Was maths created or discovered?

I don’t know much about “maths” but it just seems like a language to describe relationships. I would say humans created it.

I can’t remember how to do long division, however…

Today I learned that ebenezer is from the US and shrubbery is not. Didn’t even have to look at anyone’s profiles. Awesome.

This really depends on how you look at Maths, if you approach Maths as merely a way of finding the relationships between objects then no, humans didn’t create Maths. There are some things in Maths which are so ridiculously complicated that you struggle to see how Maths isn’t just some construct.
The Mathematical relationships have always been there, but how we solve and write Mathematical equations would differ from if someone else had developed Maths- for example the different numerical systems that societies used to have in place. In time we have found that the Arabic numerals introduced to Europe by the Moors are a far more effective way of dealing with numbers. This is also evidence that there is something beyond just an invented system which we have created, societies have developed Mathematical and numerical thinking independently of each other; there must be some underlying principals which humans have attempted to explain and calculate using Maths.
Again with time, people have developed independent ways of measuring time, so there has to be some underlying basis for being able to measure time and to use Maths.

In conclusion, Maths and time have been discovered in natural phenomena and measured and solved. We now come to the point where we are so accurate and advanced in our Maths that we begin to think we may be just creating Maths, because we’re doing things with numbers that we wouldn’t see in the real world.
Both have physical and natural fundamental principals, but we’re pushing these sometimes.

Time is an Illusion. Lunchtime Doubly So.

Wait, so, across the puddle people say “Maths”? As in plural? Wouldn’t it be ”Were maths created…?” I’m so confused…

Haha in answer to andrew yes we say maths, but it’s not so much in a plural sense so we don’t use ‘were’ in this context. Don’t ask me where it all comes from, it’s just what most Brits have grown up with.

In answer to shrubbery erm. I don’t know. It’s a confusing thing but I’m intrieged to know how it would have been ‘discovered’. One thing I always think about also are measurements. Who decided how big a millimeter is? Mad stuff this math stuff.

Well, I think cause of course it’s mathematics, doesn’t it follow to say maths with an s? It’s not just Brits, Australians too

I think what I mean by discovered is that the numbers were already there, the ratios were already there, the equations were already there for us to put symbols in and give names for…? Anyway, it’s open for interpretation I guess…

Ah I see. Well saying that I think that maths is just a language of intepretation. Because you can explain some of these ratios I’m sure with English, or French, or German, or maths. You see where I’m coming from? I think that maths is just a way of looking at it, giving it a standard and making it somewhat internationally understandable. (Unlike my English sometimes)

When the aliens landed in Egypt and S America they put the math concept inside the head of the ancients. Somehow we screwed it all up. We were supposed to be peacefully cultivating moths.

I want so badly to try to form an opinion on this question but each time I type something it looks stupid and uneducated. So I’m, going to shut up and listen.

The answer to this question, shrubbery, has been debated since the time of Plato and Aristotle who both had different ideas about it. To this day, the question is not fully resolved. The answer seems to be both. That is to say, there are mathematical principles apparent in the universe and in nature. We use mathematics to describe them, but we also go beyond that and have mathematical contructs and systems that are driven by our human intellect.

I’ve thought about this too, in my amateurish way, and I won’t pretend to have a definitive answer; but I’m more and more inclined to see math(s) as neither creation nor discovery, but as a recursive insight into the organizing principles of our own intellect. Now let’s see if I can talk my way through this (I’ll not defend any of it too vigorously).

The stuff of the intellect is pattern. Our entire conceptual model of reality is based on it. The brain encodes sensory input in terms of pattern and then uses those stored patterns as a way of making sense of new experience. The entire Universe seems chock full of patterns because that is the internal language by which we represent reality to ourselves.

Semantics and math are our intrinsic rules for pattern identification. But do number and meaning exist objectively, independent of the intellect? I don’t think so. My hunch is that pattern can’t be divorced from mind. Number can’t exist until the mind posits discontinuity; e.g. I can’t have two of something until I determine what constitutes one of something, and that comes down to a semantic determination.

So I suspect that what we’re doing when we look at mathematics is turning inward and unpacking the rules by which we organize our representation of reality. I don’t think that really fits the definition of either “discovery” or of “creation”.

Yes, ‘Maths’ was discovered in a sense that mathematical constructs reflect real relationships, patterns and structures.
And, yes, ‘Maths’ is a product of a human mind in as much as it reflects the way we percieve and analyse reality. I am sure that creatures with different wiring would create a different math-like system.

Didn’t Al Gore discover math?

Knotmyday: Wow, Al is unstoppable. The internet, math.. what will he discover next? Global warming? (oh, wait…) =)

I think we created a way to do math and we also call it math for simplicity. Math has always been there but most people think of math as in “doing math” like an activity.

Does that make sense?

math is a tool, we created it. numbers do not exist outside of the definitions we’ve created for them. operations are a tool to mix numbers and give us other numbers.

the way i think of it is this… someone says he has two snowflakes. this would require both snowflakes to be exactly the same, otherwise he have exactly 2 snowflakes, he’d have 2.4 or 2.0009 snowflakes. and no two snowflakes are the same, so this is impossible. of course, we can have two whole snowflakes, according to the system that we have created, such that it allows us to do such things. to nature, each snowflake would be unique and you couldn’t really compare them.
this analogy falls apart at some point, and isn’t meant as an argument for it, just a way of interpreting it.

