Maths: Discovered Or Invented?

[naomi24]

”Magic Numbers: Hannah Fry’s Mysterious World of Maths”, a BBC Four documentary series in which Dr Hannah Fry explores the mystery of maths and asks “Is maths invented like a language or is it discovered and part of the fabric of the universe?”

https://www.bbc.co.uk/programmes/b0bn9dth/episodes/player

Your thoughts?

[ichkeria]

“Give me binary choice, oh Lord!”

:-)8

[Peter Pedant]

// Jim, remind you? How? I guess you're going to have to remember.//

hey you're back! always meet someone half way thats what I say !

I will half answer for Jim - Maff men are divided into two parts, not equal -we call these parts "sets" Plato history or ideas.

ideas have an independent existence and so Maff people just wander along and find an idea that says - "hullo I am an interesting idea and I am waiting to be discovered!" - n Jim he say hey everybardy I am gonna be famous ! Ideas may be A or -A , and incredibly they may coexist ! - see euclids fifth axiom
https://en.wikipedia.org/wiki/Parallel_postulate.
Wiles with Fermat's Last theorem deffo wanted to discover a proof and not invent one

or you may be in the other set and subscribe to Brouwer 's idea ( ha! yes pun ) which is maff is just a series of symbols which is manipulated according to various predetermined rules.
the interpretation is as you make it
https://en.wikipedia.org/wiki/L._E._J._Brouwer

glum dutchman sounds like

90% of people like Jim when asked say they are platonists

I wondered about watching Hannuz program - is it any good ?
I thought her idea about maff was trailing her coat ( = see her next episode ) - a bit like a prog about light - and "that raises the question is the speed of light constant? see you next week !"
or AOG - will we all be killed in our beds tonight?

If you subscribe to Brouwer's idea - then you will be naturally interested in Proof Theory and Mathematical Logic

[Peter Pedant]

so Plato's idea and Brouwer's idea
were they always there, and waiting to be found ?
or were they invented by people manipulated symbols ?

or

like Jim sitting on a fence - - a mixture of both (boo! - Brexiter cant decide what he wants and when he gets it he wants something else)

yeah hey - I am Brouwers idea of mathematical symbols and their manipulation and you know what - I have always been here !

[jim360]

Once again, PP, but in coherent sentences this time please :P

[Peter Pedant]

oh dear
Jim
see Brouwer - he was the one who said maff was just a series of symbols manipulated to order

I am truly truly shocked a maff grad is unaware of this !

[Old_Geezer]

The trouble with numbers is that whilst they exist, they don't exist is the way most things do. No one has seen a three, they see three of something, or a symbol representing three, but that's it. Yet who suggests three doesn't exist ? It exists as a concept and just needed to be noticed. Pretty much all maths seem to be in the same situation.

[Old_Geezer]

Both the pattern and the means to understand it must already be there though. Folk didn't invent 1 nor 3 but even before they were aware of it 1 plus 3 would equal 4, and adding one apple to three apples would have resulted in four apples.

[Khandro]

In Euclidean geometry the fundamental 2 and 3D forms; that is to say, perfect circles, spheres, rectangles, cubes and pyramids etc. do not exist in nature, so analysing them must be to some extent a 'man-made' discipline. This is a top-down science, i.e. creating a formal abstraction and subjecting it to study.

Non-Euclidean "projective" geometry, is (to me) quite different, and closer to the natural order of the world and its universal laws of growth and structure. It is therefore more revealing than inventing.

So the answer to the OP is, as jim says, something of both.

[jno]

OG, I think Fry's suggestion was that a minus 3 was a trickier concept, one that wasn't lying around waiting to be discovered but rather one that had to be invented.

[ToraToraTora]

discovered 100%

[ToraToraTora]

forget maths there's a nobel prize for anyone who can comprehend WT\F PP is on about!

[jim360]

I've explained why I disagree with you above, TTT, but mainly -- why Nelson?

[ToraToraTora]

Humans have invented terminology and found applications for maths but it's always been there to be discovered. In the whole universe 2 + 2 = 4 and SOH CAH TOA is true, many alien civilisations will no doubt have discovered what we have, they will no doubt have different notation but in the end their maths is our maths.

[ToraToraTora]

jim:"A thing can, presumably, only be discovered if it exists in the universe. But mathematics, in at least some senses, may even go beyond the universe. In that case, isn't some of it perhaps invented, rather than discovered? " - maths is what we use to play around with these ideas, the ideas of multiverses etc are human notions to fit the equations, not an actual discovery of any extra-universal existence. I still say discovered. Can you give me an example of any maths that is "invented"?

[retrocop]

//TTT, but mainly -- why Nelson?//

Trafalgar Day 21st October.

[ToraToraTora]

no particular reason for Nelson, just sticking with the theme of great British heroes really.

[jim360]

"...maths is what we use to play around with these ideas... not an actual discovery of any extra-universal existence."

Surely, then, if you are saying that maths isn't an actual discovery, then that makes it (at least partly) an invention?

One example of something that is (probably) invented might be the real numbers. Most quantum theories of the universe assume that, at some point, space and time stop being perfectly continuous and instead are in discrete units of Planck Length (or time). Hence, the absolutely perfect, unbroken, continuous line of real numbers could be said to be a human invention.

[spathiphyllum]

We invented the language but not the tools. For example aliebra, is invented, the number 4, is invented.. four items adding to four items to make 8 items, is not invented, fractals are not invented, numerical, geometrical repetitions in nature are not invented. The language to help understand them is.

[steg]

I was wondering what would happen to OG’s 4 apples if maths suddenly didn’t exist

[ToraToraTora]

I see where you are going jim, I just think for the most part at least all things we where taught in school would still be true if we never knew about them. I guess at the more esoteric end there are arguments for invention but I think they are mainly devices to aid notation. Eg the concept of real numbers may struggle with quantum/planck aspects when used in that arena but day to day they stretch to infinity uniformly as far as arithmetic goes. Similarly the imaginary numbers may be considered an invention but is that not also the discovery of the perpendicular (to the standard number line) imaginary number line? A grey area perhaps.