Is Mathematics There To Be Discovered Or Invented?

[JustNotCricket]

This is a question that I have pondered for some time.

Which numbers can be found in nature?

I raised a question two months ago asking -

Who invented binary numbers?

This led to the answers that I wanted and also to an interesting thread about the nature or lack of it of mathematics. So, I thought that I would put forward this question. If you are interested in the idea I would encourage you to look at the thread about Who invented binary numbers? which should not be too difficult to find. But please, do not continue that discussion on that thread. Start the new discussion here. Thanks.

So, this thread should be about whether mathematics exists and is to be discovered or whether it is an invention. If some mathematics exists and some must be invented then the thread may be about what exists mathematically and where can it be discovered.

And before we begin...
I hope that you enjoy this.

[jim360]

I've been thinking about this question very hard for about ten minutes and, obviously, not got anywhere.

I think that you have to invent the ground rules, the axioms, of mathematics, certainly (although even this might be up for debate). Beyond that I think it's a journey of discovery. You follow the axioms where they lead you. Or, in the case of most of theoretical physics, you make it up as you go along and hope that someone else clears up the mess a few years later. But even then, the making-up process works, and leads to useful results.

So it's probably a mixture of both.

[woofgang]

The facts are there to be discovered. The language to talk about them had to be invented.

[Octavius]

Marcus de Sautoy suggested that “The invention of the number zero was a very modern concept — seventh century A.D. by the Indians."

[heathfield]

Surely, all mathematics is measurement, pure and simple. At some point in human pre-history, mankind decided on a need to measure things, like 'how many beans make five?', whereupon mathematics was invented. What, in nature, carries out measurement beyond a realization in some living things of 'there' versus 'not there'?

[ToraToraTora]

It's discovered in the sense that when a technique is divised it is merely a root to further discovery like the invention of a tool. It's like cutting a lawn it works prefectly well with a pair of scissors but the invention of the lawnmower makes it easier, so the invention of techniques to do things easier is analogous to say multiplication which is basically a repetitive add. All numbers are there in nature in all bases, waiting to be discovered and in some cases labelled, we happenned to settle on base 10 but all maths works on all bases and has to be consistent, so 2+2 in base 10 = 4 regardless of symbols But 10+10 in binary = 100 so 10=2dec and 100=4dec so it's all convertable.

[Prudie]

Well I don't agree that maths is just measurement by a long chalk:-) In answer to "What, in nature, carries out measurement" how about what tells a daisy to grow about 3 inches whereas a dandelion more like 10 and a hollyhock 6 feet? Why do some flowers have 5,6,7 or multi petals? Why do some climbers grow in clockwise helixes and some anticlockwise? Just a few of millions of examples of maths in nature - there to be discovered.

[jomifl]

Mathematics was invented by man to decribe the relationships found in nature. The relationships have existed since the big bang, long before maths of any kind was invented.

[sandyRoe]

I agree. Pi was always going to be 22/7 whatever it was called.

[pixie373]

Mathematics just is. We can learn it, we can't invent it

[jomifl]

We did invent it pixie, it is the relationships that always existed. The 12 times table did not exist before man because nobody needed to invent it.

[pixie373]

I think it always "existed". We just named it.

[Old_Geezer]

Folk don't seem to agree about this. IMO it is discovered, but I'm unsure the disagreement will ever be sorted.

For example, no one invented binary numbers, just that someone suddenly realised one can represent quantities in that form, so started using it.

[jomifl]

whatever...

[bert_h]

Well, yes, we invent the notation, but the mathematical facts that we describe with it are there - and always have been there - no matter whether a notation of any kind for them exists or not.

[jomifl]

So, before man all these binary, tertiary etc. numbering systems existed, and quadratic equations were happily solving themselves and meteors falling towards planets were doing a quick bit of calculus to make sure that they landed at the right moment? All maths was invented to solve problems, the problems were man's problems not natures problems.

[jomifl]

Bert, where exactly were these mathematical 'facts'.

[Old_Geezer]

As you will be aware maths does not solve itself, but it still already describes whatever is occurring. Thus it is already there just unused by any sentient being.

[pixie373]

Same as a tree making a noise, when no one is there to hear it

[bert_h]

Jomifl - these mathematical facts just seem to be built into the universe. The behaviour of objects around us is, to a very very good first approximation, described by remarkably simple mathematical equations. For example, the distance covered by a falling object in time T being G * T^2 / 2. Not T^1.873, or T^2.006, but T^2 as exactly as we can determine. There are thousands upon thousands of others.

[jomifl]

Bert, I think that says more about the numbering system we use than anything else. What you a saying is that there are simple relationships which we have been able to describe with maths. That is all. You could equally argue that one object is not bigger than another until it has been measured.