Is mathematics discovered or invented?

[@subscribefornoreason542]

Mathematics is a discovery. Our way of expressing it is invented.

[@TheJackTheLion]

This

[@kanhaiyalalrajput3215]

Exactly 💯

[@ZebecZT]

If all of the eloquence and beauty is discovered, it leads to a fundamental theological question.

[@LuisAlbertoRodriguezGoff]

Discovered, the symbols and operations to describe are invented.

[@Theo_Caro]

In virtue of what is 7+5=12 true?

[@jabibgalt5551]

@@Theo_Caro 7+5=12 is true in virtue of Reality. Truth is that which corresponds with Reality. The statement 7+5=12 is true by definition. Seven units, plus five units, equals twelve units. The unit is any aspect of Reality. Seven lemons plus five lemons equals twelve lemons. 3+3=5 is false by virtue of Reality. We know that adding three units and three units, we get six units, not five.

[@LuisAlbertoRodriguezGoff]

Bigsey yes. Such is what I meant to communicate. Though apparently I failed at it.

[@LuisAlbertoRodriguezGoff]

Theo_Caro meaning.

[@kilian8250]

@@jabibgalt5551 but who decides what numbers mean?

[@BlahBlahBlah13623]

I was actually having a heated conversation about this with a few friends a month or two ago. I'm no expert, although think this ultimately comes down to what 'mathematics' actually is. Is mathematics the study of the patterns we observe in the natural world or is it those actual patterns? After some quick research, the definition of mathematics seems debatable and subjective, so I think the answer to this question is the same. If it is the actual study and description of the patterns and relationships in the physical world - the medium in which we explain these patterns - then it would be invented. Although, if mathematics is those actual observable patterns, then it is discovered. Eddie raised an interesting point about how something's discovery implies it is independent of human measurement and observation, and I agree. Personally, I think that mathematics actually IS those relationships that we explore and explain through the language of mathematics. Hence, it is discovered, but I totally understand why someone would be inclined to think the opposite. Very interesting. I wish I was in this class.

[@alessioandreoli2145]

Well no. There is a branch of mathematics that believes that numbers exist as entities and are everything but a tool or something that you can invent. If you think about, you will see that at the very least is not falsifiable

[@glennsnare09]

Me too

[@Fedreal_Bureau_Of_Investigaton]

We discover the laws of the universe and invent, formulate the rigourus language we can talk about them, since math is not perfect and sometime needs updates because It's just an aproximation of reality it's invented. Think for example about limits or irrational numbers, they were added to keep touch with our new discoveries about reality. This doesn't mean it's not important, absolutely.

[@KEvronista]

patterns only exist when their parts are put into a set. only minds create sets. KEvron

[@hypersonicrush]

Comment - *7 years ago* Replies - *1-2 years ago*

[@verstengenericks]

The passion that comes through in the posing of this question--is wonderful, even beautiful...

[@sirtthetea1904]

In my opinion, universe is as it is. Mathematics is a tool we invented to describe it.

[@WaWa-cn2ff]

Or is it a tool that we discovered to describe it?

[@Theo_Caro]

@@WaWa-cn2ff Mathematics does not describe the world. If it did Euclidean Geometry would be false in its entirety. Mathematical statements are only true or false within an axiomatic system.

[@54eopifkg3ehfkj43]

@@Theo_Caro All youve done is push it back. There exists a collection of all axiomatic systems, and mathematicians just search through this collection finding tautologies within it. Thus, mathematics is discovered.

[@ianwybul6183]

@@Theo_Caro It does a very good job at empirical description

[@nikitabrykov5824]

@@Theo_Caro in that sense doesnt describe reality either. The point is that mathematics forms good models in some cases

[@ragerecords2476]

the basic fundamental concepts(such as lines,points,integers) are invented and discoveries are based on those concepts

[@DeJay7]

Mathematics really is both a discovery and an invention. We Invented symbols to describe things we discovered. We discovered the speed at which objects fall due to gravity, and because of that we had to invent a way of describing it.

[@rollingdownfalling]

I think the notations, numbers, operation are invented. Then the axioms are discovered, like the associative, reflexive, the existence of dimension etc. And then you put them together you discover more law or more weird things happening and then you invent more ways to group certain things together and to label certain things and such.

[@antoniomonteiro1203]

My opinion is that there are things that are discovered and things that were invented. In the first case are for instance numbers like pi or e, because the numbers themselves always existed. We just didn't know what they were or, in other words, what properties those numbers have. Likewise, relationships of angles and segments related to circles or triangles, were discovered. In the second case I see the tools, like complex numbers or derivatives or integrals, that were created to help us solve some problems.

[@SocksWithSandals]

Mathematics is based on axioms: Arbitrary laws and definitions from which we all agree whether or not they are true. From these, logical investigations follow. Occasionally we stumble upon a mathematical relationship that describes the physical world, but there's no reason why any given phenomenon should follow any given equation. Just sometimes it does.

[@inlandviews]

Always thought of it as a language used to describe reality.

