[kosta50]

The example you gave me does not prove that something is true but cannot be proven. Just because someone writes p(x1,x2,...xn) = 0 does not mean the equation is true. Researchers were able to show that no such equation is theopretically possible, not that the equation is true but cannot be proven.

Such mathematical arguments are equivalent to theoretical discussions how many angels we can fit ona pin of a needle. I am quite familiar with such polynomials with respect to aspheric surfaces.

They have no bearing on the real world beyond the 5th order simply because production and shop testing techniques can be carried out only to finite precision; the rest is simply theoretical.

Give me a real life example of something that is true but not provable.

[conservonator]

Give me a real life example of something that is true but not provable

Pi? At least not yet.

BTW, I really find your posts interesting. It's particularly fascinating to read you shred the "inerrancy" of Scripture while knowing that you are a faithful Orthodox. It's an excellent reminder that the Church and Christianity are not book bound, so to speak, content to experience the Divine in print and paper only but to undergo, endure, contemplate divinization or theosis. Tahnks.

[D-fendr]

Just because someone writes p(x1,x2,...xn) = 0 does not mean the equation is true. Researchers were able to show that no such equation is theopretically possible, not that the equation is true but cannot be proven.

Huh? Diophantine equations are definitely possible. Hilbert's tenth problem is about whether such forms are solvable in a finite number of steps.