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May 2nd, 2014, 10:26 PM   #31
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I think there is a mixture of discovery and invention.

Mostly, it's discovery. The natural numbers were there, the shapes were there, the symmetries were there, etc.. We had to invent a language to talk about them, but there were there alright. And then from what we have we discover new things, new theorems, new techniques.

But just occasionally, we find that there is nothing there to carry us forward until someone says "let us suppose that this thing exists". It might be zero, it might be negative numbers, it might be $i$ it might be non-Euclidean space, it might be something else. But the curious thing is that the blockage removed by these inventions might be something of our own invention too, a limit placed there by our lack of invention, or our lack of dedication to push past the blockage. Even, perhaps, a lack of vision to see the value of what we might add.

But when we add the new item, it seems to fit seamlessly into the fabric of mathematics and the waves of discoveries begin again.

So we have invention when we need something completely new to progress (although, like all inventions, it is invented to solve a problem, to fit a requirement). And then we discover more and more about how the elements of mathematics combine together.

And what should we learn? That whenever we find that "there is no answer", we are looking at the brick wall invented by our minds. And if we think instead of what we would need to have an answer, we are beginning to invent the next part of the rich tapestry and pave the way for years of discoveries.

Quote:
 Originally Posted by Deveno ...it is "peculiar" that we are so well-adapted to the world we live in (the temperature range is right, the gas mixture of the atmosphere works with our lungs, etc.)...
This, I think is quite wrong. If we were not well fitted (not adapted) to the world in which we found ourselves, we would die out. We are able to consider our place in the world to be peculiar only because we were lucky enough to be so well fitted to it. It may be that, if conditions had been different, some other race would have been in our place now.

It is true that we should (probably) consider our part of the universe to be unremarkable. But we must remember that, the coincidence of many possibilities (however unlikely) have brought our immediate surroundings to where they are and put us among them. So in that sense we this corner of the universe is far from unremarkable. But we should not congratulate ourselves or anything else for our good fortune. It's all cause and effect, with some of the probabilities being rather small, but most being just an expected outcome of the circumstances that prevailed at the time.

 May 20th, 2014, 05:44 AM #32 Senior Member   Joined: Jul 2013 From: United Kingdom Posts: 470 Thanks: 40 Distances, areas, volumes, quantities, spaces, division, multiplication, addition and subtraction can be seen in nature. Shapes can be seen in nature. They are natural - and had existed before man became aware of them. Through evolution and trial and error, our brains became more sophisticated - and we began to ask more specific questions. We also gave our natural observations definitions and meanings. These definitions were created using systems of measurement (that can be described as man made), but since our brains are products of the universe and the evolutionary paradigm - we can probably exclude the idea that our thoughts are in some way 'artificial'. Meanings were developed by attaching pictures, sounds, feelings and tastes to certain words. Together definitions and meanings were used to create the mathematical structure we have in place today. Mathematical concepts are constantly being re-defined as they are a work in progress. Nothing is set in stone. The best mathematical concepts will withstand the weather of criticism, vigorous testing and questioning. Was mathematics invented or discovered? I'd say it was neither invented - nor discovered. It owes it heritage to natural selection - and the physical processes at play in the universe at the microscopic and macroscopic levels.
 May 26th, 2014, 05:44 AM #33 Senior Member   Joined: May 2014 From: Allentown PA USA Posts: 109 Thanks: 6 Math Focus: dynamical systen theory Re was mathematics discovered or invented My opinion ( take it or leave it ) is that nature puts forth the problems ( e.g. planetary orbits ) and humans come up with describing them, math- ematical or otherwise. Hopefully that will answer your question. Sincerely yours Carl J. Mesaros
 January 30th, 2015, 08:30 AM #34 Member     Joined: Jan 2015 From: Rajasthan, India Posts: 55 Thanks: 24 Math Focus: Algebra & Geomectry I think it is invented Since, We can discover only those things which are already present in this world. But, before invention of maths, here were no numbers, no counting, no geometry, even then no language.So, we made this...
 January 30th, 2015, 08:49 AM #35 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 879 Thanks: 60 Math Focus: सामान्य गणित i think its an instinct
 May 29th, 2015, 02:18 PM #36 Member   Joined: Jan 2014 Posts: 86 Thanks: 4 I thought about it recently and concluded that absolutely it is discovered. Mathematical ideas are a form of energy and energy cannot be created, only moved around. We discover that energy, the ideas, and not invent, i.e. create, it.
May 29th, 2015, 03:45 PM   #37
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Quote:
 Originally Posted by Tau Mathematical ideas are a form of energy
Ideas use energy, they require neutrons to fire. They are not energy themselves.

 May 29th, 2015, 04:19 PM #38 Member   Joined: Jan 2014 Posts: 86 Thanks: 4 They are energy patterns. Without that medium though you can have no patterns.
 June 12th, 2015, 09:33 PM #39 Senior Member   Joined: May 2015 From: Varanasi Posts: 110 Thanks: 5 Math Focus: Calculus I would say discovered, because mathematics was present in nature way before human knew it, and all such things comes under definition of discovery.Invention is something that you built and was not in nature before you did it, like Edison invented bulb.but discovery is something which you found although it was existing before that, like newton discovered gravity.so mathematics was discovered would be a correct statement.
 June 13th, 2015, 11:24 AM #40 Newbie   Joined: Dec 2014 From: Hyderabad Posts: 10 Thanks: 0 Math Focus: Primary and secondary school math I am sure it was discovered. There is nothing to invent in maths. It is all around you. From the shapes that you see everyday to the money that you earn at the end of the day.

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