[@ChauTu]

Nice lesson. Can I say both? We invent mathematical tools in order to make new discoveries.

[@raj-2093]

Mathematics is a way to quantify the physical nature around us.

[@Veins1]

um... where's the rest of the video? or better, where the results of this question?

[@nicholaschin8804]

The result is left as an exercise to the interested audience.

[@sadudas11]

In the comments section

[@marktyronebarandino3147]

h

[@sirmarkkevin954]

You should include the debate of students

[@thisnamegoeseveronandonove7824]

Invented, based on discoveries, I guess. (e.g. *one* twig is fundamentally different from *two* - an observation.)

[@dejremi8190]

To me, the mere fact that every physical model has to be changed to another every now and then to fit the new empirical data is a testimony of the fact that it's an invention However, Mathematics within it's own range of formal application is invented then discovered. I mean it in the sens of: We first invent maths(the rules and the objects) then maths is there and we discover the implications of what we've invented, in the same way that we invented chess, but still, in the beginning, didn't know what was the shortest game possible for example, then we discovered that through the examination of the objects(the pieces and the Board) and the rules that tie them together. Overall, I think we need to redefine what is discovering. I don't think that discovering is to unearth patterns that are Independent of the human mind but rather becoming aware of things that are dependent of our mind but whose place in our inconscious we didn't realise. Really I think that the Idea that the mind is able to generate so powerful abstractions is even more beautiful than the one stating that we can only slightly intersect a physical reality whose victims we are.

[@Lleanlleawrg]

The symbols and operations seem to me to be invented, but the underlying quantities and relationships are seemingly discovered. They would exist without anyone to observe or define.

[@bm148]

In my opinion mathematics are a ''human model'' of making sense and translating the behaviour of natural patterns. I'll say mathematics it's us, it's the way we interpret the world around us based strongly on the interconnection between our senses, structure of our brain and surrounding environment. I'd rather say that mathematics is like a 'print on our lenses' that is changing accordingly to our evolution. Maybe one day we'll see mathematics as a primitive tool but very efficient one in its time, day in which the new model of making sense of the natural laws will be different from what we know as mathematics(for that we need to wait). Let's say that on an alien planet, fungi, trees and many other plants exist, but no animals. The fungi and trees evolved a conscious mind. The first environment of the fungi to deal with in its early evolution would be one of 'electricity, chemistry and quantum phenomena'. Same with trees, no manipulative members, no eyes, no ears etc. but still evolving a spherical vision in an environment where there is not much physical movement apart from the movement at the chemical and quantum level. I bet they will have a different model to make sense of the patterns of their natural world, but in some sense their models would be similar to our mathematics according that the laws of nature are the same, and not continuously evolving, as new conscious species 'add' new undiscovered laws in the universe. As a sphere of influence in the local universe around them, by the act of observing(with a different mentality) the quest for discovery :)) So, contradicting myself, my ''today' opinion about either mathematics is discovered or invented, I'll say neither. I'll say it's evolved and very specific to our own way of 'absorbing reality'.

[@jagatchaitanyaprabhala8668]

Basic high school and applied engineering mathematics is discovered but higher mathematics like abstract algebra is invented but yes the invention was triggered by observable patterns

[@MLGTommy47]

he predicted the 2020-2021 Big Questions Debate resolution

[@wieczor3000]

It depends what do you call mathematics :) That what is mathematics for most of people (symbols, formulas etc.) is invented. But it's not mathematics. It's language of mathematics. So mathematics is discovered - language of mathematics is invented (same as in other sciences i.e. physics).

[@johnshannon9656]

The notation in math is invented. E = mc2 could've been written as P = kc2 (but note the "2" is fixed!) The rule/law/axiom behind any notation is discovered.

[@XlancerTHEgreat1]

Mathematics is a tool that we invented to help us explore & discover the universe around us. Because whenever we discover something that disagrees with our current version of mathematics, we update our mathematical tools to better explore and discover the universe in the future.

[@junkyyard2273]

its like a language. The image itself or the concept is already there, we're just finding ways to describe it in paper

[@andrewshirley9240]

I think it's a little bit of both. To explain, we can use an analogy to science- Say, combustion. It is a discovery that the gas emitted from gasoline is combustible. It is discovered that air will move from a higher pressure to a lower pressure. The ways forces and angular momentum all fundamentally work are discovered. But an engine is decidedly an invention. It's a human who has taken all of the innate traits of reality and molded them into something useful to us, in a way that can only be done if the discovered reality is understood. Similarly, math just IS. It's a set of laws that can't be changed, merely discovered. Even if you consider the possibility that some of our axioms are false or incomplete, mathematics IS the framework that describes the interaction between such axioms, no matter what set of axioms is chosen. But humans have made tons of discoveries in math among our chosen set of axioms and have begun putting them together. This often leads to more discoveries, sure, but specific instances of those concepts become useful tools for us to better handle the world around us. Mathematics (the field) is discovered, while Applied Mathematics is invented.

