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So I think this is more a philosophical question but ... As humans, we created mathematics, this is something we created from "nothing"(?) in order to explain,

So I think this is more a philosophical question but ... As humans, we created mathematics, this is something we created from "nothing"(?) in order to explain, rationalise things we observe. Now, how can we assume that the universe is logical, and that it can be explained by mathematical equations that WE create? This is bugging my mind every time I think about it.

hliyan 12y ago
As humans, we created mathematics That depends on whether we are talking about mathematics, the method of rigorous notation or, mathematics, the inquiry into quantities without reference to quantities of what (i.e. numbers). We created the former but discovered the latter. I'm neither mathematician nor philosopher, but there seem to be some a priori truths in mathematics (I hope I'm using that term correctly) which are not defined or created by us: the ratio between a circle's circumference and diameter (Pi), the distribution of prime numbers, etc. If you are bugged by where those come from, then I don't think you're alone!
AnimalMuppet 12y ago
If our brains are kludges hacked together by evolution, it is very difficult to understand. If God is a mathematician, and he created humans in his own image, though, then it makes perfect sense.
AngrySkillzz 12y ago
This question is usually called the philosophy of mathematics[1] which is distinct from mathematical logic and has essentially no bearing on the actual practice of mathematics. Some people are Platonists and think that mathematics exists as a sort of idealized mental realm (similar to Plato's theory of forms, but more reasonable in this context). If this is the case, we would say that mathematics is mind-independent and trans-universal; mathematical truths are true regardless of whether we exist to observe them, and they are true in all possible worlds. Others think mathematics is a linguistic "game" played by man, that it is mind-dependent and completely of our creation. Still others think mathematics is a set of derivations within a "formal system" (or formal language); this is sort of a middle ground, as it implies that mathematics is a construct of man but that it has a weaker mind-independence/trans-universal property, namely that any entity in any universe examining the same formal system comes to the same conclusions. But as I said, how you feel about this question has no effect on the real-world practice of mathematics. Most mathematicians you ask will have some opinion on the matter, but it's not like you can say "I'm a Formalist so I don't believe in that theorem." The human process of doing mathematics and the validity of theorems with respect to their assumptions has no relation to the questions of the ontological or metaphysical status of mathematics as a whole. [1] https://en.wikipedia.org/wiki/Philosophy_of_mathematics https://en.wikipedia.org/wiki/Philosophy_of_mathematics
snarfy 12y ago
Did we create mathematics, or discover it? I'd argue a number is just an idea, and all ideas exist whether you've thought of them or not.
ttctciyf 12y ago
Mathematics, in one sense, is an exploration of universal, repeatable, rule-following procedures - if you can't get the same result as me, today, yesterday, and next year, by following my procedure, then whatever my procedure is, it can't be a mathematical one. Therefore the practice of mathematics can only take place in a universe where universal, repeatable, rule-following procedures are possible. It has effective regularity in the cosmos as a dependency. Looked at this way, the thing to be surprised at is not so much the effectiveness of mathematics at describing the universe, but the universe's admission of regularity - once that is granted, both mathematics and its effectiveness seem to follow unproblematically, imo.
nilkn 12y ago
You couldn't ever teach general relativity to your dog. It seems absurd to me to think that there is no theory about the world which is unteachable to humans. We're not that different from dogs in the long run. Perhaps phrased in a more rigorous way, the universe is a spectacularly huge and complex system, and a single human brain is a positively tiny piece of that system, which is very much a part of the system and not external to it. So the question really becomes something like this: to what extent can a tiny little piece of a huge system contain within it a fully functional model of the entire system, which inevitably means it contains a model of itself?
api 12y ago
We didn't create mathematics from nothing. It's a language that we created to describe certain patterns that we saw in the universe, beginning with elementary patterns such as counting and working up to things like calculus. Mathematics is not unreasonably effective any more than English is. Some of these patterns appear so fundamental that it's virtually impossible to imagine them (in a detailed way) as being different. Maybe this is because our brains, being physically embodied, are constrained by these same properties of nature in terms of how they process information. We can't picture 1+1=5 because we literally can't think it. Once you have a language with a grammar, you can also start exploring the "pure" properties of the language. Writers do this with written languages, constructing oddities like Ulysses and "a rose is a rose is a rose" and buffalo^8: https://en.wikipedia.org/wiki/Buffalo_buffalo_Buffalo_buffalo_buffalo_buffalo_Buffalo_buffalo https://en.wikipedia.org/wiki/Buffalo_buffalo_Buffalo_buffal... Since the language was induced from nature, exploring its structure can sometimes let you deduce very strong and powerful hypotheses about nature. But these hypotheses are not true (a.k.a. theories) until they are confirmed by experiment or observation. The combinatorial rule space of a language is so large it will contain an effectively infinite number of meaningless coincidental patterns, and Turing proved that the halting problem is undecidable so you can never be "done." The inverse is also true: there will always be facts of nature that cannot be hypothesized by studying any language or logic system. This is the primary consequence of Godel's incompleteness