Was math invented or discovered?

[itstimaifool]

Of course, I didn't think of this question, I saw it on the internet. I'm just curious as to what the citizens of the KSP forums feel about this: Were numbers and math invented by people, or are they a fundamental attribute of the universe that we gave words and symbols to?

By 'numbers' and 'math,' I mean the underlying ideas that those represent. Obviously, the symbol that looks like '2' is not a fundamental universal constant; it's a product of the development of written language. The same goes for the symbols '=' and '+'. But these symbols represent meaningful ideas, just like the string of symbols 'cat' represents an organism that exists in the universe independently of that string of symbols. So in the context of this thread, the words 'numbers' and 'math' don't refer to the symbols, but to the ideas that those symbols represent.

(I'm sorry that this is probably worded terribly. Things always sound better in my head than they look written down.)

This is a mostly philosophical question, and I can see evidence for both opinions. On one hand, 'quantity' seems like a fundamental aspect of the universe. If you have 2 apples, no matter how you say it or what symbols you have, there's still two apples. It follows, then, that if you add two more apples to the pile, there's then 4 apples. Call it what you want, but adding 2 apples to a pile of 2 apples results in a pile of 4 apples. So it seems that math was discovered by people, and all we invented was a set of symbols and words to describe it.

But on the other hand, higher math, like calculus, is a lot harder to justify as "fundamental." A lot of laws of physics seem to fit nicely in with math, but is that because the universe is fundamentally mathematical, or because we humans invented math to explain the universe?

In my opinion, math was discovered, just like the laws of physics. However, my only justification is "If the universe is not fundamentally mathematical, the how else could it be explained without math?" which seems like a pretty weak argument.

So what do you all think?

Edited May 15, 2015 by itstimaifool
Does anyone ever read this?

[HoloYolo]

Math was invented. Equations to describe a rule. Like 2+2=4. We invented that. E=mc squared was invented as well. The rules of the universe were there, and we discovered them. Math was invented to explain them.

[How2FoldSoup]

Math was invented. Equations to describe a rule. Like 2+2=4. We invented that. E=mc squared was invented as well. The rules of the universe were there, and we discovered them. Math was invented to explain them.

My almost exact thoughts when reading the OP. Well said.

[Bill Phil]

Numbers and Math weren't discovered or invented, they just are.

Discovered is probably the best fit, though.

[LABHOUSE]

If it was invented, explain how it governs all things.

[windows_x_seven]

I'd say it was discovered.

[JedTech]

If it was invented, explain how it governs all things.

It doesn't govern all things, we invented it to explain and quantify all of our discoveries. So I'm saying math and numbers are human inventions.

Edited May 15, 2015 by JedTech

[Camacha]

If it was invented, explain how it governs all things.

It is a method that was invented to describe how things work. It governs nothing. You could find other ways to describe things, say, use an octadecimal system instead of a decimal system, and the mechanisms it covers are still the same. In fact, computers readily switch between decimal and binary. It is just a tool.

[Xannari Ferrows]

Invented. Math is a construct. One could argue that the laws of physics always existed, but who gave them their name? You cannot move faster than C, but it wasn't always called C, or the speed of light for that matter. We invented mathematics in our own right, and the universe in another. Whether or not they're similar is something we can never know.

Languages are constructed. Math is the language of logic.

You cannot type pro-n-ounce as a whole word for some reason...

Edited May 15, 2015 by Xannari Ferrows

[alexman142]

Because I am a devout Christian, I view Math as God's invention but Man's discovery. I think that God is using man made symbols to describe God's handiwork.

[Bill Phil]

The numbers representing quantities in math were invented, but not math itself.

If you observe two objects that appear naturally, would you say they are invented? If not, then why would math be invented? Math is a compilation of theorems based in logic, many of which stem from earlier, and simpler, theorems. But the theorems are not invented, they are the product of thinking about an observation and coming to a logical conclusion. That observation may be of a previous theorem, or not. But one of the first theorems probably would have been an addition theorem of sorts...

Thing 1's quantity added to Thing 2' quantity equals Thing 3' quantity.

That stems from an observation of nature. Seeing two objects as no longer separate but as one. That is not invented, but it is observed.

However, the numbers used to represented those quantities are invented constructs. They had to be invented for us to understand math, but they aren't math. One could just as much use letters as numbers in math, or any other symbol of your choosing. Those symbols are inventions created to help people do math. Without them, math is impossible to do.

These numbers let us say "2+2=4". With each "2" being individual objects, and the "4" being the collection of those objects.

So, math's many discoveries were only possible because of the invention of symbols representing quantities.

[itstimaifool]

So it seems that a main disagreement here is a matter of semantics. 'Numbers' could mean two different things:

1- The symbols that most humans currently use to represent quantities, which look like this: '1234...'

2- The concept of quantities in the universe.

So basically, whether 'numbers' means the symbols or the idea they represent.

The same problem exists for the definition of 'math.'

