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jimgavagan

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One example would be an applied math thing - I want to understand what about electromagnetism exactly the Maxwell equations are describing exactly so I can gain insight into what math equations are describing exactly when they refer to the physical world - I then also want to understand how the combining the equations for magnetism and the equations for electricity lead to the math-based discovery of electromagnetism (Maxwell equations) in order to gain insight into what math-based discoveries of physical phenomenon look like, just for its own sake.

(Ultimately, though, once I figure out through the examples above what about the physical world that mathematical equations are describing, I want to use this info in order to make my way into the even more abstract world of theoretical math, if that helps with your replies.)

So I can start visualizing math better...Are there any websites or anything with pictures of mathematical concepts/abstractions given a particular equation, or even, perhaps, given just a particular branch of math in general?

Thanks!