Math: Discovered or Invented?

Great Debates
#1

In a recent conversation with a friend, I was arguing that the perception of the world according to the laws of math/science/physics was more reliable than a perception of the world as spiritual/divine.

She argued that since the laws of math and science fail to answer every question, it cannot be judged more reliable than any other paradigm. How, she asked, is math/physics any more reliable (as a way of explaining the existence and mechanics of the universe) than religion, since neither explanation is completely satisfying?

And I argued that whereas religion was invented and then applied to the world, math was discovered and then used, and perfected with time.

But in our conversation I was unable to logically prove my point. My question is: Is there a way to prove the point that math is different from religion because it was discovered, rather than invented? Or do I need to reword it somehow to make it more logically sound?

(I’m worried I’m not articulating well… if this question is ambiguous, let me know and I’ll try my best to clarify.)

#2

I don’t understand why math and religion are even being compared.

#3

I see them as two different ways of explaining the world… they can exist together, of course, but the two points of view that I am contrasting are:

  1. All the universe operates according to the laws of physics and math. If there are things we do not know, it is because we haven’t yet progressed that far in our understanding of science. Math works; it is something we have discovered in the world, and it has not yet failed us.

  2. There is something divine that has a hand in the way the Universe works; e.g. God created mankind, there is Intelligent Design behind the origins of life. Human studies such as math, Newtonian physics, and Quantum mechanics cannot solve all the mysteries of the universe. Math works only because we invented it and then applied it to our surroundings; we made it work.
    My question: Is there a way for me to prove my opinion that the laws of math/physics are true, and that the assertions of divine control/inervention are relatively arbitrary?

#4

It appears that the OP believes that mathematics exists out there, to be felt and experienced and used and honed, whereas religion is a fabricated concept. As such mathematics is more a reliable facility with which to grasp things in the world than is religion.

I’m not sure it follows. Whether mathematics is discovered is a big debate on its own. Wherever you fall on that debate, it’s clear that mathematics requires assumptions and that assuming other things achieves different results: is or is not Euclidean geometry part of a reliable physics? Your assumptions may seem eminently reasonable to Joe Sixpack, but one assumption isn’t necessarily better than any other. You’re guessing something you can’t prove to arrive at useful things. This is what some people think about religion.

#5

Basically, no.

A lot of folks have argued about the discovery/invention of math, and it’s pretty clear that it’s not a question of evidence; people have something they believe, and nothing will change that. While the question may be interesting, it’s not at all relevant to doing math.

#6

The terminology bothers me some. One could presumably “discover” God if he could find Her hiding place. And saying God was invented merely begs the question. If It exists then It was not invented by us; if He does not exist, then He is an invention of ours.
Yeah, I know, my changing God’s gender in the previous graph will befuddle some, but it does point to the biggest problem with God’s existence: no two people (synchophants excepted) agree on just what the Divine Being is.

[Math has been perfected?? I take it you’ve never wandered into one of the “Does 0.999… Equal One?” threads here!]

#7

I might suggest that both refer to idealism, the idea that reality lies in a realm transcending phenomena. Are you being deliberately disengenuous?

#8

Okay, I’ll accept that I can’t prove my opinion. But still feel like it is logical to argue that math is more reliable than divinity/spiritualty as an explanation…

This is something I see as true only for the religious paradigm, not for math/science. The whole basis of science is that it does change… once facts begin to contradict eachother, people can experiment and hypothesize and create new theories. For instance, the theory that the sun revolves around earth had to change once evidence pointed to the earth revolving around the sun. Or, the dependence on Newtonian physics had to be questioned once scientists got down to the subatomic level. Whereas… for instance… creationists still hold that God created Adam and Eve, even though solid evidence points to the evolution of humans from ape-like ancestors.

I hold that science/math is discovered, not invented, and my evidence for that is: new discoveries are still being made in those fields.
Does this work as a compelling argument?

#9

You’re going to have some unproved assumptions somewhere in your argument. For example, you claim that “math works; it has not yet failed us.” You’re assuming that what has worked in the past will continue to work. This is a reasonable assumption, but it’s not one you can prove.

When it comes to religion, the question is muddled: what do you mean by “religion,” and which religion(s) are you referring to? Certainly, some parts of religion(s) have been invented (even today, people keep “inventing” new religious rituals, prayers, hymns, etc.). And some parts have been discovered: theologians have attempted to deduce things (about God, for instance, or morality) based on what they have observed or experienced or other things they already accept as true.

And when it comes to religion, there is a third alternative to invention and discovery: revelation. Most major religions (including, certainly, Judaism, Christianity, and Islam) believe that some parts of their religion have been revealed by God to someone who passed them along or wrote them down.
(Of course, if you don’t believe in God, you won’t believe in revelation; and even if you do believe in God, you can still believe that some or all of the “revelations” attributed to God are really inventions or delusions.)

If you’re really interested in whether math is invented or discovered, there have been other threads on this, such as the General Questions thread Epistemologically is mathematics considered more of an invention, or a discovery?

#10

Aghk, so my main question has been discussed already in GQ! Thanks for the link… and my apologies as well for the repeat thread; I only glanced through GD before I posted.

But while I’m here, I should make my definition of ‘religion’ less ambiguous… I was using it to mean, any explanation of the world/universe/general-state-of-things that assumes ( i would argue arbitrarily assumes ) that math/science can never fully explain existence, because something divine and conscious created everything.

#11

Seems to me that math boy has come face to face with the notion that math and science are just like any religion or belief system for that matter. The basic truth of this is hard to avoid. However, I find that this discussion has the potential for much more.

