# Mathematics -Invented or discovered?

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Had a debate with my chemistry teacher about this.I myself believe maths is discovered, but he believes maths invented.My maths teacher agrees with me?

What do you guys think? Do you believe maths is discovered or invented?

What do you guys think? Do you believe maths is discovered or invented?

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#2

I believe its invented, its just a way we attempt to understand what we observe around us through maths. Its a good subject for debate though.

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(Original post by

I believe its invented, its just a way we attempt to understand what we observe around us through maths. Its a good subject for debate though.

**Chucklevisionary**)I believe its invented, its just a way we attempt to understand what we observe around us through maths. Its a good subject for debate though.

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What about the fact different countries have rediscovered the same mathematics, pythagoras for example? To me mathematics have always existed, not to mention maths is always certain unlike science once the theorem is proved.

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**Chucklevisionary**)

I believe its invented, its just a way we attempt to understand what we observe around us through maths. Its a good subject for debate though.

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I know.Surprised no one on tsr ever debates this.It's always just threads on religion, race blah blah.Never any good stuff like this.

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#5

(Original post by

Had a debate with my chemistry teacher about this.I myself believe maths is discovered, but he believes maths invented.My maths teacher agrees with me?

What do you guys think? Do you believe maths is discovered or invented?

**Kadak**)Had a debate with my chemistry teacher about this.I myself believe maths is discovered, but he believes maths invented.My maths teacher agrees with me?

What do you guys think? Do you believe maths is discovered or invented?

This is actually a topic within the Philosophy of Mathematics more especifically the ontology of Mathematics. Some people call platonists believe that maths exist independently of our human brains while some believe that it is just a human tool to understand the world.

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(Original post by

Wrong forum. This goes in the Philosophy forum.

This is actually a topic within the Philosophy of Mathematics more especifically the ontology of Mathematics. Some people call platonists believe that maths exist independently of our human brains while some believe that it is just a human tool to understand the world.

**Juichiro**)Wrong forum. This goes in the Philosophy forum.

This is actually a topic within the Philosophy of Mathematics more especifically the ontology of Mathematics. Some people call platonists believe that maths exist independently of our human brains while some believe that it is just a human tool to understand the world.

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(Original post by

Yeah, I'm a platonist. If possible, can you ask a mod to move thia please? Anyway are you a platonist?

**Kadak**)Yeah, I'm a platonist. If possible, can you ask a mod to move thia please? Anyway are you a platonist?

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#8

(Original post by

[Surprised no one on tsr ever debates this.

**Kadak**)[Surprised no one on tsr ever debates this.

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(Original post by

If only that were true.

**Mr M**)If only that were true.

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I've never seen any other threads on it though.

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#13

I think it's both. Some things can't be changed and are solid facts - the discovered aspects. Other things we seem to have placed together because they make sense - invented.

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#14

Math in a nutshell is deriving things that you know must exists from a set of given Axioms; and these Axioms we set by observing the real world. Without axioms, you can't prove even the most basic seeming things like 1+1=2. You start with basically obvious, common sense, like things that we get by observing the real world; axioms of addition like a+b = b+a we intuitively learned about, we learned about addition and subtraction by the notion of moving objects into and from sets, then multiplication as simply repeated addition, and division the opposite of multiplication.

Why do we say parallel lines exist in Geometry? Actually we can't, but it is an axiom. Something so obvious, but thousands of years ago, when Euclid wrote the Elements, he struggled to prove that parallel lines existed; and in the end, just included that as an axiom of geometry. Why such an axiom? Because it is useful for us, since it is similar to a lot of the universe around us, it is a model for flat surfaces.

But if you were trying to add degrees in a triangle that you derived from these parallel line axioms that can only exist on a flat surface, while your triangle was on say, a spherical surface, your result wouldn't actually be a model for the real world. The angles actually may not add up to 180 degrees!

Just my two cents.

Why do we say parallel lines exist in Geometry? Actually we can't, but it is an axiom. Something so obvious, but thousands of years ago, when Euclid wrote the Elements, he struggled to prove that parallel lines existed; and in the end, just included that as an axiom of geometry. Why such an axiom? Because it is useful for us, since it is similar to a lot of the universe around us, it is a model for flat surfaces.

But if you were trying to add degrees in a triangle that you derived from these parallel line axioms that can only exist on a flat surface, while your triangle was on say, a spherical surface, your result wouldn't actually be a model for the real world. The angles actually may not add up to 180 degrees!

Just my two cents.