I’d like to introduce into evidence in this discussion the peculiar case of Daniel Tammet, the English prodigy who performs truly gigantic mental calculations (including pi to 22,514 places). The reason I think this has a bearing on this question is that Tammet does not do these calculations algorithmically. He doesn’t, in fact, do the calculations; his role is more one of passive observer as the calculations perform themselves in his mental space.

He explains that he experiences number as shape, and that calculations unfold as dynamic transformations of those shapes. This happens without any exertion on his part; he simply reads the resulting shape to arrive at the answer to the calculation.

It’s significant that this is not some technique that he invented, nor did it come from observation of any exterior phenomena. All of this was simply part of his mental equipment.

This is one of the reasons I feel that number is an innate property of of mind and not a concept that we derive from experience.

@Harp, an alternative explanation for the phenomenon might just be a unique, extreme (savant) aptitude for interpreting a natural form? By “natural form” I mean- quantities irrefutably exist in nature, hence the numbers were always there. Humans just verbalized them for convenience.

I guess I’m not convinced that number does exist outside of our minds, Knot. My instinct is that we project number onto our experience, and not vice versa. But I’m totally open to discussion on that point.

Great documentary.

As for patterns in nature, yes patterns themselves exist, and we describe them with functions or equations of the tool we created call mathematics. With these equations/functions we can create an analogy of the natural pattern with a pattern of numbers and as humans, we make the connection between the two.

Numerical relationships exist in our spacetime and we invent maths as tools to explore them. Just as time has always existed (least since Big Bang) and we invent timepieces to explore it.

@Harp That is fascinating. Would you describe his experience as a form of Synesthesia? it alsmost seems that way.

@Marina
Yes, that seems to be the concensus.

@Harp Almost in my last post. Typo. I could have used that ability on that pre-college test in which you had to look at flat boxes and pick which shape they would be folded up!

It feels like it must be true that some stuff exists, and we develop models (i.e. mathematics) that ignore certain details (i.e. the differences between two snowflakes) and hence highlight a certain a deeper, abstract relationship (i.e. the number 2). The weird thing is that math can also be developed on its own with no respect to the outside world, and then become highly useful centuries later. It’s hard to come to terms on why that should continue to happen.

It’s a touch question, is my point.

Thanks for linking to that documentary, Harp, very interesting

@Marina Synesthesia can come in really handy with stuff like that! It makes playing sudoku really boring, though. :(

Okay, sorry to sound like a retard, but what the hell are “maths”?

“maths” is how the word “mathematics” is abbreviated by Her Majesty’s subjects.

A very interesting topic indeed. I will think it is being discovered.

Math is a tool that we use to describe things numerically. 1,2,3, ..etc are just something that we create to measure what is out there and formulas are created to simplify our understanding of the universe numerically.

I agree that mathematics was created, as opposed to discovered. Mathematics is a tool only, for reasoning and hypostulating – not an end in itself. Kind of like a form of transportation you can use to get from A to B, but you have to know why you’re trying to get from A to B. And, the better your mode of transportation is, the farther along you can be carried. In other words, I suck at math(s) but appreciate the talents of others.

if you think of math as the language of science, then math like language is developed (created) rather than discovered. If math was discovered, then couldn’t it follow that a physical reality can be changed by changing it’s mathematical model?

The physicist Eugene Wegner speaks of the “unreasonable effectiveness of mathematics.” Yes math is a tool that can be used by science but it also stands on its own. Why should numbers be so effective in explaining so many things. I take a mystical Platonic approach to math. It is as close as I will get to relgion and I make no apologies about it. I believe that math exists outside of the Universe and is the framework around which any reality must coalesce.

sounds cool, but “framework around which any reality must coalesce”? that’s more than getting close to religion…it is asserting a religion.

Not quite. I am saying that math provides the possible list of patterns that are followed. I am not saying that it explains which patterns are selected.

but those patterns are no more the things they describe than a noun the object it refers to. this will go on and on…i guess that’s part of the beauty of maths…science and art

I agree that we have a fundamental disagreement and I am not going to try to convince you, but I do resent the religion label. I do like your analogy though. There may be a sense in which the noun precedes the object or at least the possible types of object.

This is a dispute that goes on among the highest levels of philosophers. All I am saying is that nobody has yet explained the uncanny ability of mathematics to model the universe. It is especially interesting when things are examined at a large scale with regard to emergent phenomena and common patterns of chaotic behavior. This question will still be around even if the holy grail of a Theory of Everything is ever devised.

@Harp I’m not so sure that the innate pattern-grasping ability of our minds is entirely “phenomenological” or all in our heads. It may well be that the distinction between the “noumenal” (the world independent of our senses) and the “phenomenological” (the world as we perceive it) breaks down at the point of consciousness.

