Math: Did we discover or create it?

[CraigD]

Just like we didn't create all the atoms and photons either.

They're just there.

Math has been there too, until we uncovered all these formulas.

 

We discovered the Atom like we discovered Math.

In humble opinion,

 

The Periodic Table of Elements was there before we had a Periodic Table...

In another sense, mathematical and chemical artifacts such as the Pythagorean equation and the Periodic Table mat be defined as purely physical objects, arrangements of atoms of ink and paper in books, of magnetized particles on disk drives, and neurons and chemicals in human brains. That these mathematical and chemical objects describe the very energy and matter of which they are made makes them, though strangely self-referential, none the less physical.

 

Although it’s arguably likely that similar objects have been created by intelligent creatures elsewhere in the universe, it’s reasonable to assume that at some time in the past, no arrangement of matter/energy existed that corresponded to the Pythagorean equation or any version of the Periodic Table, so, at some specific regions in space-time, they existed for the first time. It’s also reasonable that, at some point in the distant future, no such objects will exist, although the physical phenomena they describe will continue to occur.

 

Alternately, we may define Math as the phenomena of creating these physical objects – Math notes and publications, and brain configurations embodying mathematical knowledge and understanding.

 

Regardless of which of these 2 definitions is used, Math is a created artifact, distinct from any physical phenomena it may be used to describe.

[Racoon]

In another sense, mathematical and chemical artifacts such as the Pythagorean equation and the Periodic Table mat be defined as purely physical objects, arrangements of atoms of ink and paper in books, of magnetized particles on disk drives, and neurons and chemicals in human brains. That these mathematical and chemical objects describe the very energy and matter of which they are made makes them, though strangely self-referential, none the less physical.

 

 

Math is a truth like other truths.

It is.

Like the Laws of Physics. We discovered them. We did not create them; only in our conceptualization.

As we evolve our understanding, so too may the Math we think we know..?? or don't know

 

The atom bomb was discovered before it was created.

 

What came first? the chicken or the egg?

[CraigD]

Math is a truth like other truths.

It is.

Like the Laws of Physics. …

There is a critical difference between Math and Physics. Math is equally good at describing physical reality – truth, if you will – and systems not corresponding to physical reality – fantasy, if you will. The Law of Physics must correspond to our best understanding of reality.

 

The idea that even mathematical ideas explicitly not describing physical reality have a real, objective existence – that they are discovered, not created – is the philosophical school of thought known as Platonic idealism, Greek or Aristotelian formalism, and several other equivalent terms. According to this school, the whole of Physics is less real than the collection of ideas, and all mathematical theorems in all formal systems already exist in the supra-real realm of the Forms.

 

As Philosophy “seldom affirms, never denies, always distinguishes”, it’s inappropriate to attempt to decide if idealism, or materialism (the position I was expressing in post #86). IMHO, materialism has fewer problems, and is more practically useful and emotionally satisfying than idealism, in much the same way that academic Math and Science is more satisfying than academic Philosophy.

[ughaibu]

CraigD: Diogenes Laertius claims that Greek thought divided into two basic "schools", one following Pythagoras and the other Anaximander. In Diogenes' classification, Plato appears in the Anaximander lineage, ie at variance with Pythagoras. What, if anything, do you think Diogenes felt were the distinguishing features in the relationships of mathematics with a supposed reality espoused by Pythagoras and Plato?

[Racoon]

There is a critical difference between Math and Physics. Math is equally good at describing physical reality – The Law of Physics must correspond to our best understanding of reality.

 

The idea that even mathematical ideas explicitly not describing physical reality have a real, objective existence – that they are discovered, not created – is the philosophical school of thought known as Platonic idealism,

 

You're a tough nut to crack CraigD :hihi:

I suppose you are right.

I was thinking Math has been around before we consciencely called it "Math"

like:

E = MC^2 was part of the Universal structure/disorder before Einstein flashed upon the equation while pondering dust particles in the window light.

It had been there all along.

Now Einstein could translate that small phenomena to paper using numbers and symbols

 

The thread is a poll asking whether created or discovered?

my philosophical response was discovered.

It took brilliance and hard work absolutely to bring Math to the level and understanding it is today.

That was/is definitely created.

[InfiniteNow]

The dynamics of the universe are there with or without humans. However, math, the language we use to describe and attempt to understand those dyanmics, was created by us. That is how I opine on the subject... It is based on... well, based on my opinion. :hihi:

[Tormod]

To quote this week's New Scientist editorial:

 

"Constants, like laws of nature, are human-made."

[questor]

"Constants, like laws of nature, are human-made." not so! the discovery and promulgation of a law of nature may be human made , but the law itself exists without the human.

