In mathematics, there are fairly few such 'meta-results', and each one is duly celebrated as impressive; the one that comes to mind is Curry-Howard corresponden

In mathematics, there are fairly few such 'meta-results', and each one is duly celebrated as impressive; the one that comes to mind is Curry-Howard correspondence... but in more 'traditional' maths, it's very hard to find general high-level translations. There are many cases where automatic syntactic low-level constructions can bring huge improvements, in compiler design, etc, it's more that they are less susceptible to be directly useful to laymen.