theorem. TL;DR: Languages are induced to describe reality, therefore you can make conjectures about reality by playing with them. But not all such conjectures are true, and some things must be true that cannot be thus conjectured. Edit: Come to think of it, I am not certain that "The combinatorial rule space of a language is so large it will contain an effectively infinite number of meaningless coincidental patterns" is true, or at least I'm not aware of a proof of this akin to Godel's theorem (wouldn't this be the inverse of Godel's theorem?). It could be that all theorems and patterns in mathematics (and other languages for that matter) either directly reflect something in nature or are isomorphic with something that reflects something in nature. If this were true it would be impossible to make a meaningless statement that is syntactically correct in any language. Tolkien's endless discussions about orcs and elves are talking about something, just maybe not literal orcs and elves.
vinchuco 11y ago
https://m.youtube.com/watch?v=X8aWBcPVPMo https://m.youtube.com/watch?v=X8aWBcPVPMo
heed 12y ago
We didn't create mathematics, we discovered it.
- ruggeri 12y ago
  Kinda both, right? Mathematics is a human-created formalism inspired by, and intended to explain, the natural world. Mathematics is not the real world; it's a map, not the territory. But of course it's not surprising if a map resembles the real world...
- BrainInAJar 12y ago
  we created mathematics as a logical progression from axioms. We invented the axioms (they're about whatever seems "reasonable" to us) and they're the structure on which we build everything in mathematics.
- deleted 12y ago
  [deleted]
- amelius 12y ago
  "God made the integers, all else is the work of man." -- Leopold Kronecker
  - aikah 12y ago
    If mankind could come up with Math and Physics, it's more likely than mankind made up God too. The modern monotheist God isn't that old ,roughly 3000 years. "History" itself is between 10,000 and 20,000 year old. Gods come and go as men do and undo them.
    - AnimalMuppet 12y ago
      But the only value in "coming up" with physics is that it corresponds to the external world - that it's not just a game inside our heads. That is, I don't think you can use mankind coming up with physics to support your argument - unless your argument is that mankind's idea of God also corresponds to the reality of what exists outside our heads.
peterlk 12y ago
Yes, I think this is a philosophical question. The way that I've always come to terms with this question is that humans are a natural outcome of pattern in the universe. We are, after all, just atoms observing other atoms. Fortunately, we're rather complex patterns, so the emergent patterns that form from us are also complex. Math is just a language for describing pattern. The further you go into math, the more patterns on patterns you discover (that's the point of abstraction). To answer your question, I think it's some amount of both. There are basic patterns in the universe that allow for emergent patterns/behavior. So the mathematical equations that we create are just eddies in abstract, emergent pattern.
john_b 12y ago
This may be interesting reading for you if you find this question compelling. https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.htm...
pjungwir 12y ago
Sometimes this is called "the unreasonable effectiveness of mathematics"---if you want something to Google for. I feel like the order of the world is vaguely miraculous. You might also want to read about Euclidean and Non-Euclidean geometries and the history of the parallel postulate for how humans have grappled with this question in the past, and how our thinking has evolved in the last 150ish years. This is a fantastic book with a mix of math, philosophy, and history: http://www.amazon.com/Euclidean-Non-Euclidean-Geometries-Development-History/dp/0716799480 http://www.amazon.com/Euclidean-Non-Euclidean-Geometries-Dev... (I'm sure you can find a used copy for a lot cheaper than that link!) It's sort of an open question whether mathematics is invented or discovered.
walterbell 12y ago
From Eduard Glas, Between Form and Function, Social Issues in Mathematical Change, http://logica.ugent.be/philosophica/fulltexts/42-3.pdf http://logica.ugent.be/philosophica/fulltexts/42-3.pdf "The opposition between the analytic and the synthetic approach to mathematics in the first half of the nineteenth century is well-known.. Less well-known is that both distinctions were rooted in a cultural clash, in the period of the first French Republic, between the established analytical tradition, guided by Lagrange and Laplace, and a new, geometrically-oriented approach, swayed by the revolutionary upstart Monge. These mathematicians had been assigned by the government to normalize and rectify mathematics to a perfectly transparent and hence universally learnable 'language'" Gaspard Monge was the Director of Ecole Polytechnique, the pioneering French military engineering school, educational predecessor of West Point, MIT and others (http://www.uh.edu/engines/asmedall.htm http://www.uh.edu/engines/asmedall.htm). "Monge... expressly rejected the reduction of mathematical reasoning to a formalism. He insisted on the indivisibility of form and content, and denied that any rules, mechanical or otherwise, could be given for the conduct of mathematical investigations. For him, analysis was not a language, closed in itself, but merely the 'script' for the notation of reasonings about quasi-empirical, especially geometric contents."
exelius 12y ago
Think of math as a more precise version of spoken/written language. We use math to describe the world around us in very precise terms. Ultimately though, it's impossible to completely abstract mathematics from language - something that should be taken into account by a discerning reader. All we can do is observe that the behavior of an object in the physical world behaves as the model predicted. With enough observations and enough predictions, we can say with some certainty that the model is accurate. We invented the model, then we tested it and confirmed that it approximates reality, usually within a known range of uncertainty. The universe is still logical in that causality is relatively logical. We're just describing the universe as we see it.

