invented or discovered?

Mark (Discovered)

When considering all fact-based evidence, we can only conclude that mathematics is indeed a discovered concept. Math is reflected in the natural order, demonstrated by the Fibonacci Sequence and the Golden Ratio method. These patterns exist independently of human observation and have been observed consistently across cultures, showing they are intrinsic properties inherent in the natural world. 

Similarly, all equations result from a concentric loop of indisputable facts. Math is simply the language of showing what already exists and is observable in nature. Math expresses the way the world works, not the other way around in which humans invented math, and now the world happens to work that way. Science equations like those found in chemistry operate by the same principle. The periodic table describes a material reality that already preceded its existence.

If humanity suddenly ceased existing, mathematical truths would still prevail, just as the words “first” and “last” would exist, even if the terms had never been established. Math preceded humanity and gave us a clearer understanding of universal law. Plato theorized that math existed long before man, even attributing it to God. The Bible also reflects this same concept, positing that nothing in creation originates from man. Math is a concept—which can only come from a mind—and it was made discoverable.

The theory of discovery is further supported by famed mathematicians Isaac Newton and Gottfried Liebnitz. Both men arrived at the same discoveries, independently of one another, long before such concepts existed. It actually incited some conflict between them, but this further reinforces the idea that math is governed by one undeniable law of truth. As with science, our understanding of mathematics grew through research and exploration, making it a discovery as it's far too complex and irrefutable to have been invented.  

Andrew (Invented)

While the relationships between numbers, shapes, angles, etc., are essentially laws of nature, the ways in which we describe, manipulate, and use these relationships are completely man-made and invented. A clear example of a mathematical invention is “PEMDAS,” an acronym for remembering the order of operations: Parenthesis, Exponents, Multiplication, Addition, Subtraction. This is an agreed-upon and standardized method that is totally arbitrary and a complete human fabrication. This organization of relationships and accepted method for organizing numbers is what mathematics is at its core.

It is possible to “discover” that if you have two eggs and find two more, you have four eggs. But this isn’t math. The invention of math allows humans to add, subtract, multiply, and much more with any number of abstract hypothetical eggs and understand the quantity. In other words, the invention of math is an abstraction of real-world phenomena. Likewise, this principle of abstraction allows us to ensure that our knowledge is absolute. We can measure the angles of a triangle and find that, added together, they equal one hundred eighty degrees. Still, our abstract knowledge of this concept allows us to demonstrate that a triangle of any size or shape will always have the same principle.

The most difficult math questions require a great deal of human ingenuity to solve. The answers are not found or discovered but arrived at through a process that is both creative and scientific. Mathematicians must invent new and clever ways to approach problems in order to solve them. If they used the same old discovery methods, many of these problems would go unsolved.