1-MMW: Is Math Invented or Discovered?

Michael Lessel 2016 (3)

According to realism, math exists objectively and independent of human thought. Mathematical concepts are disembodied in the universe and available for us to uncover and bring into practical use.

Michael Lessel 2016 (8)

As far as we know, only humans necessitate a mathematical system. Modern studies in animal cognition have shown that concepts like quantity, magnitude, and configuration are not unique to us, but this hardly constitutes math.

Michael Lessel 2016 (4)

Discovery seems to imply that the thing in question was there beforehand, while invention implies an original concoction. If you sail to an uninhabited continent, you would likely claim that you discovered it. In order for Christopher Columbus to have invented the New World, by general understanding, he would have had to physically construct the land mass, bringing it into existence.

Michael Lessel 2016 (5)

If you were the first to run electricity through a wire, under given circumstances, you can claim to have invented the light bulb. Electricity was certainly around before we had anything to do with it, but a light bulb only existed once humanity brought it into existence. he materials that went into making the light bulb already existed, but the inventor does not claim to have invented them; rather, they were discovered.

Michael Lessel 2016 (1)

Invention & Discovery In this discussion, we shall utilize these terms as they are commonly used. In the vernacular, we say that one invents a clever excuse, a fictional story, or a new technology. One might also discover a solution, a new species, or a problem in a design. Merriam-Webster1 generalizes these uses as follows: Invent — to create or produce (something useful) for the first time; to devise by thinking Discover — to see, find, or become aware of (something) for the first time

Paul Ernest n.d (2)

Many modern writers on mathematics share this view, including Roger Penrose in The Emperor's New Mind, and John Barrow in Pi in the Sky, as indeed do most mathematicians. The absolutists support a 'discovery' view and argue that mathematical 'objects' and knowledge are necessary, perfect and eternal, and remark on the 'unreasonable effectiveness' of mathematics in providing the conceptual framework for science.

Ted Ed (4)

Math is like a language used to describe things that already exist. Math wouldn't even have been invented if it weren't describing something already there that works.

Ted Ed (2)

People invented a system for notating mathematics, but we didn't invent the mathematical properties themselves. It's sort of like how we invented the word "tree," but we didn't invent trees, or how we invented a method for creating and using fire, but we didn't invent fire. Imagine if we arbitrarily decided that pi (technically not a "natural" number) were some other number than what it is, 2.4, for example. Later, you're using this number to calculate how large of a fence you would need to completely enclose a circular yard. The result is that you would fail to completely surround the yard, because pi is what it is, regardless of what we say it is. As for curved surfaces, this does not result in new laws of mathematics, just new variables affecting the outcome of the same mathematics. Angles differ on curved surfaces, because the curve is part of the equation. Compare this scenario: Suppose I say two plus two equals four, then someone says that if the equation only works if the first two were alone. If a third item were present, before the two more were added, the result would be five. This would hardly prove that two plus two equals five in certain cases, because the one extra item would change the starting values. Adding an extra item to an addition problem is not much different from adding an extra curve to a geometry problem. You still use the same math, just with another variable to consider.

Michael Lessel 2016 (6)

Perhaps the belief that mathematics is discovered or mathematics is invented is just a belief and cannot be said to be right or wrong.

Paul Ernest n.d (1)

The absolutist view of mathematics sees it as universal, objective and certain, with mathematical truths being discovered through the intuition of the mathematician and then being established by proof.

Michael Lessel 2016 (2)

The fundamental units of mathematics are elements and sets, which given their abstract rather than tangible nature, seems to suggest that mathematics defines itself.

Michael Lessel 2016 (7)

The process of questioning and debating is the cornerstone of philosophy and can be very powerful when done properly. But why does an answer seem so evasive? It is entirely possible that this question creates a false dilemma between invention and discovery.

Paul Ernest n.d (3)

They claim that mathematics must be woven into the very fabric of the world, for since it is a pure endeavour removed from everyday experience how else could it describe so perfectly the patterns found in nature?

Ted Ed (1)

We discovered math, but we invented numbers and symbols to understand them

Ted Ed (3)

math and its fundimentals have existed for all time, but numbers and math as we know them were invented to identify it, like words were invented to identify objects and ideas.