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January 25th, 2013, 12:57 AM   #21
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Re: Was mathematics discovered or invented?

Have you ever had someone, upon hearing that you enjoy or are "good at" math, say, "Oh yeah? Then what's <insert huge number here> times <insert another huge number here>?" And then look expectantly at you to be some kind of savant? I find this naivety amusing.
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January 25th, 2013, 02:09 AM   #22
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Re: Was mathematics discovered or invented?

And like math is just about muliplying large numbers :P
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January 28th, 2013, 04:38 AM   #23
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Re: Was mathematics discovered or invented?

well, if only someone would give me ackermann's third number of dollars....or maybe tree(3).
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January 28th, 2013, 04:47 AM   #24
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Re: Was mathematics discovered or invented?

Quote:
Originally Posted by Deveno
well, if only someone would give me ackermann's third number of dollars
man, that's a lots of money

Well IMO, math is about numbers but no just numbers. It's about numbers, generalization of numbers, generalization of those generalized numbers and so on. but math is also about metamath, metametamath, etc. Base of mathematics is numbers but there are still something beyond numbers, something which controls number; i.e. if we can know all the zeros of zeta then we will be able to know the positions of all the primes.(just an example)
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January 28th, 2013, 07:43 AM   #25
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Re: Was mathematics discovered or invented?

Quote:
Originally Posted by Deveno
well, if only someone would give me ackermann's third number of dollars....or maybe tree(3).
Might as well wish that the world economy collapsed...!
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February 17th, 2013, 06:13 PM   #26
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Re: Was mathematics discovered or invented?

I would like to say numbers were invented for the ease of communication by early human beings.
But geometry might have been discovered,because it was all around them and somebody took it seriously and developed geometry.But I don't know how it got connected to math for math was considered all about numbers.Maybe when they found application of numbers in geometry.
I can also think that algebra was also invented out of numbers.
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February 18th, 2013, 05:15 PM   #27
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Re: Was mathematics discovered or invented?

Quote:
Originally Posted by MarkFL
Have you ever had someone, upon hearing that you enjoy or are "good at" math, say, "Oh yeah? Then what's <insert huge number here> times <insert another huge number here>?" And then look expectantly at you to be some kind of savant? I find this naivety amusing.
If you tell someone you are a linguist or a linguistics student or professor, the all but inevitable question is "how many languages do you speak?"
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February 18th, 2013, 05:17 PM   #28
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Re: Was mathematics discovered or invented?

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Originally Posted by agentredlum
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.

Finding that you can bend metal (or carve wood, bone, rock, etc) in a certain way to create an implement that is useful for certain things is a discovery.
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June 18th, 2013, 09:39 PM   #29
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Re: Was mathematics discovered or invented?

Quote:
Originally Posted by mathmaniac
I would like to say numbers were invented for the ease of communication by early human beings.
But geometry might have been discovered,because it was all around them and somebody took it seriously and developed geometry.But I don't know how it got connected to math for math was considered all about numbers.Maybe when they found application of numbers in geometry.
I can also think that algebra was also invented out of numbers.
I am quite much agree with your post. Discovery of geometry does make sense as the previous architecture that still exist and the measure they took. Also the numbers were invented. I think that too that numbers were invented so my conclusion is that math is combination of discovery and invention.
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April 29th, 2014, 01:25 PM   #30
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Originally Posted by CRGreathouse View Post
I fall into the "discovered" group. Mathematics represents eternal truth; we are explorers in this strange new world. We can fail to discover some truths, but we cannot create nor change them.
I agree.

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Originally Posted by Eureka View Post
Discovered through life. There is no mathematics for a rock or a lake. The human mind saw it reasonable to abstract symmetry and repetitiveness into natural numbers. And then the miracle happened. These two simple rules themselves produced further patterns that we keep discovering till today. Just to name a few, the Pythagorean Theorem and Prime Number theorem, e, ?, ?, i and the algebraic closure, Euclidean and non-Euclidean geometries and so on. Ok, not a few but you get the point.

It might seem like this view leeds to logicism championed by Russell and opposed to formalism (i.e. mathematics is just a series of games with the goal being consistency, championed by Hilbert). But my own view is that of Platonism, also hold by Godel. This view supports mathematics is embedded into reality, we discover it because we are alive and sufficiently intricate to conceive it, we are alive because of an statistical anomally of the physical reality. Of course, if you believe in god and creation, Platonisism seems even more probable but my view is you can also believe, with good foundations, in it even by working only with the evidence you have.

For certain, it boils down to whether the axioms of mathematics are "real" or just seem real to us mortal men. Since the minimum axioms boil down to symmetry (relationships to 1) and arbitrary extensionality (in theory infinite computations with 1), we must question these. Are crown is certainly 1. This is the chief axiom. Artificial intelligence will begin to compete us when it will have "common sence" to reckognize 1 chair, 1 human, 1 self- itself. This giant step, if realised, will change the face of the world.

If we have sinned, it may be in our notion of arbitrary extensionality, or infinity. Does our universe have an end? Even more important to mathematicians - is there a point, an insanely large number after which no new theorem can be obtained. The answer amazingly is no. Think simply the never ending primes and the infinity of computations to get the "exact" ?. Can it be our abstraction of infinity be an act of genius afterall? Max Tegmark through his Mathematical universe hypothesis explains the possibility whatever entity existing in the mathemtical world occupying a physical counterpart somewhere, sometime. Of course! If the universe is unlimited this is not even a chance - it is a possibility with 100% chances of happening!

But don't let infinity fry your minds, like Cantor and Godel. We are humans and we can only live with 1. Infinity is our ally but a superior one we should use with caution. To get a foot in reality and support my Platonic view (thus math is discovered) I support symmetry is a physical law and so not just a man made axiom. See the three components of our surroundings - they end up being either the Up or Down quark, or an electron. Why is it that way? Why aren't there an infinity of different particles. The answer is because our reality is symmetrical, thus we have right to devise arithmetic.

This discussion can lead to the basic foundation of what is - or the absence of any basis. Who made symmetry? Taking a cue from some remarkable piece of proofs by Cantor, the number line is a line because of the uncountably many transcedental numbers - the numbers constructed by infinity. Our reality as it seems is not transcedental- we have finite particles afterall that support that. My conclusion is our universe is a statistical abnormallity. There exist infinitely more universes without any law, just chaos. Is there life and consciousness in those universes? Maybe we don't invent anything, we just discover...
I dont understand all this, but I agree with what I understand.

I think math was invented, but not by humans, rather by God.
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