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This is a question Ive seen on at least two other forums. I did a search here but couldnt find any thread on this topic so I thought Id start one.

Was mathematics invented or discovered?

My humble opinion is that mathematical truths and ideas were discovered, but the tools and equipment we use to study them were invented. As an example, take this statement: 1 + 2 = 3. My belief is that the truth behind the equation was discovered, but the symbols 1, +, 2, = and 3 were invented.

Any thoughts?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I think all of it was only discovered. When I think of it now, everything that exists in this world was only discovered, even though we call some things inventions and not discoveries.

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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If you are a Platonist, you will believe it is discovered. The inference is that it exists in nature and therefore is incredibly deep and meaningful.

If you are a Formalist, you will believe that it is an invention of man like a game such as chess. It has rules and is logical but it is artificial.

*Last edited by bobbym (2013-03-09 03:10:37)*

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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Well, something was invented if it hadnt existed before and was brought into existence by human agency; on the other hand it was discovered if it has always existed, even before humans were aware of it.

Thus the natural numbers were discovered. They existed before the first humans were aware of them, and would have continued to exist if there had been no humans to be aware of them. But after discovering them, the humans needed a way to represent them concretely. The Romans came up with I, II, III, , while the Chinese use 一, 二, 三, . Our modern notation 1, 2, 3, , was first used by the Indians who could thus be said to have invented it. Similarly the arithmetical operation of addition and the relation of equality were discovered, while the symbols + and = were only first used in the 16th century by the Welsh mathematician Robert Recorde and since he was the first to use them, we say can say that he invented them.

http://z13.invisionfree.com/SAKE/index. … wtopic=267

*Last edited by Nehushtan (2013-03-17 12:43:54)*

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**bob bundy****Moderator**- Registered: 2010-06-20
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hi

Nehushtan wrote:

My humble opinion is that mathematical truths and ideas were discovered, but the tools and equipment we use to study them were invented.

I'm happy with that. I might say that the tools and equipment are the axioms and the discoveries are the theorems. That works for me.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
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But then you would be making a difference between a written word and number. They both always existed, someone just had to find them.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bob bundy****Moderator**- Registered: 2010-06-20
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Six sheep can exist without humans having to be around at all. But calling that amount of sheep 'six' is a human invention. I thought I had established that all numbers are inventions.

Let's imagine a few seconds after the big bang. No intelligent life around. Where is the concept of number then?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
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It is still there. Waiting and waiting for someone to discover it. Maybe nobody ever would and maybe someone will.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**n872yt3r****Member**- Registered: 2013-01-21
- Posts: 392

I think it was invented, because numbers don't exist. They are a placeholder we use for a certain amount. They're not exactly one thing, if they were, shape-shifting could exist, because numbers would be everywhere. They're sort of a principle.

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**digits****Member**- Registered: 2013-01-02
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Mathematics is an artifact of the human mind, and a tool whereby the human mind wraps itself around reality.

Cheers!

digits

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**Mrwhy****Member**- Registered: 2012-07-02
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digits wrote:

Mathematics is an artifact of the human mind, and a tool whereby the human mind wraps itself around reality.

Cheers!

digits

Yes, exactly right, digits.

EVERYTHING we think and talk about - even you, digits.

The brain, we think (imagine?), receives things we call "sensory nerve signals".

This is the stuff from which the BRAIN dreams up the "world" and calls it "real" (in order to prolong its sanity!) The ones who thought the sabre tooth tiger "not real" got eaten.

If you doubt this, tell me how you know right now you are not dreaming!

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**pellerinb****Member**- Registered: 2012-12-26
- Posts: 43

n872yt3r wrote:

I think it was invented, because numbers don't exist. They are a placeholder we use for a certain amount. They're not exactly one thing, if they were, shape-shifting could exist, because numbers would be everywhere. They're sort of a principle.

The idea of a placeholder makes sense.

Objects counted any other way would still be just as numerical. The numerical quality itself perhaps comes with objects being physical. There might be 1 x 10^80 atoms in the physical universe ... it's an intrinsic quality/principle of the universe, we might say?

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.

In biology, we use math like we know what we are talking about. Sad isn't it.

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**bobbym****Administrator**- From: Bumpkinland
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Wasn't it Kronecker who said,"God invented the integers, all the rest is man's"

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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some of the posts here are deleted?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
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Hmmm, that is difficult to say. Was GiB in this thread?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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I do not think so.

Why is that difficult?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,303

Because that is rarely done unless he is involved, then it is common.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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But this discussion is very important. You should not delete things here.

Putting something like [comment removed; sexual slur] should be enough

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,303

Who said I did? I do not remember it or have any record of that. I was just saying it probably could only occur with him.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Some concepts feel more invented than discovered. For example, semigroup feels more invented whereas group feels discovered. Quaternion feels invented whereas rotation matrix feels discovered. Or maybe it's just me who lacks understanding.

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