The recent exploration of mathematical truths, particularly in the context of diophantine equations, reveals significant insights into the undecidability properties of various numerical fields. Comments point out the distinctions and relationships between complex numbers and integers adjoined with imaginary units, which impacts the discussion of undecidability. Matiyasevich's result, likened to Turing’s Halting Problem, suggests that diophantine equations, while simpler in form than computations done by Turing machines, present compelling insights into mathematical logic limits. The notion of cutoffs and undecidability in various subrings of integers is raised, prompting discussions on the foundations of mathematical and logical theory. This reflects a growing interest in the philosophical implications and application of these proofs.