Mathematics Is An Invention Or A Discovery?

[Newstein]

Dear All

THANKS for such a grand discussion!!

[Turtle]

Dear All

THANKS for such a grand discussion!!

What will you be doing with our words, if I may be so bold as to ask?

[Newstein]

Dear @ Turtle

 

By means of your words, its very relevant to know the view. And this question is not so anatomically simple. Also you may give a look towards

https://www.researchgate.net/post/Mathematics_is_an_Invention_or_a_Discovery

 

So that everything gets clear.

[DrKrettin]

 

BTW, this is the 21st century, idc where in Britain you're from, nobody uses the word bollocks anymore. 

 

To be honest, if I were to ask for advice about vocabulary, you would not be my first choice. That's litotes, by the way.

 

Linguistically I suck at math.  

 

I admire your ability to write utter meaningless bollocks even with five words. That takes skill.

[exchemist]

To be honest, if I were to ask for advice about vocabulary, you would not be my first choice. That's litotes, by the way.

 

 

I admire your ability to write utter meaningless bollocks even with five words. That takes skill.

But, credit where it is due, he has corrected his spelling of ballocks from bullocks to bollocks. :)

[Turtle]

Dear @ Turtle

 

By means of your words, its very relevant to know the view. And this question is not so anatomically simple. Also you may give a look towards

https://www.researchgate.net/post/Mathematics_is_an_Invention_or_a_Discovery

 

So that everything gets clear.

I see nothing at that link on this discussion and it's not clear that you answered my question. Unless you link to this discussion from elsewhere and give proper credit, you may not copy and use our words. That would be a copyright violation. If you want to discuss, then discuss. If you want to pirate, then duck & cover.

[exchemist]

Both, even the scientist doesn't know what the results of invention could yield. A lot of basic calculus was built upon a lot of work by Leibniz, Newton et el. Today our repertoire of calculus extends into largely many unknown types of mathematical procedures compared with back then, many of which significant theories are built upon. So mathematics was not only an invention to help describe the world, the world of calculus and other mathematical disciplines where as much that as it was a discovery built within its own scientific method. 

Yes I think on reflection that is arguable: that there is an element of discovery of investigating the logical implications of a set of axioms. 

 

However I would not describe the process as a "scientific method", because there are no observations of nature involved in mathematics.

Edited June 10, 2017 by exchemist

[MaanasArora]

As an intuitive learner and firm believer in specific branches of metaphysics, at this moment I'm trying to prevent myself from bursting out, so please forgive if any kind of anger is showing through my response ^_^

 

Math is a discovery. It's not us who decided that 2 + 2 is 4, 2 + 2 just is 4, and 2 + 2 cannot be 6 just because some despot says it is. All things we write down in our exams existed in some form or another in nature, including complex numbers (yes, they do show up in physics and here's an interesting article about why they do so, if you stop to look at it) and vectors (they're everywhere) and sets (no doubt on that) and cardinal numbers (yes, they do but I'm not able to find an article on them) and infinity (it shows up in the maximum size of our universe) and everything in math. You just have to think about it a bit.

 

And yes. Mathematical Notations are an invention. We say 2 + 2, but we could also in some other way say hala dera dono (that's not a real language) and write sets without braces, if that's what you mean by math.

 

And, of course, specific interpretations of mathematics may also be an invention. There are other ways of looking at universal sets and probability, but I don't consider them different 'mathematics-es' if you get what I mean.

Edited June 13, 2017 by MaanasArora

[DrKrettin]

Math is a discovery. It's not us who decided that 2 + 2 is 5, 2 + 2 just is 5, and 2 + 2 cannot be 6 just because some despot says it is. 

 

Who could argue with that?  :eek:

[MaanasArora]

Who could argue with that? :eek:

OMG I didn't see that coming. It was a typo. I hope so, for the sake of my pride.

Edited June 13, 2017 by MaanasArora

[DrKrettin]

OMG I didn't see that coming. It was a typo. I hope so, for the sake of my pride.

 

I am very relieved - I thought it was some metaphysical statement way beyond my ability to understand. :shocked:  :shocked:

[wiseshopper]

I think it's both an invention and a discovery.

It's an invention - because even during the ancient times, mathematicians and physicists such as Newton, Leibniz, Lagrange, etc., needed to work on inventing techniques to solve a certain problem. Hence, calculus - courtesy of Newton and Leibniz - was born.

At the same time, it's a discovery - because going along the way, certain techniques that can lead to new Mathematics can be discovered, formulated, and later on, verified.

[Moronium]

Haha, what a good question. 

 

I have always taken the position that it is a human invention, being a quantitative branch of logic. However, being a branch of logic, it contains things that are unambiguously and objectively true, once the starting axioms are defined. This leads some people - wrongly in my opinion - to think that mathematics somehow exists in nature as it were, and is a physical thing, to be discovered, when it is in fact abstract. 

 

But I'd be interested in what others think. 

  I (mostly) agree with your position here, and all the other comments you've made in this thread.  Math, like language, can be used to describe many relationships which we observe in the physical word.  But, like language, math is an invention and a tool, not something which exists independently of the minds which create and employ it.

 

My only quibble would be with your use of the phrase "objectively true."  Kant distinguished between a priori, analytic "truths" and "truths" which were a posteriori and synthetic.  Math is only analytically "true" and not "objectively" (i.e. synthetically) true.

 

Numbers and numerals do not exist as "objects" in the physical world.  There are merely mental constructs.  Hence they are not "discovered," but rather they are invented.

 

As you note, like logic, math is purely formal with no substantive content whatsoever.  The logical implications which follow from the basic axioms/premises will follow irrespective of whether they are "true" in the physical world.  A logical argument can be perfectly valid, but also completely unsound.  Logic, in itself, cannot tell us if valid arguments are in fact sound.

Edited April 14, 2018 by Moronium

[exchemist]

  I (mostly) agree with your position here, and all the other comments you've made in this thread.  Math, like language, can be used to describe many relationships which we observe in the physical word.  But, like language, math is an invention and a tool, not something which exists independently of the minds which create and employ it.

 

My only quibble would be with your use of the phrase "objectively true."  Kant distinguished between a priori, analytic "truths" and "truths" which were a posteriori and synthetic.  Math is only analytically "true" and not "objectively" (i.e. synthetically) true.

 

Numbers and numerals do not exist as "objects" in the physical world.  There are merely mental constructs.  Hence they are not "discovered," but rather they are invented.

 

As you note, like logic, math is purely formal with no substantive content whatsoever.  The logical implications which follow from the basic axioms/premises will follow irrespective of whether they are "true" in the physical world.  A logical argument can be perfectly valid, but also completely unsound.  Logic, in itself, cannot tell us if valid arguments are in fact sound.

Fair enough. I have no training in philosophy so I may well use terms in ways that a philosopher might quibble with. What I intended by "objective" truth was "not subjective", i.e. true for any reasoning mind, irrespective of point of view or experience. So yes, perhaps analytical, or a priori truth is what I meant.

Edited April 15, 2018 by exchemist

[inverse]

I am a mathematician :)

 

I think it is a bit different. it is more akin to DREAM :)

 

but according to my experiences ,I do not recommend the pure mathematics.

 

I highly recommend engineering ,especially if you are talented