# Trigger reflex

When I see a statement like that, I just cannot stop myself from pulling the trigger:

Why does Wittgenstein want surveyability? He seems to think that to be capable of the specific use of a theorem which a new proof makes possible we must be able  to reproduce its proof. This is just false, indeed perversely so — without understanding anything about Wiles’ proof of Fermat’s Last Theorem you can use it to rule out the truth of $$a^{17} + b^{17} = c^{17}$$ where $$a$$, $$b$$ and $$c$$ are any three integers, even hundreds of digits long — for example I know that $$123456789^{17} + 12233445566778899^{17}$$ can’t be equal to $$12345678901234567890^{17}$$ without needing to calculate any of the three powers. [Edwin Coleman, The surveyability of long proofs, Foundations of Science, 14, Issue 1–2pp 27–43.]

Indeed, I believe most mathematicians will make an instant observation that $$17$$ is a odd natural number, and therefore the last digit of $$9^{17}$$ is $$9$$, and therefore the last digit of  $$123456789^{17} + 12233445566778899^{17}$$ is $$8$$ and does not equal to the last digit of  $$12345678901234567890^{17}$$ , which is, of course, $$0$$. One does not need Fermat’s Last Theorem for that (and, for the sake of historical integrity of the narrative, the case $$n = 17$$ had been settled by Kummer in 1847).