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What branch of mathematics lends itself best to general problem solving skills?

Once I've saved up enough for school I'd like to major in mathematics. What draws me to mathematics is how mathematicians are renowned for their problem solving skills, even in fields not directly related to their specialties.

So I'm curious as to whether there are branches of mathematics that benefit general problem solving skills more than other branches? Not the math itself being applied to said problems, but learning to break down problems and find solutions regardless of context.

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