Mathematics - Created Or Discovered?

[ToraToraTora]

I think discovered. It was and is all there we just found what works and devised a syntax and methods. presumably there is still a lot left to find too.

[Khandro]

NJ; Read jim;
"But it's probably both. A thing can only be discovered if it exists in nature.//
The periodic table of elements exists throughout the universe, & would be known to the intelligent inhabitants of Pluto.
The nine times table is a human invention & may not be.

[KARL]

I would make a clear distinction between arithmetic and mathematics (although, strictly, the former is a small branch of the latter). The nine times table is arithmetic and the periodic table belongs to chemistry which in no way can be described as any form of mathematics. Maybe I have misunderstood the OP, maybe TTT would care to elaborate on its scope.

[JimF]

"The periodic table of elements exists throughout the universe"

Not quite. The elements described in the periodic table certainly do, but the periodic table itself is a human invention to assist in the classification of the 100+ elements according to common properties.

[Khandro]

jim//the periodic table itself is a human invention to assist in the classification of the 100+ elements according to common properties.//

Sort of correct, but I would think an intelligent being would see that the number is the atomic number and this reflects the number of protons in the nucleus of each element's atom. Every element* has a unique atomic number.

* 118 when I last counted :0)

[JimF]

Yes, I know, and these numbers of protons were there before the elements were discovered in nature (or created artificially). E.g. hydrogen was discovered / identified / isolated in 1766 - obviously, hydrogen has existed in nature since the birth of the universe.

[Old_Geezer]

Tbe periodic table is a logical arrangement of the elements based on their characteristics which result from the elements' composition. Any species recording such information as charts/pictures will come up with the same thing. Has to be questionable to call it an invention. Just a recording of data into their natural pigeonholes really.

[Khandro]

jim //hydrogen has existed in nature since the birth of the universe.//

Certainly, but Mendeleev discovered the relationship between it & the other elements & produced the table.

[ludwig]

You've said it yourself in the question. Mathematics is the syntax and methods that we devised to describe stuff. It's not the stuff itself.

[Old_Geezer]

Yes; but whatever symbols you choose, the underlying maths operations described & used remain the same, and thus are neither created nor invented.

[OrionD]

I've recently been reading "The Death of the West" by Oswald Spengler,

He provides an interesting perspective into mathematics. Namely that the culture of Classical History would have never allowed for the Mathematical comprehension we have today. The number zero for example was never even concieved of by the greeks. Let alone any conception of irrational numbers.

The Greeks would be utterly perplexed by conceptions such as -2 x -4 = 8 and dismissed as absurd, that is notwithstanding the immense usage of mathematics within a lot of the artistic remnants of the Ancient Greek today.

In order to answer your question directly however, one must be able to define what mathematics are, you'll have to forgive my limited understanding of many complicated mathematical concepts as they have never been my forte.

It seems to me that mathematics operate merely as an abstract logical representation of reality, It's intangbile so I could easily just conclude that they don't actually exist in reality at all.

Axiomatic truths have no value or meaning devoid of objects for them to apply to.

This line of reasoning does agree more with mathematics being discovered rather than invented.

[New Judge]

"...but I would think an intelligent being would see that the number is the atomic number"

But what if you don't count in tens? Suppose you count in twos or twelves? The atomic number will be different.

[zebo]

//It could well have been the Egyptians. The original Cairopractors.//

Did they need Napier's Bones as well?

[Peter Pedant]

// I'm sure Jim360 gave a deep and lengthy view on this some time back//
he sure did - he who is just about to present a PhD in pure maff
two schools of course: Platonists - history or theory of ideas - held that they were independent and discovered - "hello I am a little theorem and I am waiting to be discovered"

and a fella named Brouwer who in the 19th cent said that it was all a question of combining symbols according to rules and then interpreting them - 'ah yes so this means...,.......'

https://en.wikipedia.org/wiki/Brouwer%E2%80%93Hilbert_controversy,

and the answerbank thread is
https://www.theanswerbank.co.uk/Science/Question1629117-2.html
(Mathematics created or invented?) Nigh in a reflective mood



but the pure mathematician was moved to quip side splittingly
//Once again, PP, but in coherent sentences this time please :P//(*)

as Brouwer da hoover meant absolutely nothing to him. A really depressing day in my life as maff on AB meant nuffin except an opportunity to say really clever things - even for the graduates in the subject. another normal day on AB clearly

and a thread on which TTT himself shone with a few one-liners - I think he was a platonist that time ( always there waiting to be discovered)

(*) this is equivalent to a physicist quipping playfully
" Ein stein? is that what you say when you go into a bier keller? ter daaah!"
or a pharmacist: "morphine? hey but when did you have the first feen? ter daaah !"or
Sqad, : I am not angry I have just run out of patience !

I still recommend Jeremy Gray ideas of space and time
see other thread