Earlier quoted context omitted.
Discovering underlying principles and predicting outcomes is two sides of the same coin in that there is no way to confirm you have discovered underlying principles unless they have some predictive power. Some had tried to come up with other criteria to confirm you have discovered an underlying principle without predictive power, such as on aesthetics - but this is seen by the majority of scientists as basically a co…
If all you can do is predict an outcome without being able to explain how then what have you really discovered? Asking someone to just believe you can predict outcomes without any reasoning as to how, even if you're always right, sounds like the concept of faith in religion.
for many basic/fundamental mathematical objects we don't (yet) have simple mechanistic ways to compute them.
so if a probabilistic model spits out something very useful, we can slap a nice label on it and call it a day. that's how engineering works anyway. and then hopefully someday someone will be able to derive that result from "first principles" .. maybe it'll be even more funky/crazy/interesting ... just like mathematics arguably became more exciting by the fact that someone noticed that many things are not provable/constructable without an explicit Axiom of Choice.
https://en.wikipedia.org/wiki/Nonelementary_integral#Example...