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?

[rowanwitch]

As a species we seem to respond to pattern and rhythm and we have developed language for that, maths seems to be a language for science. Like all languages it has to be learned, and it is far easier to learn if you live with it. A musician learns the language of music, a mathematician the language of mathematics. The patterns are there it's the symbols and structures that grow as more is learned. That's my take on it anyway

[naomi24]

So invented?

[rowanwitch]

Sorry so invented to make sense of the structure of the universe.
On other worlds they might have other ways of defining the way things are, and predicting the patterns. Maybe some will use god as an excuse for not learning

[jim360]

Remind me to post here later. But, short answer, probably a mixture of both.

[naomi24]

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

[spathiphyllum]

Considering it makes perfect sense and there are things like pie, and the golden ratio, i think it is discovered. Humans have to realise there are 4 bricks to a wall they didn’t invent 4 for that to be the case

[Prudie]

I'm not going to join in the thread beyond this but I have always considered Maths to be discovered not invented.

[Khandro]

Maths is discovered

[Old_Geezer]

I don't see how one can event such a thing. It's a whole system one stumbles across to find it works and would have worked already before someone actually noticed it. Can't be anything other than discovered. Reflects reality; probably fundamental to everything.

[jakep]

Discovered

[naomi24]

More thoughts.

https://www.huffingtonpost.com/derek-abbott/is-mathematics-invented-o_b_3895622.html

[rowanwitch]

The patterns are discovered....... I see maths as the language used to explain those discoveries. As individuals we understand the basics as we grow, we start with Apple, another Apple, lots of apples until someone teaches us the language of numbers. We apply that language and we are taught that there are more patterns things like prime numbers, Pythagoras, etc. Some go on to fall in love with the language and go down pathways that lead them to discovery of ever more complex patterns but still using that language growing it for new ideas and theories. Some stick with arithmetic because that is all they need.

[jakep]

The team working on Higgs Boson particle knew it should exist before they discovered that it did.

[1ozzy]

Some will understand numbers.
Some wont.

[Old_Geezer]

IMO maths isn't the language, I learnt maths at school using English. Maths is that which is being described.

[rowanwitch]

But as I said it's a pattern. The language of maths and science was used to interpret the existing data and form a theory which predicted the existence of the Higgs Bosun. What existed wasn't mathematics but a thing explained by a language, like explaining a pattern of sounds in the language of music. Although it could be explained in mathematics in terms of soundwaves and oscillation.

[jim360]

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?

[spathiphyllum]

maths is a perfect fractal. fractal aren't created by man they're discovered by man

[spathiphyllum]

for example.. A snowflake, perfect maths, no interference by mankind, symmetry and perfect geometry.. We did not invent any of that. However we did invent the word "maths" to apply to these geometrical, numerical and other natural wonders such as the golden ratio.

[jim360]

In point of fact, nothing in nature actually matches the perfect "golden ratio", but rather various approximations of it. Snowflakes are the same. The golden ratio is then a mathematical abstraction of the physical world.

I'm not arguing that mathematics isn't discovered at all, but rather I don't think it's a binary choice. There's a mixture going on. The physical world drives mathematical discoveries, which are taken further by the capacity for human invention.