Ace of Mind Posted July 31, 2020 Share Posted July 31, 2020 I've been having discussions with some IRL friends recently who seem to be of the opinion that mathematics is more or less something we (humans) have made up. I personally am more of the opinion that almost every area of mathematics and the fields that require mathematics (physics, etc) are based on discovery rather than invention. The axioms that math builds on have been found to be self-consistently true on a fundamental level; they would continue to be true even if humans had never begun to think about them. Even the intermediately complex topics like physical properties or equations of motion or energy were distilled down from observations of nature; although they may not be watertight axiomatic proofs due to their dependence on observation and data, they work; we didn't conjure some fiction and hope reality agreed, they are THE way to describe and predict those requisite parts of reality, insofar as the parts of reality we have been able to measure. I figure the equations and laws that describe all this would be our there and would still be true regardless of whether we figure them out, so I say such things have been discovered. What do you think, discovered or invented? Link to post Share on other sites
weird elf Posted July 31, 2020 Share Posted July 31, 2020 Why not both? The principles are discovered through the "language" that's been invented to describe them. Link to post Share on other sites
Sarah-Sylvia Posted July 31, 2020 Share Posted July 31, 2020 I read the title as 'match' not math, so I thought it was about relationships lol. I'll go ahead and say that it's invented, because are there really any 'units' in life? Or are we the ones that seperate things and try to say it matters if they're added together or divided? Life doesn't care that there are numbers or not, it just is. So yeah I'd say it's invented and only has any meaning because we give it. The principles work because of logic though, so in that sense we're just discovering what's logical Link to post Share on other sites
RoseGoesToYale Posted July 31, 2020 Share Posted July 31, 2020 Invented. All human concepts of knowledge, right down to language, are socially constructed. Somebody first had to call an apple an apple and not a "gesyubblebutt". Imagine how life would be different if we ate gesyubblebutt pie. Human society today would be significantly different if algebra was based not on the Arabic number system and, say, the Gwandaran language's base 12. Link to post Share on other sites
Purple Red Panda Posted July 31, 2020 Share Posted July 31, 2020 I once watched a multipart TV show about this presented by mathematician and queen of the ginger people Dr Hannah Fry and I'm still none the wiser 🙃 Link to post Share on other sites
Guest Posted July 31, 2020 Share Posted July 31, 2020 Given its incompleteness i want to say invented but given how math is constructed from simple arithmetic rules I want to say discovered. I'm not too deep into math anymore but I would like to hear what others say too. Link to post Share on other sites
Epitaph Posted July 31, 2020 Share Posted July 31, 2020 The blueprints were discovered. The methodology to actually read the blueprints was invented. Link to post Share on other sites
Purple Red Panda Posted July 31, 2020 Share Posted July 31, 2020 22 minutes ago, CBC said: It's just that personally I find such discussions ultimately incredibly useless I once watched a debate about what shape time is, I find it odd that people not on shit loads of drugs actually sit around thinking about such things. Link to post Share on other sites
Homer Posted July 31, 2020 Share Posted July 31, 2020 Invented. The concept is man-made, no? I might ask a maths teacher about this. Link to post Share on other sites
nanogretchen4 Posted July 31, 2020 Share Posted July 31, 2020 Clearly the names and symbols we use to represent numbers are arbitrary, and if we used a different base calculations would look different. I think the axioms of math are objectively true and discovered. However, if our brains and culture were a little different some facets of math might be more obvious to us and others might be less obvious. We might have discovered things in a different order and have different technology. As for the laws of physics, I'm not so sure. They are only accurate to a finite number of decimal places, and their accuracy is circumstantial. For example, if we evolved in a very strong gravitational field, classical physics might not be very accurate and general relativity might seem obvious. If we rediscovered math and physics on a generation ship traveling near the speed of light, special relativity might be easier to discover. Link to post Share on other sites
Karekare Posted July 31, 2020 Share Posted July 31, 2020 I say discovered. Even if humans didn't know about it the fibonacci sequence and the way atoms swap numbers and all that would still exist. We invented the word "math", but not it itself Link to post Share on other sites
GingerRose Posted July 31, 2020 Share Posted July 31, 2020 55 minutes ago, Ace of Mind said: What do you think, discovered or invented? Both. We discovered it but we need inventions to prove that those discoveries work. We discovered that a circle is 360 degrees, but we needed compasses and equations to prove it. Link to post Share on other sites
Phi! Posted July 31, 2020 Share Posted July 31, 2020 I understand and basically agree with all the points regarding invented but I would still say that overall it was discovered. Think Pythagoras or Fibonacci or Euler, they didn't just make that stuff up, they saw patterns and connections and used their discoveries to come up with theorems/sequences/formulas. Link to post Share on other sites
Sarah-Sylvia Posted July 31, 2020 Share Posted July 31, 2020 8 minutes ago, Phi! said: I understand and basically agree with all the points regarding invented but I would still say that overall it was discovered. Think Pythagoras or Fibonacci or Euler, they didn't just make that stuff up, they saw patterns and connections and used their discoveries to come up with theorems/sequences/formulas. Well, someone could say the patterns exist, those things exist, but math is just trying to 'describe' those things with numbers and logic as a language. So the things in the universe are discovered, but the language is invented. I guess some others kinda alluded to that, being a language. Link to post Share on other sites