[@maviemhoniqueg.prosia7801]

Damn

[@Wintersghost135]

Some may have different opinions on which invented math system is best; numbers of base 10, base 8, base 12, etc. These were invented to describe the things that are discovered - such as each block of iron on a theoretically perfectly balanced teeter totter must have the exact same number of atoms to remain balanced. If any atoms are added or subtracted, then they will be out of balance, regardless of one’s opinion.

[@DevSharma-in5qy]

What about mathematics being a subject to express Express different ideas. For example mathematician wanted to name something as square root of negative 1 (√-1) so they gave it a name " i "so I think mathematics is an invention.

[@lm58142]

If homework is not given - is it still difficult?

[@nvvam7597]

I am not proficient in math and the level of my knowledge in math does not extend beyond simple algebra, which is to say very little. From a philosophical point of view, because I can't explain in it scientific terms, I am inclined to believe the laws of math are innate within our physical universe. These laws were discovered by mathematicians. The mathematical symbols that perhaps represent a specific law were invented in order to explain said law, and apply it accordingly in the real world. I believe if we were to go back in time and begin all over again, the equations, theories, symbols would be fairly similar to the ones we have today. For example I conclude that E=mc2 , would be repeated nearly identically if not verbatim . Because this theory is a scientific law, a smart person like Einstein , or ever someone else, would come up with this equation to explain the law. I contend mathematical law has always existed, there for it is discovered more than it is randomly invented.. Could someone please comment on what I postulate and tell me if I make or don't make sense..

[@khaledyasser8293]

nv vam makes sense

[@majid__jafari]

I think it is discovery. Because we dont get to choose how many apples we would have if we add up 2 apples with 3 apples. It will always be 5. There are lots of math problems that are yet to be solved. If math was invention we could just set an answer for these problems. Just like a puzzle that needs to be solved. Its all about rules and you cant just change them. But the symbols are just invented to help us talk about these rules.

[@tom_curtis]

In the words of Henri Poincaire, mathematics is convention, but not arbitrary convention. This is most immediately obvious by considering the various non-standard mathematical systems, such as those that only use finitary methods, or the debate around the axiom of choice. What it means for this question is that in mathematics some features of mathematics are invented, but the consequences of those features are a matter of discovery; as also are the practical uses of the formal system based on those inventions.

[@konmingyew7282]

I see it this way, the universe laws and how it works are independent of human input. Mathematics is the language by which we explain the laws and come to predictions. So in some extent mathematics is tied to how the universe works, but apparently there are arguments that maths is able to explain things out of this reality, like for example a fourth dimension, not based on observations but pure mathematics, what they call if I'm not wrong 'a platonic world.' Mathematics is a concept whereas language and units are invented, like m/s or inches for example. So really the question is whether mathematics is a language of this universe that we humans use, or is it a concept that exists past this reality.

[@anEyePhil]

Great video, but you left out the cognitive neurology of the human brain. Mathematical abstractions emerge as the human brain finds patterns in the multitude of perceptions it receives and attends to. For example we finds "twoness" in the following - AA. BB. CC. DD. ZZ. The number "two" exists only in the brain's interpretation of the pattern in perception, not in what it actually perceives. Good question: "Can animals count, do they know maths and numbers?"

[@michaelbell5984]

It seems to me that the whole of maths, at least the bits that I have studied, depend on a system of counting. And counting presupposes the existence of distinct and equal entities. But fundamentally these may not really exist except in the imagination. To quote Bertrand Russell '"Two entities and two entities are four entities." When you have told me what you mean by "entity," we will resume the argument. ' You could therefore are that Maths is humankind's best approximation to understand the natural world. As such it is therefore invented.

[@encounteringjack5699]

I think it was discovered but the symbols and formulas were invented.

[@starofdc]

Although laws of nature are inherent, mathematics was invented as a means to describe these laws. Mathematics is a philosophy that humans have formulated from man-made definitions based off observations. This is to say that fundamental postulates such as 1+1=2 were invented as a means of communicating quantitatively. To discover is to come across new information such finding new planets. We may discover new approaches to calculate or model concepts, however these discoveries are found by utilising the invented tool of mathematics. For Newton's Second Law of Motion, we may state that an object will speed up if a force is applied to it from mere observation or 'discovery'. However, we equivalently use the mathematical description F=ma (using units that humans arbitrarily invented) to describe this discovery. Mathematics is the language in which we use to describe these conditions. Just like every other language, it is an invention, not a discovery.

[@Mr_T.]

No it wouldn't exist if there were no humans left. Mathematics is an idea not an object. It's good for descriptions, measurements and models but possesses no physical properties of it's own. When birds sing, it doesn't mean music theory exists. To capitalize on Daniel's point, mathematics is a language that describes form and function but cannot exist as a form or function of its own independent of the human mind. To say that mathematical laws exist in nature is to anthropomorphize a mental construct into natural unguided processes.

