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How would I go about finding said problem? Sorry if this seems stupid. There is no real problem that piques my interest right now perhaps because I don't really know the field all too well. I just want to enjoy learning math and get better at solving problems.

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Actually, this is what the book "Who Is Fourier?: A Mathematical Adventure" is about. It's the adventure of a group of families who wanted to learn more about languages, which led them to sounds which led them to learn about Fourier transforms. It's a lot of fun and it actually has real math that you often get to learn in a signal processing class in college. While it is very focused, this book and the approach will pique your interest in other topics.

It depends on where your interests lie. Math is all around us and is involved in most everything we do, so any subject will work.

When was the last time something made you stop and think "that's cool--how does it work?" What was it and what about it caught your attention?

Just live your life and something will eventually catch your eye. Every "huh, that's interesting" moment is an opportunity to dissect it and learn the math that's involved.

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