What is that method?
If you know the form you want you can curve fit.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.
I don't follow... how will curve fitting help you factorise a^6 + 8b^6 for example?