Mathematics - Discovered or Invented?

Well, I think the most one can ask for is "supporting argumentation." This kind of purely philosophical position is always going to rest on a foundation of suppositions and beliefs, and not on anything that rises to the level of hard, objective "data" (which term, to me, implies stuff that lies firmly within the realm of the (natural and social) sciences).

 

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I agree that there is a large amount of philosophy embedded in my original question. I was tempted to post this topic in the philosophy section of this forum, but I wanted to get feedback from the math people especially, so I posted here.

 

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Mathematics are a human invention; proportion is a property of the universe, or more than that, a property of existence itself.

Mathematics were invented to deal with the universe.
A universe that was proportional to begin with.

If not, mathematics would not sync with the universe and enable us to understand it.

 

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I think it may be more of a debate over semantics. Mathamatics is an outgrowth of philosophy, of logic in particular. It seems (subject to a variety of epistemological qualifications) likely that logic exists independently of mankind, and in that sense "mathematics" can be thought to exist independently in the abstract.

That said, the universe does not really "use" math, the universe is merely governed by consistent and stable rules that can be described, often very precisely, by mathematics.

Mathematics seems to be an area where neither the term is wholly adequate

 

At this point, what you're talking about isn't math as such, but rather physics phrased in terms of math.

You could replace the word "math" in the above quote with "human language" and not change its meaning whatsoever, note. That aspects of nature can be described with math doesn't imply any separate, objective existence for mathematics, outside of the human mind. It just means that math is a sufficiently powerful descriptive system to convey ideas about physics (and other natural sciences).

 

This might be more related to semantics than to math or philosophy.

BTW: Those who argue for invented rather than discovered point to sculpture. Id est: Did Michaelangelo merely chip away all the marble that was not David & discover that wonderful piece of art? I think this anaolgy is weak but interesting.

 

Interesting that you should mention this. I'm sure you must be aware of the legend surrounding this sculpture:

Perhaps not the most reputable of sources, but I'm too lazy to hunt an "intellectual" citation - the story persists however, I first heard it over 25 years ago. Here is another inane link. Search for yourself, you will find numerous citations.

Point being, if you believe the sculptor's words, things are "discovered", not invented - thanks for the extra point.

 

I wonder if Michaelangelo actually said that he chipped away all that was not David. If he did make such a remark, I wonder if he was serious.

It is my impression that Michaelangelo was a bit egotistic. Is such a remark consistent with his personality?

 

Invention

Invention IMO
Mathematics is a language.
The language of the natural world.

What the language describes, Nature, is "Discovered"
But the communication of the ideas via language in concise, elegant form is what Mathematics does so well.

Also, many topics and fields of Math can be invented.
Just as one can invent a word that has no correlation to any part of present reality,
so too Mathematicians [Theoretical Physicists] can be far ahead of the reality of experimenters and invent ideas that may or may not be useful some time in the future.

 

Perhaps English (& other natural languages) need a better word than discovery for referring to advances in fields like mathematics. "Discovery" does not imply the considerable intellectual effort & ability required to advance knowledge in the field of mathematics.

Many "discoveries" in the field of mathematics are the result of as much or more intellectual effort than that taken by Michaelangleo when he "discovered" David in the block of marble.

Until a better word is found, my vote is for invention rather than discovery when referring to advnaces in the field of mathemetics. of

 

discovered! duh!

 

Do not forget discovering new species, new chemicals, new law of physics, new stars, even new islands require lots of intellectual and physical efforts! It does not make sense to compare the efforts involved in different kinds of discoveries. To make it explicit I disagree with that mathematics discoveries require more efforts than other kinds of discoveries therefore deserve a new name.

 

I think math is an inherent trait in all life. Animals have a superlative understanding of math, but in a different level from humans: a cat knows space, volume and distance, and can deduce a human cannot enter a hole - whereby it will cease running in that hole and stare at you unafraid. Speech is a unique triat with humans, but this is not thought to us - a parent only clicks a switch and we talk.

 

I agree this. Zero was discovered or invented? I'd like to say it was discovered. However, Cartesian coordinate system was discovered or invented? For this question, I'd like to answer it was invented by Rene Descartes. This, I think, reflects where we put more weight when seeing things.

 

Invented.

It is then discovered that some aspects of nature correspond to some mathematics. If gravity worked according to a ratio to the cube of the distance instead of the square of the distance then we would simply have selected different equations.

If some aliens on the other side of the galaxy use base 8 instead of base 10 will their laws of physics be different?

psik

 

Sorry to jump in so late but this is a fascinating argument. It depends on what you mean by "mathematics".

Broadly speaking, we have two big high-level branches, pure and applied mathematics. Applied mathematics attempts to describe relationships between things in the physical universe. As such, the language, forms and methods are invented, but the relationships we try to describe are discovered, and of course new ones are discovered all the time.

Pure mathematics is the study of formal structures and systems, all of which were invented. There is no such thing as "two". We created this; now, if it so happens that you have a pencil and another pencil, and you agree we can use "two" to describe something about your pencil collection, well then, wonderful and God bless you.

So I think the passionate discussion about this is quite legitimate; it is not a simple question to answer.

Regards,
Scott Anderson
Instructor in Mathematics (whatever that is)
University of Detroit Mercy
Detroit MI

 

Absolutely invented.

Language was invented to describe and communicate; things that already existed.
Mathematics was invented to describe, quantify,etc; things that already existed.

 

agreed. it's a language.

one apple plus one apple equals two apples. without the apples, the number two does not exist. it's just a concept.

if the earth disappears, the word 'earth' has no meaning except as a concept.

any number of nothings still equals nothing. pretty much makes it blatant that mathematics is an invention.

now 'formulas' and equations are a discovery but humans using mathematics to explain them.