[@elisendadomenjo3223]

Exactly is an invented tool (very very very powerfil) to describe How things are and quantiffy them, and therefore make discoveries about the wonderful laws that goverate our universe

[@encounteringjack5699]

Ozzy Puller Mathematics is the study of patterns. Logic is part of mathematics just like our heart, and skeleton, is a part of our body. Then again, logic is based on patterns, and statements that have proof supporting the claims. Mathematics is about studying patterns. Scientists have looked at many things and once a hypothesis is studied, and tested. It later turns into a theory. But those theories weren’t invented, they were observed. Mathematics is the same. We look at patterns, then we assign a meaning to it so it makes sense. Geometry is a good example of already existing data. The things in algebra are still debate-able as to how they are able to be represented by reality completely, but every property of what we know in math always existed. It just took an intelligent mind to point them out.

[@SyedAli-qz1cp]

Negative multiply by negative is positive, is it discovered or in invented?

[@Ensource]

probably taken from the "closer to truth" interviews

[@ba-fe1kx]

What a teacher :)

[@tadejsivic534]

The result is left as an exercise to the viewer.

[@biniljoy2542]

Mathematics is just the figuring out of truths in everything by humans. Same way Mathematics has a true definition we are trying to figure it out. As time progress we will get closer and clearer definitions. Let's try for it.

[@shreyjoshi2550]

I would say mathematics is invented not discovered. Why? Well we are one of the many species in the universe. Mathematics is a beautiful way to solve problems and interpreting logic but is (most probably) used by humans. Think about it, humans can only perceive objects till the 3D, what about planets where it is natural to perceive objects in maybe 7D or 24D or 88D. You never know right. Mathematics CAN only be applied to our perception. It is an invention, but the most beautiful one yet.

[@shreyjoshi2550]

1D, 2D, 3D maximum. The probably of dimensions existing above these is high, but maths can't be developed for these because they can't be perceived by us. 4D is a probable theory.

[@shreyjoshi2550]

I'm aware of the difference between theories and theorems, what I'm trying to say is Maths might not be applicable to other dimensions because we might discover something new (in maths) if we ever perceive say 4D. There might be new rules and stuff, those would most probably change quite a few things in maths, but since humanity has never experienced 'discovering a higher dimension', I can't quite say how would it impact on Maths and every science so far.

[@shreyjoshi2550]

Although my intuition says maths is discovered, but we can only discover something that already exists. Maths was created by the human society to solve real-life problems that we encounter day-to-day. There I believe Maths is an invention.

[@TheMasterfulcreator]

You keep saying that we can't have math for higher dimensions than 3D but that's false. We have lots and lots of well established math for higher dimensions. It's very easy. I mean watch, I can make sense of a 4D space simply by defining the space of 4-tuples: (x,y,z,w) where x,y,z,w are each real numbers. Tada! Now we can do calculus on that space. Just put functions on it and we know how to differentiate them using the rules of multi-variate calculus.

[@sharp14x]

Yes, but 4D space isn't "real", it's just an extension of mathematical rules.

[@ramashankarram9493]

Mathematics is discovered ,but it's rules & methods are invented so that we can understand Mathematics easily.

[@MarkMifsud]

The symbols are representations are invented. If by maths we mean the things we know about nature then it is discovered. The consistent patterns in nature are observed therefore discovered. Their properties, for example the properties of circular triangles are discovered. Pascal's triangles was discovered by many different cultures independently. Newton and Leibniz were settling the properties of calculus independently as well. If we lost all knowledge it would eventually be discovered exactly the same way. If by maths we mean The Process of studying these patterns and properties, then one might be able to make the argument that we invented it but I'm inclined to say that most of The Process is discovered. The applications of axioms, rigour and logical structure for a proof to be reliable was not merely invented, it was discovered to be the best way to go about it if we wanted our knowledge to grow over time. Hence also a discovery and again, if a disaster occurs and all knowledge gets lost, it will be rediscovered exactly as we know it today, provided we don't get stupid or go crazy.

[@rhpmike]

I hope group 3 was 'both'.

[@danpost5651]

Math is neither discovered nor invented -- it is developed. Symbolization is invented; short-cuts are discovered; but, the underlying structure of sets requires that the math itself be developed.

[@TheTurntaker]

Maths is invented to discover new things For example newton inventing calculus.

[@RonJohn63]

No. He just realized something that was already there.

[@SoloRenegade]

@@RonJohn63 But math can also be made to describe lots of things that simply don't exist in nature, even though the mathematical logic behind it works. Hard to convince me such a tool is a discovery. Seems like an invented tool to me. It's a good tough debate to have, but I just see too many things that prove it is an invention.

[@RonJohn63]

@@SoloRenegade OTOH, so many esoteric mathematical ideas which seemed to have no "practical" use were subsequently discovered to have great use in -- for example -- physics.

[@SoloRenegade]

@@RonJohn63 sure, but that doesn't mean math isn't an invention. When the airplane was first invented, nobody saw any use for it initially, owing to peoples' endless supply of short-sightedness and early aircraft being extremely limited in capability and performance. Many other inventions throughout history had the same happen. They were invented, treated as novelties until someone else came along and found a practical use for it.