Mathematics is a self-referencing system. Religion is like this as well. Something is true because “the Bible says so”. Of course mathematics and science make sense per se but answer me this, what is a “1”? I’m a one; but from the biological level I am billions of cells, or a trillion chemical reactions. What if someone has triple vision, so to speak, and perceives three of everything I see as one? Explain a color? What if what you see as green I see as the color red? It seems to me that science and math cannot escape the same subjective nature of truth that other systems are subject too. The scientific method is based on observation and this is were all sorts of doubt creeps in. Could it be that belief systems work because we believe that they work?

Another point: When you perform a scientific experiment, do you have to perform all the other experiments that your experiment is derived from? How do we know that this great pyramid of scientific knowledge holds true for every inductive leap? How do we know that it is our belief in science itself that causes it to be perceived as being something legitimate? Newtonian physics worked for 200 years before Einstein who said Newton was wrong and invented his own way of looking at things. These are paradigms as the earlier poster said. They are metal abstractions like any other and we assume they will be proved wrong at a later date. 200 years from now Einstein might be viewed as we view an alchemist today.

I’m trained in history and I have seen primary source document after document detailing miracles that some saint performed or what not. What strikes me is that the people writing this down were very religious and accounts of this nature were looked upon as official testimony. Now it would have been perjury to lie in these documents and that, to a Catholic, is a mortal sin. Are we to believe that these highly religious men and women committed moral sin after mortal sin in writing these accounts down? This poses a problem that you cannot resolve without suggesting that they were lying. However, their lying is hard to justify if you ask me. There is no reason to lie as far as I can guess. Most of you would say that they lied for money or gain of some sort but often times worldly things did not concern these people. So labeling the hagiographers as liars is fraught with peril.

Given all this, I have come to realize a few things. That I have some form of consciousness. Now whether everyone else has the same remains a mystery but let’s just agree that this is also the case. What is it that makes something that is believed real? Is it all of us more or less agreeing that it is real? Or is there really a Law of the Universe that exists beyond our perception? Any thoughts?

#12

The underlying principles math desribe exist independent of human observation or cognizance. Therefore they were discovered.

The language of math was developed to describe those principles, therefore it was invented.

Fire was discovered; controlling it and putting it to work was invented.

Just my take on the difference between discovery and invention.

#13

Huh? Haven’t we discussed before whether the quantum world is phenomenal or noumenal? Don’t forget that a reasonable extrapolation of Bohr’s observations is that the universe is not real. It is a mathematical construct. And if you want to get all Kant about it, Kant argued that morality is grounded in an objective standard outside the self; therefore, if morality is to be perceived, then God is phenomenal.

No. Are you deliberately debating by ad hominem?

#14

So, as I suggested, the reality of God, and the reality of mathematical constructs raise related questions, which makes comparing them natural and appropriate.

No. I just found your comment surprising. I should expect the occasional surprise, though.

#15

I wouldn’t say that Mathematics was discovered, rather that there is less invention in Math than there is in Religion. Religious texts present an awful lot of facts that the reader is supposed to take as true. Mathematics gives a select few truths, so that if you take those as true, you have to take everything that ‘follows’ from them as true. If there is any derivation in Religion, it is often based on other hidden assumptions. Many religions also profess to explain reality, whereas sciences only attempt to model it – though this difference isn’t strictly related to the OP.

#16

Mostly discovered. Constants like e and pi are universal and would have been found by any civilization anywhere. Ditto for most of geometry- things like the Pythagorean Theorem. The only invented things I can think of are conventions like use of base 10, use of degrees or grads for measuring angles. I find it much harder to think of invented things than discovered things.

#17

Math isn’t science, and neither is like religion. Math consists only of conditional statements about imaginary objects with arbitrarily defined properties. Science rests on a few fundamental claims that may be unverifiable or not yet verified, but have never been considered sacred. For example, when classical determinism was found to be incompatible with quantum mechanics, out the door it went.

The questions you are asking are outside the purview of science. This points up another difference between science and religion - science generally does not claim to have, or to seek, “ultimate” answers. Religious people see a religious or mystical aspect in everything, and at a deep level they may be correct, but no scientist is going to write a paper on the chemical formula for optimism or some such thing.

I think you are confusing science with what some people call “scientism”, or the claim that every phenomenon has a scientific explanation. That position is not a popular one, primarily because the only way to confirm it is to in fact come up with a scientific explanation for every single thing. Absent those explanations, scientism really is just a belief system like religion.

Oh, and math was invented, not discovered. That’s my unscientific opinion.

#18

(sigh) You people don’t get it, do you? Mathematics was given to humanity by Thoth and if you do not honor and worship him for the gifts he has bestowed on us he will cause the frog gods to stop singing the sun through the sky and we will all die forever and you, at least, will deserve it.

I swear, it’s a wonder this species has lasted as long as it has.

#19

I don’t know about all the other stuff in your post, but this statement is just plain wrong. Newtonian physics (actually mechanics) still works. Einstein did not prove Newon wrong. Newtonian mechanics is a special case of Einstein mechanics. The special, Newtonian case is that the magnitude of the velocity of the physical object being considered is so low compared to that of light that the velocity of light can be considered as infinite. Einstein’s mechanics reduces to Newton’s mechanics if you take the limit of the Einstein equations as the velocity of light increases without bound.

200 years from now Einstein will not, with a probablity of 0.99999999999999, be viewed as we view alchemy today. If a modification of his mechanics is made it will make, with a probability of 0.9999999999999, Einstein’s mechanics just a special case of the new theory. For example, it the speed of light is not constant but varies over a period of many centuries, then for any experiment lasting only a lifetime or so the speed of light can be considered as constant and you will still be able to use Einstein’s mechanics.

#20

Doesn’t this really get down to how you define the words “invent” and “discover”? I mean, we all know the history of math, and that advanced civilizations everywhere will come upon generally the same math that we have. Trying to label it is an excercise in semantics, not philosophy.