I intended those words to refer to the underlying idea, rather than the symbols humans invented. Obviously, the symbol that looks like '2' is not a fundamental universal constant, it's a result of the development of written language. But, since I'm terrible at writing down my ideas, this came across rather ambiguously. Sorry for that.

[Robotengineer]

Invented. Math is a construct. One could argue that the laws of physics always existed, but who gave them their name? You cannot move faster than C, but it wasn't always called C, or the speed of light for that matter. We invented mathematics in our own right, and the universe in another. Whether or not they're similar is something we can never know.

Languages are constructed. Math is the language of logic.

You cannot type pro-n-ounce as a whole word for some reason...

Math is the language we use to describe the universe. It is the Rosetta Stone (not the software) we use to understand the universe. The method by which we use math maybe a construct, but the underlying mathematics is here, has been here, and will always be here.

[Camacha]

A number is not a real thing. It is an abstract. We say something like two chairs, but one chair is not exactly like the other. They are just collections of somewhat, or not even, similar groups of atoms and forces. Yet numbers, or when converted to numbers, they are the same in the purest sense.

It really goes back to Plato's allegory of the cave.

[arkie87]

Of course, I didn't think of this question, I saw it on the internet. I'm just curious as to what the citizens of the KSP forums feel about this: Were numbers and math invented by people, or are they a fundamental attribute of the universe that we gave words and symbols to?

By 'numbers' and 'math,' I mean the underlying ideas that those represent. Obviously, the symbol that looks like '2' is not a fundamental universal constant; it's a product of the development of written language. The same goes for the symbols '=' and '+'. But these symbols represent meaningful ideas, just like the string of symbols 'cat' represents an organism that exists in the universe independently of that string of symbols. So in the context of this thread, the words 'numbers' and 'math' don't refer to the symbols, but to the ideas that those symbols represent.

(I'm sorry that this is probably worded terribly. Things always sound better in my head than they look written down.)

This is a mostly philosophical question, and I can see evidence for both opinions. On one hand, 'quantity' seems like a fundamental aspect of the universe. If you have 2 apples, no matter how you say it or what symbols you have, there's still two apples. It follows, then, that if you add two more apples to the pile, there's then 4 apples. Call it what you want, but adding 2 apples to a pile of 2 apples results in a pile of 4 apples. So it seems that math was discovered by people, and all we invented was a set of symbols and words to describe it.

But on the other hand, higher math, like calculus, is a lot harder to justify as "fundamental." A lot of laws of physics seem to fit nicely in with math, but is that because the universe is fundamentally mathematical, or because we humans invented math to explain the universe?

In my opinion, math was discovered, just like the laws of physics. However, my only justification is "If the universe is not fundamentally mathematical, the how else could it be explained without math?" which seems like a pretty weak argument.

So what do you all think?

you saw it on 9gag?

[itstimaifool]

you saw it on 9gag?

I actually forget where I first saw it, but I know it wasn't 9gag. I'm not actually sure what 9gag is, to be honest...

[luizopiloto]

Something else...

[Camacha]

you saw it on 9gag?

It does not really matter, those things get passed from one site to the other anyway. Funnyjunk, 9gag, Reddit, you name it. They all have very similar content.

[LN400]

The birth of mathematics as most (??) understand it was when the ancient kings and queens in ancient civilisations wanted to keep track of how many sheep and how many jars of olives the citizen produced and how much of that the citizen would have to give in the form of tax. The foundation for that started when our brains realised that 2 oranges and 1 orange is not the same amount of oranges. That goes waaaay back, long into the mist of unrecorded history. Today, we know that certain birds are capable of recognising if 1 egg is removed or added to the nest, we have also seen that a few birds have shown a form of understanding of natural numbers up to about 7. So what is the essence of maths? The ability to work out incredibly hard equations or the ability to realise that 1 is fewer than 2 is fewer than 3 etc etc?

I would say that the latter is the case and as such, it's not an invention, more a discovery, or more precicely a realization that has come through biological evolution of the brain, and not just the human brain.

Edited May 15, 2015 by LN400

[Darnok]

Depends how do you define math

Mathematicians seek out patterns[9][10] and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist.

If for you it is seeking out patterns etc etc then math is about discoveries. Of course we created many virtual symbols, formulas, units (like seconds, meters, kilograms) etc to write those patterns.

For sure geometry is only about discovery, because almost any pattern may exist in nature

Hmm instead of numbers we could use ratios as universal values.

[-Velocity-]

I think this is kind of a silly question. One of the few things that we can be certain about the universe is this: it is made of information. A lot of non-classical quantum information interacting, perhaps, and generating perhaps pseudo-classical information- but it's still information. Information can't exist if there is nothing to describe it in. Numbers are representatives of that description, and so they represent a very real thing. Numbers themselves are just marks on paper, or a computer screen.