[@RonJohn63]

@@SoloRenegade given that the balloon had practical use in many wars during the 19th century, I've very dubious that *nobody* saw a practical use for the airplane (which is not the same as seeing no practical use for the Wright Flyer).

[@jackcool5798]

its both discovered and invented. some things are discovered the laws that we cannot change. Also some things are invented to make maths easier and shorts cuts that make sense my view ^

[@whalingwithishmael7751]

Eddie Woo Our notations are obviously invented, but I’ve yet to come across a convincing argument that concepts such as numbers and polygons didn’t exist until we invented them

[@jayanthpandit3437]

Discovered. The number systems and methodology of functions and mathematical work was invented. Geometry as well. However, the laws that naturally were applicable to those inventions like addition to the number system, or distributive property to functions or area of a circle to geometry were discovered through means of number operations (invented), distribution processes (invented), and calculus (invented). However, all of it was an eventual invention after the number system was created so it is like an invention that's going to happen regardless so they are really discovered. The system was invented but the significant chunk of mathematics was derived from that basic system and so was therefore discovered.

[@KEvronista]

*"it is like an invention that's going to happen regardless so they are really discovered."* what you're describing is deduction, not discovery. KEvron

[@DarthTwilight]

Discovered, though notation is invented, which is one massive problem with the theory that we're the product of unthinking, random chemical reactions (which would mean either matter is God, or God created matter) and a cosmic jump-start.

[@kensmith8152]

Math being universal should be the first clue Secondly, you have the underlying mathematical formulae of the fractal and Fibonacci sets And finally, you have someone like Einstein admitting that the concept of the theory of relativity came to him in a dream and all he had to do was to connect the dots with formulas.

[@TheMasterfulcreator]

To say that math is invented seems to imply that we had some choice in the truth value of basic geometric truths such as the pythagorean theorem, but clearly we do not.

[@APaleDot]

How can you possibly make this argument now that non-euclidean geometry has been developed? It's clear now that euclidean geometry was simply one of an infinite number of geometries we could have invented to describe the world. The only reason we started there is because of the way our minds work, so we invented a geometry which aligns with how we understand the world.

[@TheMasterfulcreator]

@@APaleDot what i was suggesting is that after you pick your axioms you no longer have choice.

[@cincinnatusdelphiki518]

Great question. I wonder if the same applies to Time. Is Time invented or discovered? Since time is defined arbitrarily by us but it is something that exists in nature. Have we discovered it or is it a tool invented by us?

[@VikeingBlade]

What is time?

[@voluntarism335]

You're asking whether or not it's real or fake, I would say it is real and therefore we discovered it, to say that time was invented would either mean it's fake or someone somehow altered the state of reality meaning him or her is as powerful as god himself

[@osamaqtaitat]

@@voluntarism335what does god have to do with this?

[@APaleDot]

Answer this question: Was chess discovered or invented? Now, tell me how chess differs fundamentally from math.

[@aldrichemrys]

Chess is useful as a game for enjoyment, but that's all it is: a human construct for their own pleasures. Chess can be gone or 'uncreated' and the universe won't care; they don't have any scientific laws dependent on Chess. The practicality of Chess is virtually non-existent. But if we define 'Mathematics' not as a tool to discover and interpret concepts and objects, but as themselves concept and object derived from the physical and material world, then you cannot disregard 'Mathematics', as the universe would cease to exist if 'Mathematics' does not exist as the universe when simplified to time and space since 'Mathematics' are themselves constituents of time and space. The premise that time exists is obvious, and so does space. A posteriori maybe, but still obvious. E.g. If Math is just a human construct, why can't 2 + 2 = 5? (Remember, we're talking about the concept behind it, not the symbols or the representation of it) Try inputting 2 + 2 = 5 on the blueprint of the building, that building will collapse, it will fail. And so with this, you can swap out the word building with universe. You can change the rules for Chess which does not just change the representations of themselves but also the fundamental game itself, like a famous Chess variation called Chess960. If you define "Mathematics" as a tool, rather than as the very concept and object which "Mathematics" under their definition claims to study, then the practicality of "Mathematics" is vastly different to Chess. We made "Mathematics" to interpret the world we live in, we made Chess to create a world for us to play in😉

[@APaleDot]

@@aldrichemrys But you can also change the rules of math as well. 2 + 2 could = 5 if we change the rules by which addition or equation operate. As long as the change does not produce a contradiction, a valid mathematical system can be created that way. You might argue that it's a totally different mathematics and the original system is still as true and valid as ever, there's just another definition for arithmetic which is also true. But this is no different than chess as you point out. You can have infinite variations of chess as long as the rules don't produce impossible results, just like math. Your points about the physical world are irrelevant because math has nothing to do with the physical world. There is lots of math that has no practical application or physical metaphor that we can map it on to. Those areas that do approximate reality were developed specifically because people were looking for ways to simplify and analyze the world. Math is only ever an abstraction, it always contains less information than the phenomenon it's describing.

