&gt; A given non-trivial computer program can be relied on to produce results consistent with its definition (its specification), but this cannot be proven in all cases.<p>Provability is always relative to a formal system. The formal system you (should) use to prove a program correct (with respect to its specification) isn&#x27;t the program itself.<p>&gt; Gödel proved that their program was flawed. Surely you knew this?<p>Gödel didn&#x27;t prove the futility of a foundations for mathematics. Far from it. What Gödel proved futile is the search for a positive answer to Hilbert&#x27;s Entscheidunsproblem: There is no decision procedure that, given an arbitrary proposition (in some sensible formal system capable of expressing all of mathematics), returns `true` if it is a theorem (i.e., it has proof) or `false` if it is not.<p>If you want to lecture someone else on mathematical logic, I&#x27;d advise you to actually learn it yourself. I&#x27;m far from an expert in the topic, but at least this much I know.