Seriously, if you define evidence as "something that sways your beliefs because it is more likely to happen under one hypothesis than the alternative hypothesis," then Bayesianism is the math of evidence, and frequentism (which is used in "Real science") is not. (and does not even really try to be)

This looks seriously misleading to me. While it may be technically correct (because neither frequentism nor "Real science" care much about swaying your beliefs), the math of deciding what's "more likely to happen under one hypothesis than the alternative hypothesis" is a standard part of frequentist statistics where it goes by the name of maximum likelihood.

You might also be interested in the concept of Fisher information.