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Conceptual models are powerful analytic tools because they allow us to creatively define variables that might be difficult to otherwise simulate. This could be something like imagining the Big Bang, or thinking about Quantum Physics and the dimensions of space and time beyond human perception or imagining economic growth models. Mathematical models are powerful analytic tools because if a mathematic proof correctly supports the truth of an idea or phenomenon, it's basically irrefutable. If the idea is not true but the math correctly proves it, it is a big deal and we change mathematic principles and advance the field. Mathematic logic is very rigorous and methodical in how it calculates and solves the questions of the world. Both models are important analytic tools and not mutually exclusive-a conceptual model might also be a mathematical model.

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