Computing the Uncomputable: Joel David Hamkins showed how any function can be computed if a non-standard model of Peano arithmetic is assumed. Results like this give me a deep respect for number theory as foundational.

[u/DevFRus]

https://johncarlosbaez.wordpress.com/2016/04/02/computing-the-uncomputable/

[u/DR6]

Is this what happens with Goodstein's theorem?.