So, Veeky Forums, was math discovered or invented?

Logic is a subset of psychology

Veeky Forums, disregard this faggots comment. i asked because i was legit curious. please discuss.

if you had read Kant you wouldnt be asking this, OP.

They are part of the nature of the axioms. Theorems are tautological consequences of chosen axioms

Discovered, there is no way our caveman brains could have came up with something so perfect and great

i personally think it was discovered, however i don't think there is any way you could prove/disprove this.... mostly just a matter of opinion

Many theorems from antiquity were discovered in informal systesm and the axiomatic systema were selected in orther to prove what they already knew.

Just like languages, math was invented.

Then why are some proofs correct and some are incorrect? Why are some answers correct and some are incorrect? Why are some theorems correct and some are incorrect?

There is an objective external standard which would have still applied even if by change humans never evolved. Even if we never invented our symbolic representation of mathematics, in the universe will come up with a valid form of mathematics capable of which makes different from our own for given problems

There is a mold into which our mathematics must fit, and this mold existed before us and will exist after us, and applies to all aliens equally.

i laik dis pichur

i had to turn the light on to see my keyboard, but thisa guy has a pint. why isnt he wrong?

I'm not wrong, this is one of those topics that get really obfuscated by abstract psychological and normative arguments.

There may be aliens with different axioms upon which they rest their mathematics. But that doesn't mean ours are wrong or invented or anything. They just may build off of different foundations, but they have to follow the same abstractive rules.

Nobody can build off our our axioms, our mathematical foundations, and come up with a meaningfully different system of mathematics beyond conventions in common functions to use, their names, symbols, and which theorems are more important to use as well as which perspective they come from (often there are many ways to say the same thing, they may focus on some over others)

Fair enough, I kinda got my semantics mixed up when I wrote that.

Mathematics and rationality are mental abstractions of the way in which reality behaves. We discovered reality, and observed it behaving in particular ways. Mathematics isn't an object -- it's the behavior of reality. The fact that we think of it as its own object is a psychological trick, and one that's not always useful.

For instance, our notion of "authority" is something we evolved as a social species. When something was more powerful, we obeyed it, because it would be bad for our survival to do otherwise. Then, religion came around, and abused our notion of authority by abstracting out the power aspect, and said: "you must obey, regardless of power -- it is simply a brute fact." Same with mathematics. We took our notion of reality, abstracted out the behavior, then began to treat it as its own object. We make this cognitive fallacy all the time.

But then why can all of mathematics be derived solely through human thought based on the initial axioms, without observing the universe like with physics?

I would say you need observation first. We can start math with the basic concept of 1+1=2. If we take an apple and put it on a table, and then we take another apple and also put it on the table, we have 2 apples. This applies to any objects we gather.

I'm not exactly sure what you mean when you say "based on the initial axioms." What exactly are these "initial axioms"? Some platonic object we access, somehow, or what?

Also, I was going to say this: How do you know we can derive the laws of mathematics "solely through human thought based on the initial axioms", when all humans throughout history have had the powers of observation, or somebody else who who could teach them the fruits of observation?

This is something that interest's me very much in a very weird way. I wonder what the first thing to ever get counted was. Rocks? Animals hunted? And I wonder who the first was to just go "Wait wtf". Logic and everything is just such a beautiful concept and it never fails to impress me.

Another thing is like how the old mathematicians would react when they found something new, never seen before. Do they get all giggly, or dance around or cry? I wish I could find something breathtaking and experience that feeling. On a related note, I'm going to college next year. What field has the highest opportunity of me finding something really cool, but pays well at the same time. Like money isn't everything to me, but I would prefer not to die of starvation

It's most likely currency. Mathematics and written language were first utilized for currency. We have currency before either of those

Intelligence is a strange thing. The creatures whose minds better reflected the behavior of reality, and had greater potential to perceive its patterns were naturally (and unsurprisingly) selected out for their better survival capabilities. Eventually, the wishy-washy general patterns and notions of our ancestors, who were most likely not even homo sapiens, became less and less approximate, until the point at which we gained the concept of "objects", and it went on from there. I'm sure it was thrilling.

On the note of college, I'd say quantum physics research is the most rewarding. Mind blowing concepts that refine your notions about fundamental reality. However, it will take a while to get a degree, and therefore pay, and is also quite difficult -- especially for those who aren't willing to throw out everything they know for the sake of truth.

No-no, I mean like some caveman:"rock->more than one rock" but how many more? Boom. Thinking outside of the box lmao

I've already been reading up on it alot, but my physics teacher told me I shouldn't go into physics because he thinks I would do better in maths..

Yeah like I said it most likely only occurred during the invention of currency. There was no reason to keep track of numbers of things unless you have to communicate the numbers with others. Otherwise they just collected enough fish to look like they won't go hungry. The first time they'd need concepts like numbers is for trade

Depends. People who have great quantitative intelligence aren't always good at physics. Physics takes fair qualitative reasoning as well. You know, conceptualizing imagery, and such.

Mathematics on it's own isn't that bad though. Still plenty of mind blowing things to explore.