Informative article about physics and quote on "physicists don't care about precise numbers, they care about trends"
I do not agree that physicists are more concerned to obtain a qualitative analysis than a quantitative one. However, your question is not about my believes, so ...


Einstein: "If I can’t picture it, I don't understand it."
Dirac: I don't know the exact quote, but he said something like: "In order to understand a differential equation I have to be able to predict the limiting cases, and not solving the actual equation". 


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