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Name: Richard J.
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Mathematics; Invented or discovered? I'm still undecided, maybe a little of both - or am I treading on dangerous ground?

Richard, Before deciding whether mathematics was invented or discovered, we must clarify terminology. Discovered: The thing always existed. Someone found it. Invented: The thing did not previously exist. Someone created it.

Then we must clarify what mathematics is. Mathematics is a tool, a model. It is something that we can use to describe or model parts of reality, or any other system based on quantifiable things. Mathematics can be used to model finance, logic, even color. Mathematics itself did not exist before the first mathematicians. What was discovered was how to mold the model to fit reality. What was invented was the model itself. Mathematics was invented. How to use mathematics was discovered.

Dr. Ken Mellendorf


I see mathematics as a invented/developed approximation by us to describe what we find in the real world. I use the word developed because we develop closer approximations to real life as time progresses. We should realize, however, that it still is only an approximation; life itself has not been adequately described using mathematics to say that we can predict with absolute certainty future events.

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Ric Rupnik

To some extent this is a matter of definition and semantics. My opinion: Mathematics, as a formal system, is invented in the sense that one starts with a certain set of elements (usually numbers, but not necessarily so) and defines a set of rules regarding various relationships between, and operations of, those elements. And you can invent any rules of the game you desire.

Mathematics, as a discipline, may be quite a different process. One may perceive a certain pattern, regularity, or whatever word you might want to describe some insight (usually regarding numbers, but not necessarily so) and try to "explain" that insight. This process may be quite circuitous, and "illogical". There are any number of observations (conjectures) in mathematics that are put forward without any proof. Perhaps "Fermat's Last Theorem" is the most famous, but by no means the only, example of something that was found to be empirically true for a long time before it was proven in a formal sense. If you read any of the popular histories of numbers like 'pi' , 'e' , or 'i' it will be clear that there is much more discovery than invention.

Vince Calder

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