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A very known fact we live is that mathematics is not falsifiable. There hasn't been a day in history when someone came up and made an experiment to prove that the equation "x^2-5x+6=0" has solutions different than 2 and 3.

In science, if we find something that doesn't comply with mathematics, we never doubt the math, but we may change themodelof our physics, and then test whether the new model would answer more questions physically.

From this, I find that math iscompletely and totally a separate entity from nature. Nature can be represented by mathematics, however, because of it's consistency. No day will ever come when we have a single apple that becomes two apples for no reason; and bam, there you get your simplest conservation law in nature... "The conservation of apples :)"; In other words (in my view, I'm not sure whether there's a theory that supports this, please let me know), every conserved system can be described by mathematics.

Gödel then comes and says that mathematics isn't complete; why is that the case, Mr. Gödel? Because mathematics isn't completely provable...

ah, really? Big deal! We know this already! And I actually find this very natural! No one ever stated that mathematics should be proven by experiments or by any kind of complete test before axioms! I work with physics for more than 10 years and haven't seen this ever. Mathematics is naturally not completely provable because:

Mathematics, by its nature, is not experimental, and we are experimental entities. In order to realize the existence of something independent of nature, we have to interact with nature; therefore: I can't expect that I'm gonna be able to prove its completeness, since my connetion to it is through something which is achieved by experimental interaction. (Did I miss any piece of the puzzle?).

is mathematics independent from nature (physics), or is it dependent on it? In other words: do you find my conclusion above logical, and is mathematics falsifiable in any way?Now my question is:

In other words: if we exit the universe, can we ever find out that 2+2=5?

Notice that whole mathematics is built and based upon simple ideas like addition and multiplication, and you generalize that further with more dimensions, which provide us with matrices, which then we use as operators, and then when you move to continuous systems you realize that sums become integrals and differences become derivatives... So all mathematics came up just from the simple 1+1=2 and other simple statements!

Thank you for any efforts. I really need to hear specialists opinions about this.

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# Is mathematics a separate entity from nature?

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