Ask A Scientist© Mathematics Archive

name         Richard J.
status       educator
age          30s

Question -   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
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Richard,

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.

Thanks for using NEWTON!

Ric Rupnik
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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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