My father and me always debated about this
I would say that the best mathematics is discovered
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Is Mathematics Discovered or Invented?
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>Is Mathematics Discovered or Invented?
docs.google.com
At first it was invented, then discovered
yeah I'm familiar with Godel's theorem
it starts to overlap into epistemology
>Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modelling basic arithmetic. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.
how would Godel's theorem apply to the Pythagorean theorem for example?
the proof is in the pudding, there is no measuring meter accurate enough to measure the hypotenuse to the exact theoretical mathematical precision that Pythagoras' theorem provides.
>At first it was invented, then discovered
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>it starts to overlap into epistemology
things would still remain true, even if no one was around to prove them to be true
>things would still remain true, even if no one was around to prove them to be true
>he doesn't understand what i mean
>he doesn't ask for further explainations
>he posts a tom cruise picture laughing
ok, you're definitely going to solve this
I was just chegging those immediate dubs
please if you have something more to say, by all means share it here. This is more of a discussion thread anyway, there is no final solution that we can arrive at since I believe this debate will continue going on.
mathematics is true as far as it is useful
why does it matter if either is the case, and why can't it be both?
Math is a language. Languages are invented to communicate. Science is created to describe what is observed in nature.
Ok
You assume that math is one, but it's not.
It can be separated into different fields, like algebra, geometry, calculus and so on.
Those fields have different ages.
I said that it was first "invented" because the first thing is number.
People "invented" numbers to count things, to separate "few" and "many" and actually figure out how many things were "many".
Then.
They started "discovering" properties in numbers.
This is a raw hypothesis.
there's something further than that
the mathematics is describing the physical world with such precision that it belies a deeper relationship beyond just human mapping of metrics.
it implies that there is a structure to reality that we are capable of describing and using
for example, I suspect that through the use of quantum computers (real ones, not the simulated ones in laboratories), we will be able to send messages forwards and backwards in time
like in the movie interstellar
Universe is one of many simulations. Math only exists because we reside in a far-advanced computer.
>You assume that math is one, but it's not.
>It can be separated into different fields, like algebra, geometry, calculus and so on.
it's funny, Penrose mentions this in the interview:
when the ancient Greeks were studying geometry and it was based on Euclid, they did not appreciate at the time that they were actually studying physics
it wasn't until we learned more about the nature of light did we realize that Euclidian geometry does not apply to the real world
pic related
Invented by Our Lord, discovered my Man after the fall.
>They started "discovering" properties in numbers.
I would say that those properties always existed irrespective of whether or not they were discovered yet
666-witnessed
completely off topic, but this game is too good:
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never played resident evil when I was younger, but have been playing this one a lot
I used to believe this (not at all with this version with epistemology) but Math and Physics are 2 different fields that use the same language. They're exclusive to one another as fields. With Physics, we use math as tools to help better describe the observations. PURE Math, the field, they delve into finding relationships between numbers. Yes, there are spin off "tech" or formulas that find their use in Physics, but Math as a field is not the root of Physics. They require different mindsets.
the precision is anthropic.
Repetition of results is not evidence repetition will continue
What do you think about this, 42?
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Pytagoras had a sacred concept of numbers, and they "discovered" many properties.
What now you assume is in some field, could even fall into another field in the future.
this is because you're a neo-platonic and you don't know, or maybe you do.
read about that a while back
cia.gov
paleo-magnetism is a very interesting field of study
The language and technique is invented. The abstract underlying principle is inherent.
basically this
>how would Godel's theorem apply to the Pythagorean theorem for example?
the proof is in the pudding, there is no measuring meter accurate enough to measure the hypotenuse to the exact theoretical mathematical precision that Pythagoras' theorem provides.
Gödel's theorem isn't about going "Haha even the most basic theorem might actually be wrong xd." It tells you that every logical framework must have a singularity. In other words, every question-answer matrix features a paradox.
Its discovered. All knowledge exists between 0 and 1 as a decimal. If you converted every decimal to an English text string.