Math, invented or discovered?

I just got done reading The Mind of God. A good read that ask questions like can the universe create itself, mathematics and reality, real worlds and virtual worlds. An overall good read for those who like to expand their awareness. However, it asked a question that has been beating me upside the head all day. Is math already 'out there' or is it invented? Is math proof of an objective reality? Or is it simply the human mind putting chaos into order? If math is 'out there', what realm does it exist in? Just looking for some other posters thoughts to help me find some answers.

Let me ask this then: What if Euclid didn't figure out geometry and later on a few hundred years later on the other side of the world another human figured it out. Was it already there? Waiting to be found. . .or just a creation of man.

I'm not a scientist or a mathemtician or anything but if you have 2 apples and you get 2 more apples you have 4 apples. i think we discovered that rather then invented it.

its still a difficult question to answer though.. basic math like addition and subtraction seems quite obvious but higher maths like geometry... not to sure about that. maybe it is just a man made method of organizing chaos

Were hammers invented or discovered?

For example, we discovered that a nail could be driven into wood if it was hit by a rock. We discovered that fixing a stick to the rock (a handle) allowed us to drive the nail faster.

God permitted hammers to exist.

Hammers were discovered. They weren't invented.

Actually -- I am not sure that last statement is true.

How math came about is too simple. Human beings had things, be it food, clothing and you name it. They had to hide it away somewhere, for the winter, so their enemies would not find it, and so forth. So they began to make a note of it, say lines of four then a line over it. There was the math! They now knew and could visualize what they had miles away from their cache of items. Math began, if no other better explanation can arrive, as an inventory of things. Perhaps later people put things together, when it became not just an inventory, but a receipt of things, the first money only in trusted hands.

Originally posted by PontiacWarrior

If math is 'out there', what realm does it exist in? Just looking for some other posters thoughts to help me find some answers.

The part about "what realm" bothers me. Even if you say math was an invention or a discovery or whatever -- that doesn't really answer your question.

Speaking casually, I would say that mathematics exists in the mind of humans -- that is its realm -- however this is just begs the question what realm does the human mind exist in?

I'm going to look for that book you recommended -- "The Mind of God" -- sounds like it provokes some good questions!

It was discovered. See, two things and two things always equal four things, like the fellow above said.
As for angles and formulas, they are repeatedly proven to represent the actions that are occurring, whether it's working on a problem on a sheet of paper or plotting the expected course of a comet.

An invention of the mind like most other things really. I cant for one second believe the that universe intended for maths to be a part of life - in reality, it serves no purpose. It serves a purpose to us, as it organizes the life that we ourselves have created. If you delve into it, why do we do anything? Every creation is seemingly a reaction to a problem/obstacle.

One? Two? Three? Why? I think that everything is achievable as long as something poses a problem. We are creating things that science fiction of a century ago wrote about - things which held no credence back then. Numbers help us figure out problems we encounter, problems we created. Everything is limitless in potential, but thats not to say that it was discovered. Was a toaster invented or discovered? It was invented, because it posed a problem - a way to make burning bread more accessible. Just as numbers, as someone mentioned, helped organize rations for example very early on in civilization.

[edit on 13-12-2007 by 3_Libras]

The math was always there whether we knew it or not so the discovery was actually a way of expressing relationships so it could be handed on to others (cumulative knowledge and understanding was evolving). Pioneers like Pythagoras and Euclid noticed those relationships and developed a means of predicting them via symbols and formulae.

I don't believe humans, on average, are any smarter now than they were thousands of years ago. It's just accumulated knowledge in written form that allows us to pick up where the last pioneers left off.

Originally posted by Pilgrum
The math was always there whether we knew it or not so the discovery was actually a way of expressing relationships so it could be handed on to others (cumulative knowledge and understanding was evolving). Pioneers like Pythagoras and Euclid noticed those relationships and developed a means of predicting them via symbols and formulae.

I don't believe humans, on average, are any smarter now than they were thousands of years ago. It's just accumulated knowledge in written form that allows us to pick up where the last pioneers left off.

Why do you say it was always there? Was the need to measure the volume of water in a bucket always there? Why was the bucket invented? As we find out that the universe is run by laws which cant be explained through one theory of mathematics, why are we so determined to prove otherwise?

reply to post by PontiacWarrior


You know, I am not sure I understand the difference between an invention and a discovery. Is it possible that they are the same thing?

A better question -- what realm does math exist in? I think that question, posed at the start of this thread, is more problematic.

It has been there since the beginning of time because you would not have the Big Bang or creation without it.

At some point analytical man began observing and postulating, creating linear units of measure to help study and explain his discoveries. As Man began applying these units to everything he observed, Math began to reveal itself and unraveled like dominoes, just like cryptologist when they decrypt an ancient language.

I'm sure gravity played a big factor in these observations early on.
Eventually the wheel was invented and soon introduced an entire new perspective to math.

Math was discovered and in fact it is still being discovered. This will be evident when we begin to venture off to new frontiers.

