Silly nitpick: There is also a non-zero probability that your proof of a statement and Terry Tao’s proof of its negation are both valid, which can happen if both of you are making a false assumption. (You prove that Conjecture A implies X, he proves that Conjecture A implies not-X, together you’ve proven Conjecture A false.)
I endorse your silly nitpick, but of course I had in mind the situation where neither proof explicitly rests on some assumption: TT and I are both claiming to have proven X outright.
Silly nitpick: There is also a non-zero probability that your proof of a statement and Terry Tao’s proof of its negation are both valid, which can happen if both of you are making a false assumption. (You prove that Conjecture A implies X, he proves that Conjecture A implies not-X, together you’ve proven Conjecture A false.)
I endorse your silly nitpick, but of course I had in mind the situation where neither proof explicitly rests on some assumption: TT and I are both claiming to have proven X outright.