*Give a Mathematician a truth, and he will derive from it another truth that you must also give him, and from that another, and another.*
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#15

I've always found it a bit of an odd question, because really is it both, and it's pretty easy to get caught up in the definitions of 'invented' and 'discovered'. It's perfectly arguable that axioms are invented, and then everything from then on is a 'discovery' from those axioms.

But then you encounter issues where axioms have been defined just so that a certain 'discovery' becomes true, so the whole idea of maths being either discovered or invented is pretty flawed, in my opinion, if not a pointless debate

But then you encounter issues where axioms have been defined just so that a certain 'discovery' becomes true, so the whole idea of maths being either discovered or invented is pretty flawed, in my opinion, if not a pointless debate

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(Original post by

Math in a nutshell is deriving things that you know must exists from a set of given Axioms; and these Axioms we set by observing the real world. Without axioms, you can't prove even the most basic seeming things like 1+1=2. You start with basically obvious, common sense, like things that we get by observing the real world; axioms of addition like a+b = b+a we intuitively learned about, we learned about addition and subtraction by the notion of moving objects into and from sets, then multiplication as simply repeated addition, and division the opposite of multiplication.

Why do we say parallel lines exist in Geometry? Actually we can't, but it is an axiom. Something so obvious, but thousands of years ago, when Euclid wrote the Elements, he struggled to prove that parallel lines existed; and in the end, just included that as an axiom of geometry. Why such an axiom? Because it is useful for us, since it is similar to a lot of the universe around us, it is a model for flat surfaces.

But if you were trying to add degrees in a triangle that you derived from these parallel line axioms that can only exist on a flat surface, while your triangle was on say, a spherical surface, your result wouldn't actually be a model for the real world. The angles actually may not add up to 180 degrees!

Just my two cents.

**CancerousProblem**)Math in a nutshell is deriving things that you know must exists from a set of given Axioms; and these Axioms we set by observing the real world. Without axioms, you can't prove even the most basic seeming things like 1+1=2. You start with basically obvious, common sense, like things that we get by observing the real world; axioms of addition like a+b = b+a we intuitively learned about, we learned about addition and subtraction by the notion of moving objects into and from sets, then multiplication as simply repeated addition, and division the opposite of multiplication.

Why do we say parallel lines exist in Geometry? Actually we can't, but it is an axiom. Something so obvious, but thousands of years ago, when Euclid wrote the Elements, he struggled to prove that parallel lines existed; and in the end, just included that as an axiom of geometry. Why such an axiom? Because it is useful for us, since it is similar to a lot of the universe around us, it is a model for flat surfaces.

But if you were trying to add degrees in a triangle that you derived from these parallel line axioms that can only exist on a flat surface, while your triangle was on say, a spherical surface, your result wouldn't actually be a model for the real world. The angles actually may not add up to 180 degrees!

Just my two cents.

*Give a Mathematician a truth, and he will derive from it another truth that you must also give him, and from that another, and another.*Posted from TSR Mobile

Ah yes I heard that in maths a and b is not the same as b and a, and we are learning alot more about what ( and) means.

Is this why Betrand Russell went to such trouble, 360 pages of it, to prove 1+1=2?

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#18

(Original post by

I think it's both. Some things can't be changed and are solid facts - the discovered aspects. Other things we seem to have placed together because they make sense - invented.

**EllainKahlo**)I think it's both. Some things can't be changed and are solid facts - the discovered aspects. Other things we seem to have placed together because they make sense - invented.

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(Original post by

Well all facts have a big if preceeding them so not sure I would call them solid. Plus whatever we have placed together because it makes sense also qualifies as a fact. To put it in another way, I would argue that maths is not empirical. Conclusion: I don't consider maths a science.

**Juichiro**)Well all facts have a big if preceeding them so not sure I would call them solid. Plus whatever we have placed together because it makes sense also qualifies as a fact. To put it in another way, I would argue that maths is not empirical. Conclusion: I don't consider maths a science.

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Maths isn't a science because maths relies on proof, not experiments.But maths is far more accurate than science since unlike science, once something in maths is proved, it is always certain.

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#20

(Original post by

Posted from TSR Mobile

Ah yes I heard that in maths a and b is not the same as b and a, and we are learning alot more about what ( and) means.

Is this why Betrand Russell went to such trouble, 360 pages of it, to prove 1+1=2?

**Kadak**)Posted from TSR Mobile

Ah yes I heard that in maths a and b is not the same as b and a, and we are learning alot more about what ( and) means.

Is this why Betrand Russell went to such trouble, 360 pages of it, to prove 1+1=2?

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