Sentence examples for mathematical proof exists from inspiring English sources

In other words, a mathematical proof exists regardless of whether some person has discovered it.

But no proof exists.

-What physical proof exists for this theory?

What medical proof exists of a myocardial Infarction?

I'm skeptical that such proof exists, though.

Now that proof exists, in writing no less.

No proof exists that this was the case, however.

It was the first irrefutable mathematical proof that black holes - as they were later dubbed - had to exist.

Multilevel selection is gaining in favor among evolutionary biologists because of a recent mathematical proof that kin selection can arise only under special conditions that demonstrably do not exist, and the better fit of multilevel selection to all of the two dozen known animal cases of eusocial evolution.

"It's certainly not a formal mathematical proof".

"The heart of it is the mathematical proof".