Actually, there is no "proof" or "disproof" in science. Such certainties are not to be found in the real world. But yes, theories are developed by incorporating explanations which work, which were found by testing hypotheses.
But my point is that untested (or worse, falsified) hypotheses have no place in the classroom. There's not enough time in science class to teach all of even the most essential validated knowledge, it's criminal to waste students' time with "what ifs". And to date, ID at best rises no higher than the status of a "what if". At worst, it's a body of misrepresentations, fallacious arguments, propaganda, and pseudoscience.
It *could* be a valid field of science someday, at least in principle. And if/when that day comes, sure, teach it in science classes. Until then, however, it doesn't belong there (even aside from the fact that it's intended as a Trojan Horse for religious creationism), nor should it dishonestly present itself as valid science in the realm of public discourse. It deceptively pretends to be something it isn't, and tries to present itself as somehow on par with established science like evolutionary biology.
"It *could* be a valid field of science someday, at least in principle."
I've been reading and seeing a lot about it and one 'hypothesis' is that life is based on a mathimatical principal.
Which makes me wonder if an exact formula were found that explained life, would that be a basis for ID?