How do we know that π never repeats?

Mathematics is completely different. In math and really, only in math we have the power to prove things. The fact that π never repeats isn’t something that we’ve observed, and it’s not something that’s merely “likely” given that we’ve never observed a repeating pattern in the first several trillion digits we’ve seen so far.

Da Q: How do we know that π never repeats? If we find enough digits, isn’t it possible that it will eventually start repeating? | Ask a Mathematician / Ask a Physicist.