This is not quite correct: No, my original statement is absolutely correct.
Church-Turing is an approach, a labeling, a thesis, not a theorem. Not being a theorem, it is not subject to proof.
One could exhibit a plausible argument that Church-Turing is wrong but that argument would not be a proof. It would not involve a sequence of mathematical argumentation that is standard for those artifacts which we call proofs. Just no.
Pointing to a concrete algorithm would not be a "proof". Maybe it would be very persuasive and the world would be persuaded to abandon Church-Turing. Still it would not be a proof.
Edit: I will admit my claim here involves a "mathematicians' thesis" that proofs are mathematical objects rather than just extra-strong arguments. So be it. I believe the whole reason Church-Turing is labeled a "thesis" rather than a theorem was because it's framers were using this distinction. And the distinction appears in the foundation of mathematics. Philosophers still argue for and against the continuum hypothesis even it's well not to be provable or disprovable - the argument is whether assuming it's true or falsehood produces good or bad mathematics. etc.
Church-Turing is an approach, a labeling, a thesis, not a theorem. Not being a theorem, it is not subject to proof.
One could exhibit a plausible argument that Church-Turing is wrong but that argument would not be a proof. It would not involve a sequence of mathematical argumentation that is standard for those artifacts which we call proofs. Just no.
Pointing to a concrete algorithm would not be a "proof". Maybe it would be very persuasive and the world would be persuaded to abandon Church-Turing. Still it would not be a proof.
Edit: I will admit my claim here involves a "mathematicians' thesis" that proofs are mathematical objects rather than just extra-strong arguments. So be it. I believe the whole reason Church-Turing is labeled a "thesis" rather than a theorem was because it's framers were using this distinction. And the distinction appears in the foundation of mathematics. Philosophers still argue for and against the continuum hypothesis even it's well not to be provable or disprovable - the argument is whether assuming it's true or falsehood produces good or bad mathematics. etc.