I know, but it's being exhibited as an example of how back-of-the-envelope type of approximations by physicists can be just as good as rigid mathematical thinking. And I don't find this to be a convincing example of how loose physicist arguments can work.
Schwartz distributions, infintesimals; okay, fine, those turned out to be a weird trick that can be formalised. But sometimes their tricks are just plain wrong and this is one example of a trick that just is wrong and can't be formalised.
Consider, many useful primality tests are statistical in nature. It’s pure math, and exact answer is possible but it’s still useful to get a quick check to see if something is a waste of time.
Really, if a full solution takes 20 years you don’t want to actually spend 20 years without having a very good idea it’s going to work.
I think jordigh is saying that the method is not statistically sound, i.e. that it will not (necessarily) give accurate probability estimates. They're not criticizing the method simply for being statistical.
Using zero probability on infinite sets to ascertain the inexistence of an object doesn't work. Lots of things have measure zero in an infinite set. For example, out of all the integers, the probability of picking 7 is zero. Any finite set will have density zero in the integers too.
So I find his small probability, however tiny, that out of all possible integer tuples none of them are a counterexample to be utterly unconvincing and ultimately misguided.
To be clear: my complaint is that there is no way to turn this kind of argument into an actual proof. We could salvage other physicist arguments, but not this one. Probability zero on an infinite set cannot mean inexistence. And the rest of what he's doing, trying to determine that counterexamples must be rare, is "well duh, we knew that, because we've been looking for them."
Schwartz distributions, infintesimals; okay, fine, those turned out to be a weird trick that can be formalised. But sometimes their tricks are just plain wrong and this is one example of a trick that just is wrong and can't be formalised.