"All triangles have 3 sides" might be an uninteresting triviality, but "The sum of the squares of the lengths of the catheti is equal to the square of the length of the hypotenuse in a right-angled triangle" is neither trivial nor uninteresting and yet it has a probability of 1.

I love this example the most. It's the exception that proves the rule.

If you need to dig this hard to find something interesting with a probability of 1, that's pretty good evidence that the vast majority of interesting statements are not of the true/false variety.

Although I don't find it interesting, I am open-minded enough to ... embrace.. the .. uh.. diversity of the world, that allows some people, to find that interesting.

Pythagorean Theorem is "digging hard" and "not interesting"? Mind explaining?

The language that contains all Turing Machines that halt on all inputs is not decidable.

Or

e^(iy) = sin(y) + i * cos(y)

Are those uninteresting trivialities to you?

Yes, exactly. And "this code has a mathematical error in it" is often interesting, often non-trivial, and often has probability 1 (and often probability 0).

And these things are exactly the sort of thing that "differ from [trivialities about triangles] only in degree of complexity".

Note that "all triangles have 3 sides" is probably an axiom, but "all triangles have less than 11 sides" is a trivial theorem.