For math, you don't really have empirical data though. There is no trial you can do to find out whether, statistically, the proof works as intended. Because pure theoretical math rarely produces a measurable result.
This is absolutely not true. The reason nearly every mathematician believes the Riemann hypothesis is true is because out of zillions of discovered non-trivial zeros, so far 100% have been located at (0.5, <prime>). If we had only discovered 3 such points, nobody would give it much credence.
There is a difference between formulating a hypothesis based on observations and treating it as true. As I understood it, things that are not proven yet will not be used to formally prove other things.