Phi! Posted July 31, 2020 Share Posted July 31, 2020 1 minute ago, Sarah-Sylvia said: Well, someone could say the patterns exist, those things exist, but math is just trying to 'describe' those things with numbers and logic as a language. So the things in the universe are discovered, but the language is invented. I guess some others kinda alluded to that, being a language. Okay, so the language of maths has been invented but everything in maths has been discovered ?? I'm happy with that Link to post Share on other sites
Ace of Mind Posted July 31, 2020 Author Share Posted July 31, 2020 1 hour ago, CBC said: These are the sorts of philosophical discussions that make me want to shoot myself in the face because who cares. 😂 (Not saying the thread is pointless btw, I'm actually kind of interested to see what people say. It's just that personally I find such discussions ultimately incredibly useless.) Link to post Share on other sites
Sarah-Sylvia Posted July 31, 2020 Share Posted July 31, 2020 2 minutes ago, Phi! said: Okay, so the language of maths has been invented but everything in maths has been discovered ?? I'm happy with that Well math itself is the language, so it depends by what you mean in maths Math is theoretical, but you can use it to describe some things. But I guess technically you can discover some things through it, so I guess in a way it can make sense to say that. Link to post Share on other sites
Phi! Posted July 31, 2020 Share Posted July 31, 2020 11 minutes ago, Sarah-Sylvia said: so it depends by what you mean in maths I was thinking the exact same! When I think about what maths is I think about all the concepts and all the formulas. So I guess the debate now is What is maths???? 🤣 Link to post Share on other sites
andreas1033 Posted July 31, 2020 Share Posted July 31, 2020 How can maths be invented? It has to have been discovered. To invent, implies to create something new. Surely maths is facts, just waiting to be discovered. Like things like sacred geometery, and how nature grows. So to answer op Maths is something humans discovered. You cannot say you invented that 1+1=2 You discovered it. Link to post Share on other sites
Lord Jade Cross Posted August 1, 2020 Share Posted August 1, 2020 The thing is that definitions vary depending on how you look at them. For instance, you could say that 1+1=2 was invented because the numerical value doesn't really exist in nature. You can have 2 of the same something or units but those somethings are not thought of as 2 of something unless you create or invent the concept that there is a "something" and that, that something then can be counted twice to create 2 somethings or units. To put a more tangible example, think of a clock. Now a day and night cycle happens but there is no such thing as AM or PM in nature. We invented the clock to tell us the position on the sun in regards to the rotation of the earth (or vice versa since the sun is stationary and it's the earth that moves). And all of the sudden, we are amazed at these AM and PM "times" that tell us when each cycle begins/ends. Link to post Share on other sites
DarkStormyKnight Posted August 1, 2020 Share Posted August 1, 2020 I'm super intrigued by this conversation! I'm not a mathematician but it's an interesting question. Personally I agree with math being a type of language and way to describe the world around us, and that framework was certainly invented by humans. But the patterns that exist have been there for ages and those are independent of anyone putting them into place. So we invented a way to talk about the things we discovered! I don't think we can have invented it completely, multiple people deduced the laws of calculus, and we can't have discovered it because we could change what we call numbers or equations and it would still mean the same thing. So yes to both. Link to post Share on other sites
Aquatic Paradox Posted August 1, 2020 Share Posted August 1, 2020 Maths was first discovered and later manipulated to invent new things. Link to post Share on other sites
what the face Posted August 1, 2020 Share Posted August 1, 2020 We humans have evolved to prioritize finding meaning in what we perceive. This meaning can be shared with others who may agree or have found different meanings. Each of us makes up, in our minds, deciding to agree or not, these so called discoveries. What we directly observe with our senses is Truth. Discovery However we reject, accept or find meaning in our minds (from observation) is illusion. Fiction. Nearly all of what we think is made up. A story. Our stories. If we can recognize the fiction between: math and application data and interpretation. and each other's meanings, the question answers itself. Link to post Share on other sites
Knight of Cydonia Posted August 1, 2020 Share Posted August 1, 2020 Discovered. Just because we didn't have the language to communicate it at some point doesn't mean it was invented. 1+1=2 has always been true. Link to post Share on other sites
Epitaph Posted August 1, 2020 Share Posted August 1, 2020 On 7/31/2020 at 3:22 PM, Purple Red Panda said: I once watched a debate about what shape time is, I find it odd that people not on shit loads of drugs actually sit around thinking about such things. It's simply what happens when you never stop encouraging a mind to ask questions and seek answers. Link to post Share on other sites
SorryNotSorry Posted August 3, 2020 Share Posted August 3, 2020 Both. We use base 10, the Babylonians used base 60, and the Mayans used base 20. The concept of zero is really the key to making math work, and in turn figuring out how a lot of stuff is put together. Link to post Share on other sites
KiraS Posted August 3, 2020 Share Posted August 3, 2020 Depends on the technique. Prime numbers are natural. The Sieve of Eratosthenes is an invented technology (as is the Miller Rabin primality test). Link to post Share on other sites
Elsin Posted October 30, 2020 Share Posted October 30, 2020 I like this question. The truths already exist and so they are discovered. But the language necessary to state and prove the results is surely invented; without that invention the conjectures might not have even been stated, let alone proved. I'd say quite firmly that it is discovered but that the invention of the language is just as important as the discovery of the truth. Link to post Share on other sites
binary suns Posted October 31, 2020 Share Posted October 31, 2020 I say a little of both. To some extent it is invented but to another extent it is discovered. Link to post Share on other sites
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