hliyan 12y ago

As humans, we created mathematics That depends on whether we are talking about mathematics, the method of rigorous notation or, mathematics, the inquiry into quantities without reference to quantities of what (i.e. numbers). We created the former but discovered the latter. I'm neither mathematician nor philosopher, but there seem to be some a priori truths in mathematics (I hope I'm using that term correctly) which are not defined or created by us: the ratio between a circle's circumference and diameter (Pi), the distribution of prime numbers, etc. If you are bugged by where those come from, then I don't think you're alone!

AnimalMuppet 12y ago

If our brains are kludges hacked together by evolution, it is very difficult to understand. If God is a mathematician, and he created humans in his own image, though, then it makes perfect sense.

AngrySkillzz 12y ago

This question is usually called the philosophy of mathematics[1] which is distinct from mathematical logic and has essentially no bearing on the actual practice of mathematics. Some people are Platonists and think that mathematics exists as a sort of idealized mental realm (similar to Plato's theory of forms, but more reasonable in this context). If this is the case, we would say that mathematics is mind-independent and trans-universal; mathematical truths are true regardless of whether we exist to observe them, and they are true in all possible worlds. Others think mathematics is a linguistic "game" played by man, that it is mind-dependent and completely of our creation. Still others think mathematics is a set of derivations within a "formal system" (or formal language); this is sort of a middle ground, as it implies that mathematics is a construct of man but that it has a weaker mind-independence/trans-universal property, namely that any entity in any universe examining the same formal system comes to the same conclusions. But as I said, how you feel about this question has no effect on the real-world practice of mathematics. Most mathematicians you ask will have some opinion on the matter, but it's not like you can say "I'm a Formalist so I don't believe in that theorem." The human process of doing mathematics and the validity of theorems with respect to their assumptions has no relation to the questions of the ontological or metaphysical status of mathematics as a whole. [1] https://en.wikipedia.org/wiki/Philosophy_of_mathematics https://en.wikipedia.org/wiki/Philosophy_of_mathematics

snarfy 12y ago

Did we create mathematics, or discover it? I'd argue a number is just an idea, and all ideas exist whether you've thought of them or not.