[@aldrichemrys]

APaleDot Well, I disagree with just about everything you said, however that could be that you interpreted me wrong or I interpreted your reply incorrectly. But, I guess that’s the nature of Philosophy of Mathematics. I can already tell both of us will talk past each other if we continue this discussion as we will just be restating our positions. I am only starting to realize chat or text message is an ineffective way to have a dialogue or debate, and that it’s just better to leave our idea once and maybe add some clarification to bite-sized questions but that’s it. Anyway, have a g’day.

[@wick9462]

02:49 play it again .lol

[@CrashSable]

Invented. Mathematics is an invented language used to describe quantifiable "things" in the universe. You could invent an entirely separate, but equally valid form of mathematics to describe the same things, but the things that are being described aren't included under the term "Mathematics", only the language used to describe them is. Same as how any other language works. English isn't a more valid language than Mandarin or vice versa, they are just two separate means (invented separately) of communicating the same ideas.

[@RonJohn63]

How else do you quantifiably describe "1+1=2"?

[@CrashSable]

@@RonJohn63 Put a rock down, then put another rock next to it...

[@RonJohn63]

@@CrashSable my comment was about the first paragraph, not the second. Anyway, "1+1=2" is the generalization of one rock next to another rock, one sheep next to another sheep, etc. How else do you quantify that generalization?

[@VictoriaFilmsgroup]

i think the large majority agrees on it as a discovery just like philosophical concepts and a discovery that is not a result of a long process would be called a revelation, so really i dont understand how science could be opposite of religion.

[@louisrovegno542]

Euler’s Identity is a discovery. Proof by Induction is an invention. Both are math.

[@NefariousNegus30]

Arithmetic and cardinal numbers were discovered; the symbols used to express them were invented. Mathematics and logic are two sides of the same coin; one os used to quantify while the other clarifies.

[@johnSmith-my9yj]

It took centuries to discover the proof of Fermat's last theorem. Godel showed that mathematics is incomplete, that there are mathematical truths that can't be proven. Those truths exist, we know that for a proposition P, either P or not_P is true. But you can hardly claim to have invented those truths if you can never know them.

[@tom_curtis]

More correctly, Godel showed that arithmetic is either incomplete, or inconsistent; or in other words, he proved that there can be no consistency proof for arithmetic.

[@SocksWithSandals]

What if you assert " this assertion is false", for example?

[@smitsalwankar7035]

@@tom_curtis he said that if a system is more complex it better performs

[@BaldingEagle51]

Invented. In addition to this article: It's also invented to ignore almost all knowledge and data by way of reduction and selection. Only when reality deviates from mathematics is there a leap of knowledge in Physics, or another descriptive language is used for the new phenomena. Here's Weinberg. maximilion.wordpress.com/2019/06/03/is-mathematics-invented-or-discovered/

[@RonJohn63]

"1+1=2" no matter how you describe it.

[@jiviteshbakshi2093]

If I see a new animal and give it a name, I am discovering the animal as well aa inventing the word. The answer should depend on what maths mean. If it means the study of patterns we know should be true on the basis of axioms, then maths is discovered. If it is those patterns and the methods we develop to interact and manipulate the patterns, it is an invention. And in my view, it is partly both

[@nikitabrykov5824]

2:00 it was never true, it only gave good approximations hence invented(in a way). Even today, QF gives better approximations than what Einstein suggested, so how could that ever be true. Knowledge is a forever improving medium for describing reality, but it will never be perfect

[@reshiramex1399]

whys he got a smaller white board on a bigger one

[@christian2M]

Maybe all af them, discovered AND invented.

[@thsc9119]

Mathematics seems to be out there totally independent of us, and surely there are mathematical truths still awaiting discovery. Yes, we can describe them with natural language or formulae, but instances of pi and the Fibonacci sequence were certainly out there before anyone looked. Indeed, before humans even came along! The real philosophical mystery is how did that happen? Is the answer an intelligent designer, a cosmic magician? That strikes me as highly unlikely. Yet, how can such mathematical phenomena just happen?

[@KEvronista]

*"seems to be out there"* out where? in what manner does it exist there? *"there are mathematical truths"* truth values are assigned to propositions, both mathematical and conventional, thus they don't exist absent a valuating agent. *"still awaiting discovery"* math is deductive; the properties of its axiomatic systems are deduced. the universe has no need for math. stars form and explode without ever having to carry the one. KEvron

[@paulbin]

Its invented, but since math is the language of truth and everything in math is true it seems to be a discovery.

[@MetalliCxZero]

Math is an invention. The laws and physical properties of our universe are discovered, but the language we use to describe them and the method by which we discover them is math, our own invention

[@TimCrinion]

If mathematics were invented, not discovered, then shouldn't all numbers be describable? But the set of all numbers is uncountable, whereas the set of all describable numbers is countable (since the set of all English sentences is countable).

[@APaleDot]

It's quite trivial to invent concepts which are indescribable or unintelligible. Just because you can write something down, does not mean that it has to be comprehensible.

[@ronaldmarcks1842]

I think mathematics is filtered. Yes, it's "out there", but our human brains filter what can be detected and described.

[@commentarytalk1446]

Agree. Other descriptions could be used usefully too.

