Mathematics - Discovered or Invented?

Galileo had written, "Nature's great book is written in mathematical language" Discovered obviously.
 
Discovered, of course. How can something be invented that is not already capable of existing?

This in no way detracts from the ingenuity and cleverness of those involved in discovery or "invention". I simply believe that ideas, inventions and formulas are latent - awaiting the right combination of serendipity and ingenuity to bring them to light.

Perhaps it is even more important to discover and communicate such an idea to others in a comprehensible fashion. This is the way mankind advances, whether it be Newton's methodology of denoting calculus in compact form or the engineering feat of assembling a working steam engine.

In any event, it must be quite the thrill to "discover" something of lasting magnitude - immortality in a bottle... :)
 
Mathematicians discover natural patterns and formulate them. Not only that, they also invent some new patterns which do not exist in nature.

Yet when we use either one of these words, we may ignore the evolutionary construction of this discipline: Without previous knowledge, it was impossible to develop the new ones. "Discovery" or "Invention" almost equally focus on "suddenness". It is true that certain individuals come up with brand new theories and patterns, but none of them could be possible without depending upon other theories and patterns.
 
cosmictraveler said:
My point was the number more than the actual design for you need numbers to get the design and interpret it into the golden number.
Click to expand...
The ratio itself occurs all over nature.

Numbers in math are invented by humans.
Click to expand...
Not quite. What we call a "number" is simply a human way of expressing a facet of reality.
 
Dywyddyr said:
The ratio itself occurs all over nature.


Not quite. What we call a "number" is simply a human way of expressing a facet of reality.
Click to expand...

I do not disagree however I just think, IMO, that math was invented by humans to show what was already there in nature. We can pick this to death I'm sure but this is what I believe. I do see your point of view as well and respect your viewpoint.
 
Last edited:
Consider a circle, and the number pi.

The word "circle" is a designation, a human invention. It corresponds to a concept, the concept of a round shape, and the concept of the set of points in a plane that are a particular distance from a fixed point.
But the designation and the concept also correspond to real things, actual shapes. The shape of a circle is unambiguous. It has been realized independently many times, by different cultures, by other organisms consciously (e.g. dolphins making bubble rings) instinctively (spider webs, bird's nests) accidentally (ant hills, worm holes, fairy rings) and inherently (your eye, a daisy), and by non-living things such as bubbles, craters, weather patterns, stars, galaxies, and planets. Clearly, the concept of a circle is not a human invention. It is a discovery that has been given an invented designation.

The properties of a circle (radius and circumference) are part of the discovery. These properties are properties of actual circles that really exist. They may be given arbitrary designations, but the concepts themselves are not arbitrary, and nor is the relationship between them.

If pi were a human invention, if pi depended solely on its inventor, then it would be unlikely to be given the same value by two independent inventors. The fact that it has been discovered independently with the same value indicates that it relies on something beyond those inventors, something with its own independent reality.

If pi were simply an invention, why not just give it an easy value, like 3?

Similaryly, if the golden ratio is a human invention, why not invent it to be 1.5?
 
cosmictraveler said:
I do not disagree however I just think, IMO, that math was invented by humans to show what was already yhere in nature. We can pick this to death I'm sure but this is what I believe. I do see your point of view as well and respect your viewpoint.
Click to expand...

The language and tools of mathematics are certainly inventions, but not the underlying concepts they describe.

Anyone can invent a new word and validly choose an arbtrary meaning to go with it, but can you do the same with a number?
 
Pete said:
The language and tools of mathematics are certainly inventions, but not the underlying concepts they describe.
Click to expand...

That's my point.

Anyone can invent a new word and validly choose an arbtrary meaning to go with it, but can you do the same with a number?
Click to expand...

Possibly if everyone else agrees with your hypothesis.
 
Motor Daddy said:
I agree it's useful, but usefulness and correctness are not always the same.

Precisely speaking, math is incorrect. Since the universe is reality and doesn't forget things, the reality that math and the universe are not compatible is evidence to the fact that math is a man made invention that works reasonably well for man, but nowhere close to being correct in nature.
Click to expand...

No one claimed that Math is found somewhere in the nature as an element or force, of course it is man-made. Yet your "incompleteness" claim for math is equally true for human discoveries as well. That's why I asked you in the beginning if you could show us some complete or precise human discovery.

As far as I understood we are discussing because of the meaning we give to words. Correct me if I am wrong: You think that we can "discover" realities and "invent" unnatural things. What I say is this: What we think that we "discovered" is also a partial interpretation of nature. Or, if you want to give a different meaning to the word, we can get reality out of "inventions": Planes, computers, cars, bridges are all human inventions, yet they are as real as other agents of nature, they are working, they are affecting the environment, they are transforming the reality.
 
baftan said:
No one claimed that Math is found somewhere in the nature as an element or force, of course it is man-made. Yet your "incompleteness" claim for math is equally true for human discoveries as well. That's why I asked you in the beginning if you could show us some complete or precise human discovery.

As far as I understood we are discussing because of the meaning we give to words. Correct me if I am wrong: You think that we can "discover" realities and "invent" unnatural things. What I say is this: What we think that we "discovered" is also a partial interpretation of nature. Or, if you want to give a different meaning to the word, we can get reality out of "inventions": Planes, computers, cars, bridges are all human inventions, yet they are as real as other agents of nature, they are working, they are affecting the environment, they are transforming the reality.
Click to expand...

Discoveries are found by man, inventions are created by man.

Man discovered that the Earth orbits the Sun.
Man discovered that the Moon orbits the Earth.
Man discovered life in the ocean.
Man discovered gold in the mountains, and oil below the ocean.

Man invented the airplane.
Man invented the light bulb.
Man invented language.
Man invented mathematics.
 
I've always been on the "discovered" side of the fence but, in any case, this is more a question of philosophy than mathematics. And as such the demands for "evidence" are absurd: this is not a question that can be settled by performing a science experiment.
 
quadraphonics said:
And as such the demands for "evidence" are absurd: this is not a question that can be settled by performing a science experiment.
Click to expand...
Yeah, evidence was perhaps the wrong word. Supporting data would have been better.
 
rpenner said:
Not your best claim, since bees and gorillas have language to varying extent.
Click to expand...

They do. I guess it's best to say language is invented, and leave it at that.

I could say living things create language, but then I would have to define "living thing."
 
You must log in or register to reply here.
Back
Top