ttctciyf 12y ago

Mathematics, in one sense, is an exploration of universal, repeatable, rule-following procedures - if you can't get the same result as me, today, yesterday, and next year, by following my procedure, then whatever my procedure is, it can't be a mathematical one. Therefore the practice of mathematics can only take place in a universe where universal, repeatable, rule-following procedures are possible. It has effective regularity in the cosmos as a dependency. Looked at this way, the thing to be surprised at is not so much the effectiveness of mathematics at describing the universe, but the universe's admission of regularity - once that is granted, both mathematics and its effectiveness seem to follow unproblematically, imo.

nilkn 12y ago

You couldn't ever teach general relativity to your dog. It seems absurd to me to think that there is no theory about the world which is unteachable to humans. We're not that different from dogs in the long run. Perhaps phrased in a more rigorous way, the universe is a spectacularly huge and complex system, and a single human brain is a positively tiny piece of that system, which is very much a part of the system and not external to it. So the question really becomes something like this: to what extent can a tiny little piece of a huge system contain within it a fully functional model of the entire system, which inevitably means it contains a model of itself?

api 12y ago

We didn't create mathematics from nothing. It's a language that we created to describe certain patterns that we saw in the universe, beginning with elementary patterns such as counting and working up to things like calculus. Mathematics is not unreasonably effective any more than English is. Some of these patterns appear so fundamental that it's virtually impossible to imagine them (in a detailed way) as being different. Maybe this is because our brains, being physically embodied, are constrained by these same properties of nature in terms of how they process information. We can't picture 1+1=5 because we literally can't think it. Once you have a language with a grammar, you can also start exploring the "pure" properties of the language. Writers do this with written languages, constructing oddities like Ulysses and "a rose is a rose is a rose" and buffalo^8: https://en.wikipedia.org/wiki/Buffalo_buffalo_Buffalo_buffalo_buffalo_buffalo_Buffalo_buffalo https://en.wikipedia.org/wiki/Buffalo_buffalo_Buffalo_buffal... Since the language was induced from nature, exploring its structure can sometimes let you deduce very strong and powerful hypotheses about nature. But these hypotheses are not true (a.k.a. theories) until they are confirmed by experiment or observation. The combinatorial rule space of a language is so large it will contain an effectively infinite number of meaningless coincidental patterns, and Turing proved that the halting problem is undecidable so you can never be "done." The inverse is also true: there will always be facts of nature that cannot be hypothesized by studying any language or logic system. This is the primary consequence of Godel's incompleteness theorem. TL;DR: Languages are induced to describe reality, therefore you can make conjectures about reality by playing with them. But not all such conjectures are true, and some things must be true that cannot be thus conjectured. Edit: Come to think of it, I am not certain that "The combinatorial rule space of a language is so large it will contain an effectively infinite number of meaningless coincidental patterns" is true, or at least I'm not aware of a proof of this akin to Godel's theorem (wouldn't this be the inverse of Godel's theorem?). It could be that all theorems and patterns in mathematics (and other languages for that matter) either directly reflect something in nature or are isomorphic with something that reflects something in nature. If this were true it would be impossible to make a meaningless statement that is syntactically correct in any language. Tolkien's endless discussions about orcs and elves are talking about something, just maybe not literal orcs and elves.

vinchuco 11y ago

https://m.youtube.com/watch?v=X8aWBcPVPMo https://m.youtube.com/watch?v=X8aWBcPVPMo

heed 12y ago

We didn't create mathematics, we discovered it.

