[D-fendr]

I suspect it involves 'axiomatic' truth,

Nope. That's a completely different discussion.

This is just math. Diophantine equations are equations of a particular form.

[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.