[ronthepon]

"Constants, like laws of nature, are human-made." not so! the discovery and promulgation of a law of nature may be human made , but the law itself exists without the human.

 

A law is something fundementally different from a method of using a law.

Maths is just a group of rules that we use to understand and represent numbers, (and a lot of wierd things lately, like the imaginary number i) and solve the laws for values!

We created a method of expressing numbers and values, known or unknown, then developed it to such an extent that we can't say for sure now if it was natural or not!

 

If I were to explain with a good example of this being done, it would be ROMAN MATHS. So even they formed a group of rules to display numbers. But sadly, their method was'nt good enough.

 

Now, of course, numbers were something that were 'discovered' but hey! We all have heard of the set of Natural Numbers!

[IDMclean]

Just replying in knee jerk fashion to the basic question: Math, did we discover or create it?

 

Both. it's the best answer, and I suppose that if you wanted to do the math for it, it would show that.

 

See due to conservation Law, anything we discover, is something we create, to the extent that anything can be created in the universe. that is to Say that we cannot "create" anything, mearly convert it from one thing to another. 1 = 1.

 

I hope that throws a monkey wrench into any of this.

[Tim_Lou]

math is like language. we didnt "discover" language, we invented languages. much like math, we invented math so that we can articulate situations using certain "human thinking patterns".

 

edit:i think it depends on how one looks at math. if one focus on the concepts of math and views math as a law, then it is discovered; if one focus on the actualy methods and symbols of math and views math as a tool, then it is invented.

[Tormod]

"Constants, like laws of nature, are human-made." not so! the discovery and promulgation of a law of nature may be human made , but the law itself exists without the human.

 

This means that the concept of "natural law" is beyond human beings, and as such must have been discovered. But since all our natural laws have been formulated by human beings, how do you explain that we find inconsistencies in these laws?

 

There are still laws we can't explain, although we can formulate them. But the formulation of a law is still an invention. Discovery is what we observe, invention is how we explain what we observe. Formulating a law does not mean that the law is correct.

[Kriminal99]

What exists before us to be discovered is a nameless order of things. Our interpretation of this nameless order we create. Part of this can, has been, and in some cases probably still is a MIS-interpretation.

[Valliko]

I see this topic is dead since long ago. Well, i'll answer it anyway.

 

Did we, or did we not creat mathematics? Now, the answer is depending on what we mean with mathematics. For me, math is abstract and logical connections / links. It is quantities, patterns and combinations. It is probably more than so but i'll keep it short.

 

Now, i am certain, very very certain that humans is nothing but discovering the contents of math. Whilst we created the language in wich we express theese connections or quantites (2 Red Dogs and so on) we are still only expressing ourself. We do not modify or determine the quantity. 2 Red dogs will always be 2 red dogs. Even a cat would know that 2 dogs is more than 1 (prolly wont think of it in numbers, but more instinctive). Do you understand me? My english language sure isn't the best :P

 

Another example would be a lenght, strecht, line, whatever.

The distance between point A and point B is constant. We could apply our metrics system on the "subject". We could call it 20 meters or 2000 Centimeters.. Whatever we call it, the distance would be the same. We did not determine the distance and we're not in state to modify it either.

 

Yet another example is the area of a circle. The circle with a radius of 1 has the area of pi, now this is a realtionship between two constants (1 and PI) wich we cant ever, ever change.

 

This is it, i hope you understand me. Sorry for bumping a very old thread, but this was needed bring me rest.. :)

[Don Blazys]

Mathematics transcends the physical universe and as such is both indestructable and eternal. It exists as a set of absolute principles, and when this universe comes to an end, those exact same same principles will continue on into the next universe, and the next, and the next..., and so on into infinity.

 

Thus it can be said that inferior mathematics is "created", while superior mathematics is "discovered".

 

Don.

[ughaibu]

Thus it can be said that inferior mathematics is "created", while superior mathematics is "discovered".

In which group do you put hyper-dimensional geometry, sets of infinite cardinality, algorithmic randomness, incompleteness theorems, etc?

[Thunderbird]

As a sculptor and painter and by no means a mathematician I tend to see math as a creative force of nature. Basic inherent laws that govern the universe that are constant but at the same time creative.{{ Gravity, quantum mechanics.}} The periodic table of elements and structures of molecules, that all depend upon basic rules of relationships that exhibited attractions, repulsions dualities, symmetries “a music of the spheres.”

 

We also create are own mathematics based on rules of relationships. Our own invented musical scores are arranged in an order so the notes create relationships to one another. If the composer of the music is tuned in to the inherent interplay within, we can say they are “creative,” but is the composer the inventor of the music,? Or maybe they are just good listeners. I think if you ask the best of them {mathematicians/ composers} they say that they are just good at listening to what is already there.