Now as far as physical laws go, they're information too, and they arise from information (about how the universe is structured) interacting with information (about what exists in the universe). It should be no surprise that neat mathematical relationships arise.

[cicatrix]

The universe doesn't care about math or numbers. It just is. We, humans, invented languages. Math is also a language, a language to help us dealing with abstractions. If a language (any language) describes visible objects, math describes the abstract ones.

[Scotius]

The birth of mathematics as most (??) understand it was when the ancient kings and queens in ancient civilisations wanted to keep track of how many sheep and how many jars of olives the citizen produced and how much of that the citizen would have to give in the form of tax. The foundation for that started when our brains realised that 2 oranges and 1 orange is not the same amount of oranges. That goes waaaay back, long into the mist of unrecorded history. Today, we know that certain birds are capable of recognising if 1 egg is removed or added to the nest, we have also seen that a few birds have shown a form of understanding of natural numbers up to about 7. So what is the essence of maths? The ability to work out incredibly hard equations or the ability to realise that 1 is fewer than 2 is fewer than 3 etc etc?

I would say that the latter is the case and as such, it's not an invention, more a discovery, or more precicely a realization that has come through biological evolution of the brain, and not just the human brain.

Actually, it goes even further back in time. Archeologists think that at least some rows of notches made by our ancestors 13 000 years ago on bones and horns were beginnings of math. Basically they mean "I've seen IIIIIIIIIIIIIIIIIIIIIIIIIII deers. Let's go hunting". Later smart men invented words and symbols that let us compress row of notches into "27".

[LN400]

Actually, it goes even further back in time. Archeologists think that at least some rows of notches made by our ancestors 13 000 years ago on bones and horns were beginnings of math. Basically they mean "I've seen IIIIIIIIIIIIIIIIIIIIIIIIIII deers. Let's go hunting". Later smart men invented words and symbols that let us compress row of notches into "27".

That is an excellent point and interesting. I did not know about that discovery. It's an excellent point but I would still argue (albeit a bit cautiously) that maths as we know it today, with arithemtics as well as symbols for values, evolved in the civilisations 5-6000 years ago into the various fields like geometry.

I also worded myself poorly when I said "a realization that has come through the biological evolution of the brain". I would rather say through the evolution of concepts and ideas that became possible through the biological evolution of the brain. The evolution of concepts is one that does not need millions of years to "materialise" into something recognizably new, it can happen, and has happened and in leaps and bounds, sometimes making huge leaps in a very short time. One such leap was the idea that perhaps it would mean something to carve notches on a piece of rock as a representation of amounts. This would be a necessary step before more advanced steps.

It would be very intriguing if they did discover 13.000 years old markings where someone carved "Zorg killed III deer, Bam killed II deer and Zlob stole I deer from Zorg leaving Zorg with II deer before the two hunters decided to split the remaining deer between them and their 2 uncles so that each got I deer."

The interesting thing is, at one point in the evolution of concepts, that's in essence what happened.

Edited May 15, 2015 by LN400

[-Velocity-]

Actually, it goes even further back in time. Archeologists think that at least some rows of notches made by our ancestors 13 000 years ago on bones and horns were beginnings of math. Basically they mean "I've seen IIIIIIIIIIIIIIIIIIIIIIIIIII deers. Let's go hunting". Later smart men invented words and symbols that let us compress row of notches into "27".

Eh, the relationship between numbers and notches is probably more complicated than that. Notches are still in use today, as they are useful for slowly counting a small to medium number of objects when the total number is going to be unknown, especially on a substrate or with a medium that doesn't support erasing. I guess Roman Numerals probably evolved from notches, but I don't think the Arabic numerals modern people use did, at least, most of them.

In context to your example, I wouldn't be surprised if ancient peoples tens of thousands of years ago would have said something like "I saw deer of number five hands and two". Our truly ancient languages and beliefs are long lost. The common, every-day need to express numbers makes me believe that it's a certainty that there were probably countless paleolithic cultures and language systems that found ways to express numbers- at least verbally and/or with body language- without resorting to a crude series of grunts. Those people were just as smart as we are.

Haven't you ever seen someone nonverbally tell you the quantity of something?!?!?! Hold up both hands, open and close your fists five times: you just non-verbally expressed the number 50. Is it really a stretch to imagine that- or something similar to it- becoming symbolically expressed in language?!?! It would be more surprising for it not to be. Numbers are so critical to survival that any group that didn't have them would be at a big disadvantage.

"Hey, Beats-Head-On-Rock- How many men did you spy in that rival group you saw on the other side of the hill?"

NO NUMBERS:

"Duhh... derp?"

"OK, let's abush them!.... CHARGE!!!..... oh crap... why didn't you tell me that there were.... derp derp many of them?! We're dead!"

NUMBERS:

"I counted one hand hand, one hand, and four."

"Oh crap, let's slink away and go inform the village elders to rally the warriors because a major raiding party is on the way!"

Edited May 15, 2015 by |Velocity|