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]

Not sure what you mean, Peter -- but for the sake of clarification, the courses I have done pretty much throughout my time at Cambridge are all in Applied Maths or Theoretical Physics, except for one or two course in basic analysis and set theory that, to be honest, I still don't really understand. I'm not really qualified to talk about pure maths as a result. Though I could talk the hind legs of a donkey off when it comes to Quantum Mechanics and Quantum Field Theory.

[Peter Pedant]

Oh, Computablity and Logic - Boolos and Jeffrey
nw in its third exciting edition
Jim
didnt mean to be opaque, sorry about that

Brouwers is here:
http://en.wikipedia.org/wiki/L._E._J._Brouwer

altho there is not an awful lot on his ideas that maths is just a string of symbols under various rules for manipulation

..... and that is the answer to the question set - is Maths discovered or is it a string of symbols? A: 90% think it is discovered but there is a vocal minority saying it is a string of symbols, represented by Brouwers.

.

( oops I was expcting you say 'well summed up Peter....)

[thebrainyone]

Many years ago when I was studying with the Open University my tutor (Piers Bursill-Hall) posed this question and it is one that I return to and pose to others often. We (tutor group) came to no definite conclusion in the 1980s and I have received no "thought through" decisions. I am still unsure of a definitive answer although I tend towards the "discovery" option. I welcome your thread and look forward to reading the posts here.
Val

[jomifl]

I think some of you guys can't see the wood for the trees. You appear to know everything about maths except what it is.