May 28th, 2012, 06:45 PM  #11 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Was mathematics discovered or invented?
Discovered. If the Pythagoreans had had the option of not "inventing" irrationals, they wouldn't exist. But they do and their existence falsified a premise of Pythagorean mathematics. But I also think it's fair to say that inventions are really discoveries that certain things when put together certain ways can perform certain functions. Edison didn't just decide he wanted a lightbulb and then forced one to appear. He and others worked long and hard using both best available theory and lots of experimentation to FIND OUT how electricity could be used reliably to create a more of less steady amount of light. You can't just say "I have a bunch of materials x, y and z. So I'll just make them work." It's even easier to see with simple "inventions". Wheels work the way they do because of their physical and geometrical properties, not because someone wanted them to work the way they do. The earliest wheels probably were literally discovered: portions of nearly circular tree trunks were found and found to roll in useful ways. Later, people DISCOVERED methods of wheel manufacture. It's all about discovery. Oh, and the old canard: "God created the integers. The rest is the work of man." That's got to be one of the stupidest things an otherwise bright person ever said. Without getting too literal over the god issue, there can be no doubt that real numbers are real. Circles have circumferences and radii. QED. If anything, I could more readily believe that humans in some sense ABSTRACTED the simple orderliness of integers from crushed together world of the reals, but I don't find even that convincing. Integers seem special because they ARE special, being the numbers with which discrete items can be counted. 
September 6th, 2012, 01:39 PM  #12 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: Was mathematics discovered or invented?
The truths of mathematics are always discovered, but we invent uses for them, and since the field of mathematics includes both the truths themselves and our uses for them, it is both discovered and invented, simultaneously.

September 6th, 2012, 01:42 PM  #13 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Was mathematics discovered or invented?
If its about pure mathematics, its being discovered.

September 6th, 2012, 05:24 PM  #14 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,229 Thanks: 187  Re: Was mathematics discovered or invented?
I would say both, you can discover 1+1 = 2 but you have to invent fractal mathematics and tools to visualize the fractal geometry. 
September 6th, 2012, 06:15 PM  #15 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 461 Math Focus: Calculus/ODEs  Re: Was mathematics discovered or invented?
I would say that mathematicians discover the truths encompassed by the systems of mathematics that humankind invented.

October 21st, 2012, 09:54 PM  #16 
Newbie Joined: Oct 2012 Posts: 1 Thanks: 0  Re: Was mathematics discovered or invented?
I agree that Math is invented, but you can discover a lot of things using Math. Computer was invented in the help of discovered formulas, using Math. With age occasionally comes knowledge, but all too often it also provides cynicism, selfdoubt and other negatives that stop us from the intuition of youth. There are incidents that kids can think clearly than older ones.

October 27th, 2012, 08:36 AM  #17  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 5  Re: Was mathematics discovered or invented? Quote:
You may have quite a different idea of what mathematics is than I do.  
January 21st, 2013, 12:42 AM  #18 
Senior Member Joined: Mar 2012 Posts: 294 Thanks: 88  Re: Was mathematics discovered or invented?
i find this question interesting, but impossible to answer. here's the problem: we have brains. these brains come with a certain amount of functionality "preloaded" (if nothing else, even in the absence of all culture, a human being will (if he/she survives) function as an animal. the nature of our sensory apparatus, and the cellular basis for the homeostatic systems that regulate bodily functioning dictate this). so we may never have a very good idea of 'what is actually out there, and what is merely a matter of our interpretation of what is out there. that is: our capacity for thought is limited by the very thing that does the thinking. nonetheless, it is "peculiar" that we are so welladapted to the world we live in (the temperature range is right, the gas mixture of the atmosphere works with our lungs, etc.) so it seems that both humans and the earth they live on are part of some larger semicohesive structure. mathematics is one language we have invented to communicate that structure. there is no question that "addition", "natural number", "sets" and so forth, are all creations of the human imagination. but a language is not the sum total of the the things you talk about with it, nor the words that comprise it. BENEATH language is an attempt to share information, to COMMUNICATE, to express. and this "stuff" that we are trying to express with what we call "mathematics"....what is that? was it always there? is it something innately human, or do other creatures experience it as well? the prevailing belief is that there is order in the universe. no one really knows just "why", and various theories abound. but to the extent that the universe DOES have a structure, and to the extent that mathematics can communicate this structure, in that sense we are "discovering" mathematics, as well as "inventing" it to communicate our discovery, concurrently. but even that isn't the whole story. because once we "open the box", and play with these tools we have fashioned to explain something outside ourselves....the tools take on a life of their own. there are many fields of mathematical research going on right now, that have no basis in "describing an external reality" but merely an "internal one", a language of ideas that may, or may not, find application in interacting with our environment. and now we have a "chicken or the egg" dilemma...are our thoughts the byproduct of a dynamical system (the physical universe which spawned biological entities: in particular, mammals with central nervous systems), or are they "free", and now independent of the brain from which they arose? it seems, then, that such a question as: "is math created, or invented" leads one to wonder about the very nature of consciousness and intelligence themselves. and here, all but the very bravest of us go: ??????? 
January 21st, 2013, 01:12 AM  #19 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,229 Thanks: 187  Re: Was mathematics discovered or invented?
In the beginning (if big bang theory is correct) there was no spoon. Time passed and someone (or something ) invented a spoon. Is the invention of a spoon actually a discovery because all the ingredients that made up the first spoon were there at the beginning anyway? I think addition is an invention. I think 1 + 1 = 2 is a discovery. 
January 25th, 2013, 12:44 AM  #20 
Senior Member Joined: Mar 2012 Posts: 294 Thanks: 88  Re: Was mathematics discovered or invented?
my girlfriend thinks math is about numbers. i try to tell her that's not rightmath is about ideas. some of those ideas involve numbers. but where do these ideas come from? i have no idea....


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