There is no doubt that math helped develop things that we live with today, and could not live without. But how exactly does that prove it was discovered? And what has the Big Bang "Theory" got to do with math being discovered? You would not have creation without it? Who says?

Originally posted by 3_Libras
Why do you say it was always there? Was the need to measure the volume of water in a bucket always there? Why was the bucket invented?

In the case of the bucket, it was invented as a means of moving water which is a totally practical application. With a developing understanding ways were found to work out in advance what the capacity of the bucket was in terms of its dimensions and allowed the prediction of how many buckets it took to fill a reservoir of given dimensions. With or without mathematical reasoning the number of buckets taken to fill the reservoir is the same so we were simply finding a way to express our observations.

Another good example is gravity. It was a given fact that if you drop a stone off a cliff it fell down until something stopped it and for most people that was all you had to know about it. But along comes Isaac Newton who worked out the relationship between gravitational acceleration, mass, potential/kinetic energy and force which he expressed as formulae so we can now calculate everything about the event in advance with certainty without actually having to drop the stone. He didn't create the relationships but rather just observed them and put them in written form for our benefit.

Newton's observations of planetary movements became so complex he had to create a new type of mathematics to express it and that was the birth of calculus. An object in an eliptical orbit requires no knowledge of calculus - it's simply an expression of an observed characteristic we can take and apply to other problems with a high degree of certainty.

In short, the principles have always been there and we have evolved a means of putting them on paper.

Originally posted by 3_Libras
There is no doubt that math helped develop things that we live with today, and could not live without. But how exactly does that prove it was discovered? And what has the Big Bang "Theory" got to do with math being discovered? You would not have creation without it? Who says?

Even if we were to get rid of the the things you say we can't live without, math will still be there. Math has always been there because for every discovery made you almost always have another individual somewhere else coming up with almost the same conclusion. I guess the same can be said about inventions but inventions require design, which requires math.

Regarding th Big Bang I was referring to the non linear decay involved from the exact moment of combustion/ignition/bang until the time that chaos finally stabilized. This may be immeasurable because of all known and unknown elements involved but if you apply relative time constants to this non linear decay you end up with seven days of creation thus solving the 2Billion vs 6000 year old debate.

Pause for irrationality

If mathematics really is 'out there', as most people here seem to believe, how do we account for irrational numbers?

An irrational number is any number that can't be expressed as an exact fraction a/b. What this means is that b doesn't go into a an exact number of times - there'll always be a little bit left over.

Two of the best-known irrational numbers are pi, the ratio of the circumference of a circle to its diameter, and the square root of two, otherwise known as the Pythagorean constant.

The existence of irrational numbers shows that our simple arithmetic of counting, adding and subtracting, multiplying and dividing sometimes doesn't work in the real world. Whenever a case of that happens, mathematicians have to find a way to 'adjust' maths so it fits the real world better. This suggests to me that the evolution of mathematics is series of ever-closer approximations to reality, but that mathematics itself is artificial.

Fascinating topic, I must say.

I think you mean transcendental numbers whose digits go on forever if we try to represent them in a digital form (using whatever base). A shortcoming of digital representation is highlighted by this in comparison to the more natural analog system where 1/3 is more precise than 0.33333. For the purpose of electronic calculation we can just increase the number of significant digits until the error is too small to matter.

The relationships of things to each other exists whether we calculate them or not. Mathematics has evolved to allow us to describe these relationships and make accurate predictions

reply to post by Pilgrum


Irrational numbers are simply numbers that cannot be expressed as a "ratio" of two numbers (ir-ratio-nal).

So, 1/3 is not irrational. It is called a "recurring decimal" or "repeating decimal" number. But it is quite rational.

If you call someone "irrational", you are saying that they cannot be expressed as a ratio of two whole numbers!

The reason the 1/3 fraction repeats is simply an artifact of our base-ten number system. For example, if we used a base 3 number system, then 1/3 can be expressed precisely. (Specifically: 0.333... in base ten is simply 0.1 in base three.)

Transcendental numbers are a subset of irrational numbers. Pi is both irrational and transcendental -- when you speak of physical constants like Pi are probably talking about an irrational number that is also transcendental. (The mathematical definition of a transcendental number is quite confusing!!)

All transcendental numbers are irrational. However, not all irrational numbers are transcendental. Go figure.

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Now to the main question, very worthy of contemplation: is all of the above an invention? Or is it a discovery? Seems more like a discovery to me.

I have my irrational moments

The problems arise when trying to express the analog universe around us with digital maths. After all Pi is simply the ratio of a circle's circumference to its diameter. I used 355/113 as a good approximation via integers (accurate to 6 decimal places) for years before the advent of calculators and personal computers.

Maths is just a language to express observed relationships but those relationships still exist unchanged despite the language and units of measurement used.

It kind of goes back to the question "why and how did the universe start?".

Was everything always done in maths?, or did a god/creator think "hmm if i'm gonna create a universe I need some way of keeping things in order. hows about we do everything in multiples/divisions/structures/etc"