[@vanvantrunktrunk]

For me I would say invented? Because Isaac Newton a scientist was having hard time to show proof of his work. So he invented calculus. To show how his laws are a discovery?

[@nickronca1562]

I would say discovered, because 1 + 1 will always equal 2 for instance, whether or not, there is someone thinking it in their head. Calculus still worked before Newton came along, he just discovered how exactly it worked.

[@skeletonrowdie1768]

​@@nickronca1562 But 1 + 1 = 2 is not a real statement to be found anywhere. The whole concept of 'one' is a human made object. From when we're born we learn to see things discretely, and upon that we 'invented' addition. ' I see one thing, I see another thing, let's call it two things! ' (and everbody agrees that we should call it as such). We could also have made up 1+1=1, because if we put one thing and one thing together, then it becomes one bigger thing. It's a true statement, but kind of everybody agrees that this statement is very trivial, as it does not contribute to any other understanding of physical things. So in this sense, I would say we invent mathematics to be usefull to us in relation to the observations we make.

[@hunzalashahid4000]

@@skeletonrowdie1768 That's actually a pretty good explanation. However, there is a flaw in your argument related to '1+1=1'. The thing is, 1+1 is not always meant for objects coming together to form something 'bigger'. For example, if I own a calculator, then go to the store and buy another calculator, that doesn't mean that i have 1 bigger calculator. It means that my calculators have increased in number, no matter how you look at it. So arithmetic expressions are just a way we made up to explain and emphasis a change in number of substance. Although, sure, one could argue that the numerical system is something we invented for the sake of our own convenience, that doesn't mean their roots are not tied to those of reality.

[@yeet_yeet_mcskeet9511]

But we’re talking about “math”

[@aashsyed1277]

@@nickronca1562 no, Everything is possible except intelligence aliens

[@abdulhadikus6223]

Either or both, it still fails when it comes do deal with infinity. 1+2+3+4.....=-1/12 is just horse shit. I believe this is a bigger problem, if not a question.

[@CirclesOfMotion]

Axioms of mathematic was 'discovered' from our interaction with the world. Complex structures or patterns derived from applying these axioms are more crafted or 'invented' than discovered. Sometimes in math we check do some complex structures are contradict to these axioms (or are they false or true). This is mix of invention and discovery too. Simple as this.

[@varunsaproo4120]

I think mathematics is a language which help in discovering the concept and also make us understand the concept. So I think, the language is invented

[@DanZhukovin]

Exactly. That is exactly the formulation of mathematics. Unless a person is completely linguistically daft, they are going to choose "discovered". I guess there is the option "this is a loaded question", since that falls under proper interpretation of the question also.

[@MohamedKulaiay]

mathematics is invented to discover the world

[@strawberryinthesky607]

too broad of a question. Parts of it are either or.

[@pabico4973]

Mathematics is a discovery ... saying it's an invention is like saying fire is an invention. we may have invented the "lighter" but fire is certainly a discovery. `

[@pabico4973]

or better yet because we engineer a watch we say we inventented time... time is beyond humans it's naturally occuring same can be said about math

[@fexcasanova]

If we can invent Math, do you think we can invent a "new Math" that contradicts the old Math(but that new Math should be true and "applyable' to reality, like we do already through engineering)??If Math is invented that should be possible, right??

[@KEvronista]

if current math describes reality, any new math must do the same. if both describe reality, then neither would contradict the other. KEvron

[@franciscoduarte1925]

First geometry was discovered..than math describe

[@paulwillisorg]

invented.

[@xOxAdnanxOx]

If it invented then everything else is delusion.

[@GuitarWithBrett]

It’s revealed by Jesus

[@ginohanggangleeg8129]

Amen

[@krishnaasopa-the-next]

FACT, YOU ARE WATCHING THIS VEDIO IN HALF SCREEN 😹😸😺

[@maxwellsequation4887]

How?

[@krishnaasopa-the-next]

@@maxwellsequation4887 bhai I am legend

[@STaSHZILLA420]

It was translated.

[@PriyaSivashankar7]

Maths was invented to discover truth

[@krishneilsingh7550]

Maths is the study of patterns. These patterns are observed or accidentally stumbled upon. Therefore they are discovered. Also there is a lot of crossover with science which is also discovered.

[@krishneilsingh7550]

Excellent point- I can't think of a method to integrate in the real world but I think that maths was originally discovered and then this information was used to invent new branches of maths. Like elements where discovered and unnatural compounds were invented from those elements as they didn't exist before. Also I'm a school student and huge fan of your work Mr Woo, Your videos make mathematical concepts easy to understand with lots of background info which other teachers often miss.

[@zeromph8325]

Like anything ingenious, it was discovered. Already there waiting to be tripped over by nosey folk.

[@TheRemake1]

Mathematics was invented in order to discover things in our natural world aka physics.

[@FrizzelFry]

But if the physical world behaves according to mathematical rules, did the physical world not discover math before we did ?

