Is Mathematics invented or discovered?
- Thread starter Idilinaa
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Incorrect answer.
Mathematics is not a play with logic. It is a language humans invented to describe the natural/physical phenomena we discover around us.
The only reason mathematics is admirably suited describing the physical world is that we invented it to do just that. It is a product of the human mind and we make mathematics up as we go along to suit our purposes.
If the universe disappeared, there would be no mathematics in the same way that there would be no football, tennis, chess or any other set of rules with relational structures that we contrived. Mathematics is not discovered, it's invented.
Clllam
Æ
Well, the rules found within maths do concur with those in the natural world. It’s still based on the logic that if a equals b and a equals z, then z equals b. To describe is also true but modern maths is much more fluid than to just be used for the description of the world around us. You can see this with things like imaginary numbers which had no use in the 1600s but only began to find practical importance a couple of centuries after. Obviously, earlier formulations (particularly amongst Greeks) were largely practical, but then you also have abstract concepts.
But your right that the loss of the universe and therefore any of the reasoning required will render it useless.
So all together, I’d still say it’s both. You have the real world occurrences which follow logick and exert influence on our human reasoning, then you have mathematicks which doesn’t solely seek an explanation, but builds itself up through gradual abstraction all deriving from those same natural phenomena.
Not quite.
Mathematics are not as accurate and successful as the ubiquity of mathematical applications has led us to believe. Analytical mathematical equations only ''approximately'' describe the real world, and even then only describe a limited subset of all the phenomena around us. We tend to focus on those physical problems for which we find a way to apply mathematics, so overemphasis on these successes is a form of "cherry picking."
This is the realist position.
The alchemist
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I will try to, in a simple way, stream what I believe to be a valid take from a terminological weak point of view and hope that it registers anywhere close to the vague ideas I have on the matter. I think mathematics is a formalized rigid tool that imperfectly corresponds with something that exists, but math itself cannot be that thing that which we lack the means to be in direct contact with. It's a coordination system that we did not fully invent and fully not invent.
Godel's incompleteness theorem, as a prime example, tells us (quoting the Wikipedia article);
"...no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency."
^For that reason alone, I don't think we 'discovered' a system like a separate superimposed-dimensional law or something like that, only in a flawed methodological way indirectly touch upon some of the same "truths" that the other (with which there is a correlation but not direct contact) comprehensively covers.
I understand that this discussion goes into a tiny aspect of conceptual obscurities that require next level knowledge base, an innovative mind, and not least, extensive language to find a better resolution of the conversation alone, but hopefully, my lazy take is what will suffice to point to the direction of what I mean.
Godel's incompleteness theorem, as a prime example, tells us (quoting the Wikipedia article);
"...no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency."
^For that reason alone, I don't think we 'discovered' a system like a separate superimposed-dimensional law or something like that, only in a flawed methodological way indirectly touch upon some of the same "truths" that the other (with which there is a correlation but not direct contact) comprehensively covers.
I understand that this discussion goes into a tiny aspect of conceptual obscurities that require next level knowledge base, an innovative mind, and not least, extensive language to find a better resolution of the conversation alone, but hopefully, my lazy take is what will suffice to point to the direction of what I mean.
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Clllam
Æ
Well I meant axioms. All axioms are based on logical truths that apply in the real world. But as it gets more abstract, it does only ‘fits in’ or stays ‘accurate’. But then there always must be a ‘better’ substitution for physical descriptions. It Could just be a fault in observation and a wrong mathematical association than a fault in the whole system. A famous example being Einsteinian and Newtonian gravity which are both ‘true’ but the former is ‘better’ suited for physical descriptions as it incorporates a better definition of the phenomenon.
That's a bit of a problem. Logic, as humans understand it and as it relates to mathematics, is a set of artifacts like , Venn diagrams, syllogisms, rules, proofs and algorithms etc
These are definitely things that humans created. Logic that forms the foundation of mathematics itself is based on human reasoning, i can't concieve how logic can exist independently without a subject to think it.
greznigrezni
He/Him/She/Her/It/Zey/Zas/
The concepts were invented.
I believe it's the equivalent of human language to express thoughts and feelings but for the material world. It's invented but used to represent something that is investigated and discovered
Closer to the Truth is a good channel. Never thought I would see another Somali around who watched or watches the programs on there.
Anyway, From the gist of what Penrose says in the video, Math exists independent of us and we discover it. Our physical reality demands mathematics to make sense of it etc. He mentioned Euclid as an example at the beginning. Sometimes it seems the answer to be both invented and discovered. The invention being the road to discovery.
Anyway, From the gist of what Penrose says in the video, Math exists independent of us and we discover it. Our physical reality demands mathematics to make sense of it etc. He mentioned Euclid as an example at the beginning. Sometimes it seems the answer to be both invented and discovered. The invention being the road to discovery.
Clllam
Æ
I’d say the answer is the way God shaped our understanding to have an innate sense of logic. I’d also say a metaphysical analysis is suitable for an alternate reality in which our current understandings of reason are inaplicable.
mrlog
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Omar del Sur
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It is discovered. 2+2 being equal to 4 is an objective reality that exists prior to our cognition. If it were invented then 2+2 could equal 5.
Omar del Sur
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Yes, I think whoever says otherwise is a lunatic attacking objective truth.
Worth mentioning in this thread is how the Arabic numerals the world uses today came about. They were designed by Muḥammad ibn Mūsā al-Khwārizmī (780–850). Each digit represented number of angles.
mrlog
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The curlicue on that 9 though lol
Dont we discover maths through observations of the real world
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