You're confusing rigor with mathematical formality. Computing with equations that were taught to you formally, and solving mathematical problems rigorously are

You're confusing rigor with mathematical formality. Computing with equations that were taught to you formally, and solving mathematical problems rigorously are two different things. One of the easiest ways to tell the difference between the two modes of teaching is that in the former, you're taught a method and asked to apply. In the latter, you're frequently told the answer (though not always), and asked to find the method.