[@RonJohn63]

The *language that we use* to *describe* mathematics was invented (over many centuries), but mathematics have always been there. After all, "1+1=2" no matter how you describe it.

[@maxwellsequation4887]

@@RonJohn63 you are God damn right

[@Michooalgo]

Mathematics are invented obviously. We created mathematics to understand the world around us. Mathematics are a language that we created to refer to a law of the universe.

[@DanZhukovin]

It's invented. Just a descriptive fact, and all other arguments are normative.

[@whalingwithishmael7751]

It’s discovered. Objects like numbers and spheres exist and have their properties independent of our knowledge of them.

[@jet5995]

“Sanskrit”

[@MrLaTEchno]

.......discovered....take the problem away,....here you got nothing to invent. So we look first then we look for the tools there are to use...here you find rules on rules... The game is to get the simple solution...as in nature where there is a balance.... So every problem needs to be balanced... with that what nature gives us.

[@jkli6031]

Actually both

[@TheMasterfulcreator]

Could you really sensibly argue that the pythagorean theorem, for example, is invented? It seems very hard to argue that this relationship between the sides of right triangles is not discovered.

[@glennsnare09]

The relationship itself existed before humans came along and used the language of mathematics to describe it. It comes down to this. Is mathematics what is actually being observed, or is mathematics the tool we use to describe what we are observing. I think it is the tool that we use to describe what we are observing. Which means that mathematics itself is invented. But the concepts and laws that math is used to describe, are discovered

[@TheMasterfulcreator]

@@glennsnare09 nice

[@illseeyounextweek1047]

@@glennsnare09 except pythagorean theorem relies on conceptual shapes, show me where a right angle triangle (as an object) exists in reality, we created shapes, then we DISCOVERED relationships, it is something considered, not perceived. As far as evidence has shown so far, maths is a human construct, until it isn't.

[@kimsahl8555]

Some math is discovered some is invented.

[@KEvronista]

which is which? KEvron

[@kimsahl8555]

@@KEvronista Math = all quantity and their mutual manipulations. The invented math only exist in the mind, the discovered math also exist out of the mind.

[@kimsahl8555]

There will be a math that is't discovered and is't invented.

[@KEvronista]

@@kimsahl8555 *"the discovered math also exist out of the mind"* where, then, does it exist, if not in the mind, and what is the nature of its existence? KEvron

[@kimsahl8555]

@@KEvronista Definition, math = all quantity and their mutual manipulations. Ok, everything = all objects called the elements of the Nature. An element x of Nature = the quality of x + the quantity of x. Take an animal X lived mio. years ago we don't know, the quantity of X is a math exist out of the mind (X = an element of everything, so X have a quality + a quantity).

[@celeritasc9207]

How about God. Was God discovered or invented? (Feel free to substitute Religion for God). Answer is dead simple.

[@AlfredoTifi]

I'm not really sure E=mc² was "discovered", provided inertia and energy are invented concepts, over the empirical data. The premises of physics and math can be equally invented, although with different perspectives (of matching with experiment). Experiment are used anyway in mathematics too!

[@cloudgalaxy9231]

Math feels discovered when I do it. -- But I think this is a false dichotomy. What if there are additional options for math? Like, what does it mean for something to be real? I think that our concepts for things like chairs and the like are so messy and poorly defined that I believe we are just making those concepts up. We call the collection of atoms a chair. I think the ideas of causation, space, and time are all contingent on themselves to be expressed, which makes me doubt their existence. There is no proof of them but an appeal to them. I think the only thing that nothing can do without is the idea of relationships between things. This would then be the axiom of all of reality. Is math real...? The language is nothing special, and the way that it is constructed is not either. But is what the language refers to real or not? That's the real question. But what does 2 + 2 = 4 actually refer to? I don't think it refers to anything directly. It is a placeholder which objects and their relations can be described. If two things and two things are put together there are four things-- that is true of things as we experience them-- but is that the same thing as saying that the generalization of all of those cases is true? If I define perfectly what a cup is, and no one can ever doubt what I mean by a "cup" when I say "cup", then do cups exist? I don't think so. I think only the specifics actually exist. Only the individual relations which when grouped by our minds produce the kind of rules that math is. Math is just a description of reality. It is meaningless without tying to reality- and it only has meaning as it connects back to reality. Point at the math in the world without generalizing. You don't have two atoms and the number 2. That is one too many things. All you have is what is, and there is nothing else. It's the most beautiful tool that inches us closer to the fundamental relation that is everything-- but it is not itself reality. I could change my mind about that though.

[@KEvronista]

*"what does it mean for something to be real?"* it means to exist within reality, which even a falsehood may do. it's the nature of an entity's existence that we must consider: does math exist independently of the mind, or is it a construct of the mind? you seem to side with the second notion, which would put you in the formalist camp. the platonist argues that math exists independently of the mind. *"I could change my mind about that though."* the challenge for the platonist is to explain the nature of its existence, whilst avoiding occham's razor. KEvron

[@vinvin8971]

It neither both...it's ŕealization.....

[@SoloRenegade]

Math can represent things that don't exist in nature.