This conflates rigor with proof. Proof is the solve to the argument you are making. Rigor is how carefully and correctly the argument is made. You can understand something without rigor but you cannot prove it.
reply> You can understand something without rigor but you cannot prove it.
replyI think I disagree. There are formal proofs and informal proofs, there are rigorous proofs and less rigorous proofs. Of course, a rigorous proof requires rigor, but that’s close to tautological. What makes a proof is that it convinces other people that the consequent is true. Rigor isn’t a necessary condition for that.