Or to put it another way: if I haven't seen the result before I'm very likely to get it wrong.
And inferring the rules of arithmetic from examples : nope.
We're all very impressed with the large language models because human language was always very hard to get a handle one.
Now that we've made progress in manipulating natural language, we are very quick to believe that the darn thing is somehow "intelligent" because we've always attached some sort o mystical quality to language.
This demonstrates that the capacity of these systems to reason and craft high order rules from enough examples is exactly nil.