Consciousness, what we take to be our individual consciousness, may actually be a physical process, like photosynthesis (which scientists now believe is a quantum-level phenomenon). It may well be that consciousness creates a kind of mathematical space (a subset of Hilbert space), somewhat the same way that a calculator creates a computational space for all the possible arithmetic operations allowable in the space of it’s display window. (And what we see from that window is more or less constrained by our position in what biologists call “fitness space,” determined by the evolutionary trajectory of our physical and cultural evolution.)

Everywhere we look in the universe, we see fractal geometry . In fact, that may be the underlying mathematics of the cosmos, complete in it’s entirety. If so, holographic perception and memory may be coded and decoded in our experience by a kind of “fractal compression” algorithm of the sort described by the mathematician Michael Barnsley. Alternatively, since fractals are self-replicating, and have essentially the same pattern whether they are very, very, very small or the unimaginably huge, we may all literally carry a complete microcosm of the fractal universe in our heads.

This would apply not only to us, but the same mathematics of consciousness would apply to all of life. Or, to put it another way, all of life and consciousness may be deeply “mathematical.” We should be able to use such a mathematics to construct a 3D version of television, or a Star Trek holodeck someday. It might even become a medium of communication with distant alien species.

Now to the question at hand: I think that maths are discovered in the sense that when we explore mathematical space, we stumble onto relatively permanent features, like pi, phi, zero, infinity, numbers, fractals, arithmetic, ratios, etc., which exist as patterns not only form the deep structures of consciousness but “noumenal” reality as well—in everything from the distribution of the orbital rings of planets, to the distribution of capillaries and synapses. But, I think mathematics are invented to the extent that we develop a notation and a language for talking about these patterns, a set of axioms which allow for mathematically acceptable proofs, and all the other social and cultural aspects of mathematics.

Math is most undoubtedly a human creation originally used to manage things like inventory and further improved to explain or predict natural phenomena.

So easy, a caveman could do it.

We as a species don’t not invent the laws of physics, we discovered them. Math is a human construct. ... 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 is invented.

If math is invented, then how it can be an essential part of the physics that you say is discovered?

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. The LAWS of physics are universal so we had to succumb to those laws. We didn’t invent the laws.

We can’t arbitrarily make up mathematics to match it to the real world. There has to already be a set of physical laws that obey the mathematics. There is no alternative. Both relativity and quantum mechanics obey mathematical laws that are beyond the human imagination. There was some physicist who said that if quantum mechanics makes sense to you, then you really don’t get it. The mathematics is built in. We discovered it. String theory may eventually override our current physics, but it will be a refinement, just as our current physics is a refinement of Newtonian physics. So far it has not been possible to experimentally set up conditions that violate general relativity or quantum mechanics. In every case to date the laws slavishly obey the mathematics.

You folks are confusing mathematical answers with physics laws. We invented equations for statistics etc We had to discover the laws of physics as they don’t change. We had to make the equations fit the laws. Pythagoras created a mathematical equation for his theorems. A squared plus B squared equals C squared. He invented that theorem. Gravity, Thermodynamics and other laws of physics had to be discovered. You cannot write an arbitrary formula for the laws.

“You cannot write an arbitrary formula for the laws.” Exactly what I am trying to say. The mathematics is baked into the physical laws. It would apply regardless of whether or not we were aware of it. We may have had to have come up with the concept of mathematics in a simpler context before we recognized it in physics, but that does not mean that physics is not permeated with mathematics.

There are different types of mathematics only laws for physics.

That is simply not true. The mathematics for general relativity preceded the physics. I am not going to pretend that I understand the mathematics involved, but take a look at the last paragraph in this article

Therefore, the general theory of relativity did not revise mathematics at all. Quite the contrary. Einstein chose another mathematical model of space which was available thanks to mathematicians’ development of non-euclidean geometry the previous century. He formulated the simplest theory when he considered the mathematical implications of the special theory of relativity as well as other phenomena. Instead of natural science revising mathematics, it was the field of mathematics which revised natural science.

Let’s put it this way. If you type in “was matematicas invented or discovered” you find the former answer as well as the latter. I know where you are coming from but math in the form of statics is a prime example of inventing. I’m not going to change your mind and you won’t change mine so we should leave it at that. You quoted this, development of non-euclidean geometry the previous century. Development means inventing in my book, not discovering.There is no law associated with development. If you know that an apple falls so fast you have to make the formula fit that. If you realize like Pythagoras did, the right triangle, creating his theorem, he invented it. It is not a law but a coincidence.

Apologies for posting so late here. I think this is a very interesting debate. Some argue that mathematics was discovered—that it was already there, that it is the best language to describe the world and to uncover its elusive secrets.

Others argue that mathematics was invented by humans for humans.

In essence, the question you’ve asked pertains to what philosophers of mathematics would call “the ontology of mathematics / mathematical objects.”

There is no clear answer for this question. However, we can refer to these to know more about the implications of this question (don’t worry; I’m only posting links to Wiki and Stanford Philosophy):

1. https://en.wikipedia.org/wiki/Philosophy_of_mathematics

2. https://plato.stanford.edu/entries/philosophy-mathematics/