ruggeri 12y ago
Kinda both, right? Mathematics is a human-created formalism inspired by, and intended to explain, the natural world. Mathematics is not the real world; it's a map, not the territory. But of course it's not surprising if a map resembles the real world...
BrainInAJar 12y ago
we created mathematics as a logical progression from axioms. We invented the axioms (they're about whatever seems "reasonable" to us) and they're the structure on which we build everything in mathematics.
deleted 12y ago
[deleted]
amelius 12y ago
"God made the integers, all else is the work of man." -- Leopold Kronecker
- aikah 12y ago
  If mankind could come up with Math and Physics, it's more likely than mankind made up God too. The modern monotheist God isn't that old ,roughly 3000 years. "History" itself is between 10,000 and 20,000 year old. Gods come and go as men do and undo them.
  - AnimalMuppet 12y ago
    But the only value in "coming up" with physics is that it corresponds to the external world - that it's not just a game inside our heads. That is, I don't think you can use mankind coming up with physics to support your argument - unless your argument is that mankind's idea of God also corresponds to the reality of what exists outside our heads.

peterlk 12y ago

Yes, I think this is a philosophical question. The way that I've always come to terms with this question is that humans are a natural outcome of pattern in the universe. We are, after all, just atoms observing other atoms. Fortunately, we're rather complex patterns, so the emergent patterns that form from us are also complex. Math is just a language for describing pattern. The further you go into math, the more patterns on patterns you discover (that's the point of abstraction). To answer your question, I think it's some amount of both. There are basic patterns in the universe that allow for emergent patterns/behavior. So the mathematical equations that we create are just eddies in abstract, emergent pattern.

john_b 12y ago

This may be interesting reading for you if you find this question compelling. https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.htm...

pjungwir 12y ago

Sometimes this is called "the unreasonable effectiveness of mathematics"---if you want something to Google for. I feel like the order of the world is vaguely miraculous. You might also want to read about Euclidean and Non-Euclidean geometries and the history of the parallel postulate for how humans have grappled with this question in the past, and how our thinking has evolved in the last 150ish years. This is a fantastic book with a mix of math, philosophy, and history: http://www.amazon.com/Euclidean-Non-Euclidean-Geometries-Development-History/dp/0716799480 http://www.amazon.com/Euclidean-Non-Euclidean-Geometries-Dev... (I'm sure you can find a used copy for a lot cheaper than that link!) It's sort of an open question whether mathematics is invented or discovered.

walterbell 12y ago

From Eduard Glas, Between Form and Function, Social Issues in Mathematical Change, http://logica.ugent.be/philosophica/fulltexts/42-3.pdf http://logica.ugent.be/philosophica/fulltexts/42-3.pdf "The opposition between the analytic and the synthetic approach to mathematics in the first half of the nineteenth century is well-known.. Less well-known is that both distinctions were rooted in a cultural clash, in the period of the first French Republic, between the established analytical tradition, guided by Lagrange and Laplace, and a new, geometrically-oriented approach, swayed by the revolutionary upstart Monge. These mathematicians had been assigned by the government to normalize and rectify mathematics to a perfectly transparent and hence universally learnable 'language'" Gaspard Monge was the Director of Ecole Polytechnique, the pioneering French military engineering school, educational predecessor of West Point, MIT and others (http://www.uh.edu/engines/asmedall.htm http://www.uh.edu/engines/asmedall.htm). "Monge... expressly rejected the reduction of mathematical reasoning to a formalism. He insisted on the indivisibility of form and content, and denied that any rules, mechanical or otherwise, could be given for the conduct of mathematical investigations. For him, analysis was not a language, closed in itself, but merely the 'script' for the notation of reasonings about quasi-empirical, especially geometric contents."

exelius 12y ago

Think of math as a more precise version of spoken/written language. We use math to describe the world around us in very precise terms. Ultimately though, it's impossible to completely abstract mathematics from language - something that should be taken into account by a discerning reader. All we can do is observe that the behavior of an object in the physical world behaves as the model predicted. With enough observations and enough predictions, we can say with some certainty that the model is accurate. We invented the model, then we tested it and confirmed that it approximates reality, usually within a known range of uncertainty. The universe is still logical in that causality is relatively logical. We're just describing the universe as we see it.