Supposing that the definition of convexity that you're referring to is that of, for a set C with x_1 and x_2 being elements of C and for any scalar b between zero and one inclusively,

[b * x_1 + (1 - b) * x_2] always being a member of C,

I presume that you mean that errors, namely those kind of errors that are the subject of this thread's discussion, in mathematics will always symbolically be elements of some solution set of a finite number of linear equalities and inequalities (or the intersection of a finite number of halfspaces and hyperplanes).

It seems very curious to analogize mathematics results to random variables. At the least, there's a lot going into that analogy which might be worth unpacking and justifying to explain why logical inference, with its elaborate and precise chains of truth-preserving deductions, potentially collapsing at a single counterexample, can be considered remotely equivalent to something like a dice roll.